WO2023243503A1 - Method for reconstructing interior ct image, image reconstruction device, and program - Google Patents

Method for reconstructing interior ct image, image reconstruction device, and program Download PDF

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WO2023243503A1
WO2023243503A1 PCT/JP2023/021116 JP2023021116W WO2023243503A1 WO 2023243503 A1 WO2023243503 A1 WO 2023243503A1 JP 2023021116 W JP2023021116 W JP 2023021116W WO 2023243503 A1 WO2023243503 A1 WO 2023243503A1
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image
projection data
interest
region
image reconstruction
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PCT/JP2023/021116
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French (fr)
Japanese (ja)
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博幸 工藤
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国立大学法人筑波大学
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    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B6/00—Apparatus or devices for radiation diagnosis; Apparatus or devices for radiation diagnosis combined with radiation therapy equipment
    • A61B6/02—Arrangements for diagnosis sequentially in different planes; Stereoscopic radiation diagnosis
    • A61B6/03—Computed tomography [CT]

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  • the present invention relates to an image reconstruction method that measures line integral values of a physical quantity distribution inside an object and generates an image of the physical quantity distribution through data processing, and particularly relates to an image reconstruction method for interior CT.
  • CT Compputed Tomography
  • ROI region of interest
  • Current CT equipment configuration systems and data acquisition methods irradiate X-ray beams that completely cover the cross section including the ROI, even if an image of only the ROI is sufficient. Projection data on all straight lines passing through the cross section of the object is measured (see FIG. 1A).
  • filtered back-projection (FBP) method which is a calculation procedure used for image reconstruction in CT equipment
  • projection data on a straight line that does not pass through the ROI is also required to generate the ROI image. This is to become.
  • projection data on a straight line that does not pass through the ROI does not include any information about the ROI, and therefore is expected to be unnecessary. Therefore, interior CT is a CT imaging method that irradiates only the ROI with X-rays and measures only the projection data on (all) straight lines passing through the ROI to generate only the image of the ROI ( Figure 1B ).
  • This interior CT has various advantages compared to conventional CT, which wastefully measures unnecessary projection data. For example, (1) the amount of radiation outside the ROI (sample damage) is significantly reduced, (2) the detector size and X-ray beam width are reduced, (3) it becomes possible to image large objects that do not fit within the field of view, (4) It becomes possible to perform high-resolution CT imaging in which only a small field of view of an object is irradiated with X-rays and photographed in an enlarged manner.
  • interior CT projection data on a straight line that does not pass through the ROI is not measured, so a method of reconstructing an image from partially missing and incomplete projection data is required. More precisely, the definition of the image reconstruction problem in interior CT described above is as follows. Consider an object f(x, y) and an ROI S to be imaged (see FIG. 1B). It is assumed that only projection data p(r, ⁇ ) (r is the vector radius and ⁇ is the angle) in which a straight line passes through the ROI S can be measured. However, for simplicity, it is assumed that projection data is collected using a parallel beam.
  • typical methods include (1) a method in which the left and right missing portions of the projection data in each direction are extrapolated using a smooth function and then the image is reconstructed; (2) an image is reconstructed using the successive approximation method with incomplete projection data.
  • Reconstruction methods have been studied, but shading artifacts and cupping artifacts occur due to approximation errors, so they have not been put to practical use.
  • Non-patent Document 2 the 2007 paper by Ye et al.
  • the 2008 paper by Kudo et al. 1 proved that strict image reconstruction of the ROI S is possible if there is a priori information that the image value in an arbitrary small region B (a priori information region) inside the ROI S is known (method 1). ).
  • Patent Document 4 Kudo et al.'s currently pending patent application in 2017 (Patent Document 4) devised an exact solution method that utilizes partial complete projection data in fan beam CT. In other words, we proved that exact image reconstruction of ROI S is possible if we have complete scan projection data without truncation in a finite angular range E (no matter how small) in addition to interior CT projection data. (Method 4).
  • the present invention was made to solve these problems, and is an image reconstruction method that enables highly accurate image reconstruction using simpler a priori information in interior CT.
  • the purpose is to provide
  • a first aspect of the present invention is an interior CT image reconstruction method for reconstructing an image of the region of interest in a cross section of the object by irradiating the region of interest of the object with X-rays, the method comprising: a projection data acquisition step of acquiring a plurality of projection data when the region of interest of the object is irradiated with X-rays in a predetermined angle range in a direction; and when the X-rays pass through a cross section of the object according to the irradiation angle.
  • a matrix having information on pixels is a projection calculation matrix
  • b is a vector in which a plurality of said projection data are arranged
  • A is a matrix in which a plurality of said projection calculation matrices corresponding to said projection data are arranged
  • an image calculation step of solving Ax b under the a priori information C to obtain an image of the region of interest, where x is a vector in which the image values of the cross sections are arranged; is an image reconstruction method that is a summation of image values of images of cross sections of the object.
  • a second aspect of the present invention is an interior CT image reconstruction apparatus that irradiates a region of interest of an object with X-rays to reconstruct an image of the region of interest in a cross section of the object, the apparatus comprising: a projection data acquisition unit that acquires a plurality of projection data when the region of interest of the object is irradiated with X-rays in a predetermined angular range in a direction; and when the X-rays pass through a cross section of the object according to the irradiation angle.
  • a matrix having information on pixels is a projection calculation matrix
  • b is a vector in which a plurality of said projection data are arranged
  • A is a matrix in which a plurality of said projection calculation matrices corresponding to said projection data are arranged
  • a third aspect of the present invention is to cause a computer to function as an image reconstruction device for interior CT that irradiates a region of interest of an object with X-rays and reconstructs an image of the region of interest of a cross section of the object.
  • a projection data acquisition means for acquiring a plurality of projection data when the region of interest of the object is irradiated with X-rays in a predetermined angular range in the circumferential direction of the object;
  • the a priori information C is a
  • FIG. 2 is a schematic diagram showing a comparison between normal CT and interior CT.
  • FIG. 2 is a schematic diagram showing a comparison between normal CT and interior CT.
  • 1 is a schematic diagram showing the overall configuration of an X-ray CT apparatus 1.
  • FIG. It is a schematic diagram showing projection data.
  • FIG. 3 is a diagram illustrating the principle of an image reconstruction method in interior CT according to the first embodiment.
  • FIG. 6 is a diagram illustrating an example of acquiring a priori information C, which is the sum of image values.
  • FIG. 3 is a diagram showing the relationship between the entire object and ROI S, which is a region of interest.
  • FIG. 2 is a diagram showing pixels of a cross section of an object and how X-rays pass through them.
  • FIG. 2 is a diagram showing pixels of a cross section of an object and how X-rays pass through them.
  • FIG. 2 is a schematic block diagram showing an example of the functional configuration of an image reconstruction device 122 according to the first embodiment.
  • 2 is a flowchart illustrating an example of a processing procedure of the image reconstruction device 122 according to the first embodiment.
  • 2 is a flowchart showing a processing procedure of the ART method, which is an example of an iterative method.
  • FIG. 7 is a diagram illustrating the principle of an image reconstruction method in sparse view interior CT according to the second embodiment.
  • FIG. 3 is a diagram showing the results of a comparative experiment between the image reconstruction method of the first embodiment and the conventional image reconstruction method using a head CT image.
  • FIG. 3 is a diagram showing the results of a comparative experiment between the image reconstruction method of the first embodiment and the conventional image reconstruction method using a head CT image.
  • FIG. 3 is a diagram showing the results of a comparative experiment between the image reconstruction method of the first embodiment and the conventional image reconstruction method using a head CT image.
  • FIG. 3 is a diagram showing the results of a comparative experiment between the image reconstruction method of the first embodiment and the conventional image reconstruction method using a head CT image.
  • FIG. 3 is a diagram showing the results of a comparative experiment between the image reconstruction method of the first embodiment and the conventional image reconstruction method using a head CT image.
  • FIG. 3 is a diagram showing the results of a comparative experiment between the image reconstruction method of the first embodiment and the conventional image reconstruction method using a head CT image.
  • FIG. 3 is a diagram showing the results of a comparative experiment between the image reconstruction method of the first embodiment and the conventional image reconstruction method using an abdominal CT image.
  • FIG. 3 is a diagram showing the results of a comparative experiment between the image reconstruction method of the first embodiment and the conventional image reconstruction method using an abdominal CT image.
  • FIG. 3 is a diagram showing the results of a comparative experiment between the image reconstruction method of the first embodiment and the conventional image reconstruction method using an abdominal CT image.
  • FIG. 3 is a diagram showing the results of a comparative experiment between the image reconstruction method of the first embodiment and the conventional image reconstruction method using an abdominal CT image.
  • FIG. 3 is a diagram showing the results of a comparative experiment between the image reconstruction method of the first embodiment and the conventional image reconstruction method using an abdominal CT image.
  • FIG. 7 is a diagram showing the results of a comparative experiment between the image reconstruction method of the second embodiment and the conventional image reconstruction method using a polymer blend small piece sample.
  • FIG. 7 is a diagram showing the results of a comparative experiment between the image reconstruction method of the second embodiment and the conventional image reconstruction method using a polymer blend small piece sample.
  • FIG. 7 is a diagram showing the results of a comparative experiment between the image reconstruction method of the second embodiment and the conventional image reconstruction method using a polymer blend small piece sample.
  • a medical X-ray CT device will be described, but the present invention also applies to PET (Positron Emission Tomography), SPECT (Single Photon Emission CT), MRI (Magnetic Resonance Imaging), industrial and It is applicable to a CT device, a CT device for material measurement, an electron beam tomography device, etc.
  • the X-ray CT apparatus 1 includes a scan gantry section 100, a bed 105, and an operation console 120.
  • the scan gantry unit 100 is a device that irradiates a subject with X-rays and detects the X-rays that have passed through the subject.
  • the console 120 is a device that controls each part of the scan gantry section 100, acquires transmitted X-ray data measured by the scan gantry section 100, and generates an image.
  • the bed 105 is a device on which a subject (object) is placed and transported into and out of the X-ray irradiation range of the scan gantry section 100.
  • the scan gantry unit 100 includes an X-ray source 101, a rotating disk 102, a collimator unit 103, an X-ray detector 106, a data acquisition device 107, a gantry control device 108, a bed control device 109, an X-ray control device 110, and a collimator control device.
  • the console 120 includes an input device 121, an image reconstruction device 122, a storage device 123, a system control device 124, and a display device 125.
  • An opening 104 is provided in the rotary disk 102 of the scan gantry section 100, and the X-ray source 101 and the X-ray detector 106 are arranged facing each other through the opening 104.
  • a subject placed on a bed 105 is inserted into the opening 104 .
  • the rotary disk 102 rotates around the subject by a driving force transmitted from a rotary disk drive device through a drive transmission system.
  • the rotary disk drive is controlled by a gantry controller 108.
  • the X-ray source 101 is controlled by the X-ray control device 110 and continuously or intermittently irradiates X-rays with a predetermined intensity.
  • the X-ray control device 110 controls the X-ray source voltage and X-ray source current applied or supplied to the X-ray source 101 according to the X-ray source voltage and X-ray source current determined by the system control device 124 of the console 120. do.
  • a collimator unit 103 is provided at the X-ray irradiation port of the X-ray source 101.
  • the collimator unit 103 includes a collimator that is a mechanism that limits the irradiation range of X-rays emitted from the X-ray source 101, and an X-ray compensation filter that adjusts the dose distribution of X-rays.
  • the operation of the collimator is controlled by a collimator control device 111.
  • the collimator control device 111 is a device that controls the operation of the collimator and controls the irradiation range of X-rays irradiated from the X-ray source 101.
  • the X-ray detector 106 includes, for example, a group of about 1000 X-ray detection elements in the rotation direction (channel direction) and about 1 to 320 X-ray detection elements in the rotation axis direction (slice direction), which are composed of a combination of a scintillator and a photodiode, for example. It is arranged.
  • the X-ray detector 106 is arranged so as to face the X-ray source 101 through the subject.
  • the X-ray detector 106 detects the amount of X-rays irradiated from the X-ray source 101 and transmitted through the subject, and outputs the detected amount to the data acquisition device 107 .
  • the data collection device 107 collects the X-ray dose detected by each X-ray detection element of the X-ray detector 106, converts it into digital data, and sequentially sends it as transmitted X-ray data to the image reconstruction device 122 of the console 120. Output.
  • the image reconstruction device 122 acquires the transmitted X-ray data input from the data acquisition device 107, performs preprocessing such as logarithmic transformation and sensitivity correction, and creates projection data necessary for reconstruction.
  • the image reconstruction device 122 also reconstructs images such as scanogram images and tomographic images (reconstructed images) using the projection data. Further, the image reconstruction device 122 may generate volume data by stacking reconstructed tomographic images of each slice.
  • the system control device 124 displays the projection data, scanogram image, tomographic image, volume data, etc. generated by the image reconstruction device 122 on the display device 125 and stores them in the storage device 123. Details of the image reconstruction device 122 (122A) will be described later.
  • the system control device 124 is a device that controls each part of the console 120 and the scan gantry section 100.
  • the image reconstruction device 122 and the system control device 124 are computers equipped with a CPU (Central Processing Unit), a ROM (Read Only Memory), a RAM (Random Access Memory), and the like.
  • the storage device 123 is a device that stores data collected by the data collection device 107 and image data created by the image reconstruction device 122, and is specifically a data recording device such as a hard disk. In addition to the above-described transmission X-ray data and image data, the storage device 123 stores in advance programs, data, etc. for realizing the functions of the X-ray CT apparatus 1.
  • the display device 125 is composed of a display device such as a liquid crystal panel or a CRT monitor, and a logic circuit for performing display processing in cooperation with the display device, and is connected to the system control device 124.
  • the display device 125 displays the subject image output from the image reconstruction device 122 and various information handled by the system control device 124.
  • the input device 121 is a device for inputting the subject's name, test date and time, test conditions, etc., and specifically includes a pointing device such as a keyboard and a mouse, various switch buttons, and the like.
  • the input device 121 outputs various instructions and information input by the operator to the system control device 124.
  • An operator interactively operates the X-ray CT apparatus 1 using the display device 125 and the input device 121.
  • the input device 121 may be a touch panel type input device configured integrally with the display screen of the display device 125.
  • FIG. 3A is a diagram showing projection data in the case of the parallel beam method. Assume that the X-ray source is at a position rotated by ⁇ in the rotational direction. Let f(x, y) be the absorption coefficient distribution (hereinafter also referred to as image value) of a cross section of an object (subject) at a target position on the z-axis.
  • f(x, y) the absorption coefficient distribution (hereinafter also referred to as image value) of a cross section of an object (subject) at a target position on the z-axis.
  • the X-rays emitted from the X-ray source are accumulated and attenuated by the absorption coefficient distribution f(x,y) of the linear pixels (x,y) transmitted through the cross section, and the position on the axis of the X-ray detector is r, and is detected as transmitted X-ray data.
  • the image reconstruction device 122 performs logarithmic transformation, sensitivity correction, etc. on this transmitted X-ray data, resulting in projection data p(r, ⁇ ).
  • the first embodiment is an image reconstruction method for normal interior CT.
  • the principle of the image reconstruction method in interior CT of the first embodiment will be explained using FIGS. 4 to 7.
  • the subject will also be referred to as an object.
  • an image of a target cross section of an object is considered, and a region of interest ROI S is assumed to be included in the image.
  • the image is given an image value f(x,y) corresponding to the absorption coefficient distribution.
  • the support ⁇ is an object existence area that is set to include the object, and the image value is 0 outside the support ⁇ .
  • interior CT irradiates X-rays from an X-ray source to a region of interest S of an object in a predetermined angular range (for example, 360°) in the rotation direction, and projects the X-rays through a detector. Get data. For example, several hundred to several thousand pieces of projection data are acquired. As described above, in interior CT, if an image is reconstructed using only projection data, a solution cannot be determined uniquely.
  • the sum of image values of the cross section of the object is used as a priori information.
  • ⁇ is the support (the area where the object exists).
  • f(x,y) is an image value of an image of a cross section of the object.
  • C is the sum of image values obtained by integrating f(x, y) over the region of support ⁇ . Note that C is the sum of image values not only for the inside of the region of interest S but also for the entire cross section of the object.
  • the a priori information C is obtained, for example, as follows. 1. As shown in FIG. 5, complete projection data including the entire cross section of the object is acquired from one direction (one angle in the rotational direction), and the sum of the data is defined as a priori information C. Since only the sum C of image values is used, the projection data for the region of interest S may be obtained using a different device from the interior CT that obtained the projection data. Further, the projection data may have a different resolution from the projection data for the region of interest S, or the projection data may be out of position. Further, the angle may be projection data measured from any direction, and may be projection data that is noisy and has a low signal-to-noise ratio.
  • a priori information C is calculated using equation (1) from a photographed image taken at a time different from the time when projection data is acquired for the region of interest S in interior CT.
  • the sum of image values does not change much even with a moving object, in the case of video shooting, it is also possible to calculate the a priori information C using equation (1) from frame images taken at other times.
  • prescan Before imaging with interior CT, images are easily captured (prescan) under adverse conditions (low quality) such as low SN ratio, low resolution, and short measurement time, and images are generated from the reconstructed image f(x, y). Find the total sum C of the values. Since only the sum of image values C is used, pre-scanning is noisy and has a low signal-to-noise ratio, even if the image was taken with a different device than interior CT, has a different resolution, or is in a different position. It may be. Furthermore, if the subject is subject to small temporal changes, the prescan may be performed at a different time from the time at which the projection data is acquired.
  • the a priori information C is one scalar value, so it is much less information and easier to obtain. Further, since the a priori information C is only the total value C (scalar value) of the image, it is considered to be close to the minimum a priori information.
  • a solution is obtained by an iterative method using the following conditions simultaneously, and an image (image value) of the region of interest is obtained.
  • x be a vector in which the image values of the cross section of the object are arranged (each element is x i ), and let the vector in which the image values inside the region of interest S are arranged be x ROI .
  • x EXT be a vector in which the external image values of are arranged (note that the arrow symbol of the vector is omitted in the text).
  • the sum of image values inside the support ⁇ (inside the object) is C.
  • the image value outside the support ⁇ (outside the object) is set to 0.
  • the region of interest S is irradiated with X-rays within a predetermined angular range in the rotational direction, and each acquired projection data is expressed as a vector and designated as b i .
  • a matrix having information on pixels when X-rays pass through a cross section of an object according to the irradiation angle is defined as a projection calculation matrix (described later), and a projection calculation matrix corresponding to projection data b i is defined as A i .
  • equations (2), (3), and (4) are simultaneously applied to obtain a vector x that becomes a solution by an iterative method.
  • the image (image value) x ROI of the region of interest is reconstructed with high precision.
  • the iterative method used in the image reconstruction method can be any of the iterative methods known in the CT field, such as the ART (Algebraic Reconstruction Technique) method, the SIRT (Simultaneous Iterative Reconstruction Technique) method, and the statistical image reconstruction method (Transmission Maximum Likelihood, etc.).
  • the pixels of the region of interest S in this case are x 1 to x 7 .
  • the pixels of (the cross section of) the object are x 1 to x 21 including the region of interest.
  • x [x 1 , x 2 , ..., x 21 ] T
  • x ROI [x 1 , x 2 , ..., x 7 ] T
  • x EXT [x 8 , x 9 ,..., x 21 ] T (T represents transposition).
  • the X-ray l 1 passes through the pixels x 11 , x 12 , x 1 , x 2 , x 13 , and a value (based on) obtained by integrating these image values is acquired as projection data.
  • the X-ray l 2 passes through the pixels x 14 , x 3 , x 4 , x 5 , x 15 , and a value (based on) obtained by integrating these image values is acquired as projection data.
  • the X-ray l 3 passes through the pixels x 16 , x 6 , x 7 , x 17 , and x 18 , and a value (based on) obtained by integrating these image values is acquired as projection data.
  • the X-ray l 1 passes through the pixels x 19 , x 6 , x 3 , x 12 , and x 8 , and a value (based on) obtained by integrating these image values is acquired as projection data.
  • the X-ray l 2 passes through pixels x 20 , x 7 , x 4 , x 1 , and x 9 , and a value (based on) obtained by integrating these image values is acquired as projection data.
  • the X-ray l 3 passes through the pixels x 21 , x 17 , x 5 , x 2 , and x 10 , and a value (based on) obtained by integrating these image values is acquired as projection data.
  • FIG. 8 is a schematic block diagram showing an example of the functional configuration of the image reconstruction device 122 according to the first embodiment.
  • the image reconstruction device 122 includes an a priori information acquisition section 131, a projection data acquisition section 132, and an image calculation section 133. Note that the image reconstruction device 122 may be provided as a part of the X-ray CT apparatus 1 as shown in FIG. 2, or may be connected to the X-ray CT apparatus 1 as a separate body. Further, the image reconstruction device 122 may operate alone and obtain necessary information from an external server, storage device, etc. via a network.
  • the a priori information acquisition unit 131 acquires, as a priori information C, the sum of image values of images of the cross section of the object.
  • a priori information C is calculated using the following formula.
  • ⁇ is the support (the area where the object exists).
  • f(x,y) is an image value of an image of a cross section of the object.
  • C is the sum of image values obtained by integrating f(x, y) over the region of support ⁇ . Note that C is the sum of image values not only for the inside of the region of interest S but also for the entire cross section of the object.
  • the a priori information acquisition unit 131 may acquire complete projection data including the entire cross section of the object from one direction (one angle in the rotational direction), and calculate the sum as the a priori information C. Further, the a priori information acquisition unit 131 may calculate the a priori information C from the captured image including the object using equation (5). Further, the a priori information acquisition unit 131 may calculate the a priori information C using equation (5) from an image simply prescanned under bad conditions (low quality). Further, the a priori information acquisition unit 131 may obtain the value of equation (5) stored in the storage device 123 or the like as the a priori information C.
  • the projection data acquisition unit 132 acquires a plurality of projection data when a region of interest of the object is irradiated with X-rays in a predetermined angular range (for example, 360°) in the circumferential direction of the object. For example, the projection data acquisition unit 132 acquires approximately several hundred to several thousand pieces of projection data. Note that the projection data acquisition unit 132 may use projection data acquired while imaging with the X-ray CT apparatus 1, or may acquire projection data stored in the storage device 123 in advance.
  • b is a vector in which a plurality of projection data b i are arranged
  • A is a matrix in which a plurality of projection calculation matrices A i are arranged corresponding to projection data b i
  • x is a vector in which image values of a cross section of an object are arranged
  • the image calculation unit 133 defines a vector in which the image values of the cross section of the object are arranged as x (each element is x i ), and a vector in which the image values inside the region of interest S are arranged as x ROI.
  • x EXT be a vector in which image values outside the region of interest in the cross section of the object are arranged.
  • the image calculation unit 133 sets C as the sum of image values inside the support ⁇ (inside the object).
  • the image calculation unit 133 sets the image value outside the support ⁇ (outside the object) to 0.
  • the image calculation unit 133 sets each projection data acquired by the projection data acquisition unit 132 as a vector b i , and sets the projection calculation matrix corresponding to the projection data b i as A i . Then, the image calculation unit 133 calculates the measurement equation by formulating the measurement equation as shown in equation (4), where b is a vector in which the vectors b i are arranged in one column, and A is a matrix in which the matrix A i is arranged in one column. do.
  • the image calculation unit 133 calculates a vector x that is a solution by simultaneous equations (6), (7), and (8) by an iterative method, and sets x ROI in x as an image of the region of interest.
  • FIG. 9 is a flowchart illustrating an example of a processing procedure of the image reconstruction device 122 according to the first embodiment.
  • the a priori information acquisition unit 131 acquires the sum of image values of images of a cross section of an object as a priori information C (step S101).
  • the projection data acquisition unit 132 acquires a plurality of projection data b i when the region of interest of the object is irradiated with X-rays within a predetermined angular range in the circumferential direction of the object (step S102).
  • FIG. 10 is a flowchart illustrating an example of the processing procedure of ART, which is an example of the iterative method performed by the image calculation unit 133.
  • the projection calculation matrix is Let A be a vector a i T (1 ⁇ i ⁇ I) in order from the top row.
  • the image calculation unit 133 calculates a normalized vector a whose coefficient is the difference between the value b i of the projection data and the projection value by the vector a i T in the projection calculation matrix of the current x (k, i) . Add i to the current x (k, i) to obtain an intermediate vector x (k, i+1/2) (step S205).
  • the image calculation unit 133 calculates the difference between C (the sum of image values) and the sum of the image values of the intermediate vector The value divided by the number is added to the value of the element of the intermediate vector x (k, i+1/2) , and is set as the value of the element of the update vector x (k, i+1) . However, the image calculation unit 133 sets the value of the element of the update vector x (k, i+1) to 0 for pixels that are not included in the support ⁇ . (Step S206).
  • the image calculation unit 133 updates the vector x (k+1) with the update vector x (k, I+1) (step S207).
  • the a priori information acquisition unit 131 acquires the sum of image values of the cross-sectional images of the object as the a priori information C
  • the projection data acquisition unit 132 acquires the sum of the image values of the cross-sectional images of the object as the a priori information C
  • the projection data acquisition unit 132 acquires the sum of the image values of the images of the cross section of the object as the a priori information C.
  • a plurality of projection data are obtained when the region of interest of the object is irradiated with X-rays
  • the image calculation unit 133 sets the vector of the projection data to b, the projection calculation matrix to A, and arranges the image values of the cross section of the object.
  • the image reconstruction device 122 can perform highly accurate image reconstruction using simpler (ultra-simple) a priori information in interior CT.
  • the a priori information C used by the image reconstruction device 122 is a single scalar value compared to the conventional methods (1) to (4) described above, so it is much less information and easier to obtain. Therefore, the image reconstruction device 122 is very practical and easy to use. Further, since the a priori information C is only the total value C (scalar value) of the image, it is considered to be close to the minimum a priori information.
  • the second embodiment is an image reconstruction method in sparse view interior CT.
  • Sparse view CT is CT that performs imaging by reducing the number of X-ray projection directions.
  • the principle of the image reconstruction method in sparse view interior CT of the second embodiment will be explained using FIG. 11.
  • the image reconstruction method of this embodiment also considers an image of a target cross section of an object, and assumes that the region of interest ROIS is included in the image.
  • An image value f(x,y) corresponding to an absorption distribution coefficient is given to the image.
  • the support ⁇ is an object existence area that is set to include the object, and the image value is 0 outside the support ⁇ .
  • the interior CT irradiates the region of interest S of the object with X-rays from an X-ray source sparsely at predetermined intervals in a predetermined angular range (for example, 360°) in the rotation direction, Obtain projection data via a detector. For example, approximately 80, 64, or 46 pieces of projection data are acquired. As described above, even in sparse view interior CT, if an image is reconstructed using only projection data, the solution will not be uniquely determined and a highly accurate image will not be obtained.
  • the sum of image values of the cross section of the object is used as a priori information.
  • ⁇ is the support (the area where the object exists).
  • f(x,y) is an image value of an image of a cross section of the object.
  • C is the sum of image values obtained by integrating f(x, y) over the region of support ⁇ . Note that C is the sum of image values not only for the inside of the region of interest S but also for the entire cross section of the object.
  • the method of acquiring the a priori information C is the same as that described in the first embodiment. Compared to the conventional methods (1) to (4) described above, the a priori information C is a single scalar value, so it contains much less information and is easier to obtain. Further, since the a priori information C is only the total value C (scalar value) of the image, it is considered to be close to the minimum a priori information.
  • a solution is obtained by an iterative method using the following conditions simultaneously, and among them, the solution with the smallest TV (Total Variation) norm is obtained as an image (image value) of the region of interest.
  • a vector in which image values of a cross section of an object are arranged is set to x (each element is set to x i ), and a vector x ROI and a vector x EXT are determined as follows in the same manner as in the first embodiment.
  • the sum of image values inside the support ⁇ (inside the object) is C.
  • the image value outside the support ⁇ (outside the object) is set to 0.
  • the region of interest S is sparsely irradiated with X-rays at predetermined intervals within a predetermined angular range in the rotational direction, and each acquired projection data is represented by a vector and is denoted by b i .
  • a matrix having information on pixels when X-rays pass through a cross section of an object according to the irradiation angle is defined as a projection calculation matrix
  • a projection calculation matrix corresponding to projection data b i is defined as A i .
  • equations (9), (10), and (11) are simultaneously applied to obtain a vector x that is a solution by an iterative method.
  • x is determined such that the TV norm expressed by equation (12) is minimized.
  • This TV norm is calculated as a value based on the magnitude of the horizontal difference and the vertical difference when x is viewed as a two-dimensional image.
  • the x ROI of the obtained x is used as the image of the region of interest.
  • the image of the region of interest x ROI is reconstructed with high accuracy.
  • the iterative method used in the image reconstruction method of the second embodiment is the same as that exemplified in the first embodiment.
  • the initial value of the vector x when solving by the iterative method is not particularly limited.
  • FIG. 12 is a schematic block diagram showing an example of the functional configuration of an image reconstruction device 122A according to the second embodiment.
  • the image reconstruction device 122A includes an a priori information acquisition section 131, a projection data acquisition section 132A, and an image calculation section 133A.
  • the image reconstruction device 122A may be provided as a part of the X-ray CT apparatus 1 as shown in FIG. 2, or may be connected to the X-ray CT apparatus 1 as a separate body. Further, the image reconstruction device 122A may operate alone and obtain necessary information from an external server, storage device, etc. via a network.
  • the a priori information acquisition unit 131 is the same as the a priori information acquisition unit 131 of the image reconstruction device 122 of the first embodiment, so a description thereof will be omitted.
  • the projection data acquisition unit 132A acquires a plurality of projection data when the region of interest of the object is sparsely irradiated with X-rays at predetermined intervals in a predetermined angular range (for example, 360°) in the circumferential direction of the object. For example, the projection data acquisition unit 132 acquires about 80, 64, or 46 pieces of A projection data. Note that the projection data acquisition unit 132A may use projection data acquired while imaging with the X-ray CT apparatus 1, or may acquire projection data stored in the storage device 123 in advance.
  • the image calculation unit 133A sets a matrix having information on pixels when the X-ray passes through the cross section of the object according to the irradiation angle as a projection calculation matrix
  • b is a vector in which a plurality of projection data b i are arranged
  • A is a matrix in which a plurality of projection calculation matrices A i are arranged corresponding to projection data b i
  • a solution is obtained so that the TV norm is minimized, and an image of the region of interest is obtained.
  • the image calculation unit 133A sets a vector in which the image values of the cross section of the object are arranged as x (each element is x i ), and determines the vector x ROI and the vector x EXT as follows.
  • the image calculation unit 133A sets C as the sum of image values inside the support ⁇ (inside the object).
  • the image calculation unit 133A sets the image value outside the support ⁇ (outside the object) to 0.
  • the image calculation unit 133A sets each projection data acquired by the projection data acquisition unit 132 as a vector b i , and sets the projection calculation matrix corresponding to the projection data b i as A i . Then, the image calculation unit 133A calculates the measurement equation by formulating the measurement equation as shown in equation (15), where b is a vector in which the vectors b i are arranged in one column, and A is a matrix in which the matrix A i is arranged in one column. do.
  • the image calculation unit 133A combines equations (13), (14), and (15), and uses an iterative method to find a vector x that minimizes the TV norm expressed by equation (16). Then, the image calculation unit 133A sets the x ROI of x as the image of the region of interest.
  • FIG. 13 is a flowchart illustrating an example of the processing procedure of the image reconstruction device 122A according to the second embodiment.
  • the a priori information acquisition unit 131 acquires the sum of image values of images of a cross section of an object as a priori information C (step S301).
  • the projection data acquisition unit 132A acquires a plurality of projection data b i when the region of interest of the object is irradiated with X-rays at predetermined intervals in a predetermined angular range in the circumferential direction of the object (step S302).
  • the image calculation unit 133A calculates a vector in which a plurality of projection data b i are arranged.
  • A is a matrix in which a plurality of projection calculation matrices A i are arranged corresponding to projection data b i
  • x is a vector in which image values of a cross section of an object are arranged
  • the image calculation unit 133A uses, for example, the ART method as the iterative method, and the processing procedure is the same as that in FIG. 10.
  • the image calculation unit 133A sets the obtained x ROI of x as the image of the region of interest (step S304). This concludes the explanation of FIG. 13.
  • the a priori information acquisition unit 131 acquires the sum of image values of cross-sectional images of the object as the a priori information C
  • the projection data acquisition unit 132A acquires a predetermined angular range in the circumferential direction of the object.
  • a plurality of projection data obtained when the region of interest of the object is irradiated with X-rays at predetermined intervals is acquired, and the image calculation unit 133A sets the vector of the projection data to b, the projection calculation matrix to A, and generates an image of the cross section of the object.
  • a vector in which values are arranged is x
  • the image reconstruction device 122A can perform highly accurate image reconstruction using simpler (ultra-simple) a priori information in sparse view interior CT.
  • highly accurate image reconstruction can be performed even in sparse-view interior CT, which is more difficult than normal interior CT.
  • the a priori information C used by the image reconstruction device 122A is a single scalar value compared to the conventional methods (1) to (4) described above, so it is much less information and easier to obtain. Therefore, the image reconstruction device 122A is very practical and easy to use.
  • the a priori information C is only the total value C (scalar value) of the image, it is considered to be close to the minimum a priori information.
  • FIGS. 14A to 14E show the results of image reconstruction performed on head CT images through simulation experiments. Except for FIG. 14D, the display range of image density is [-20HU, 90HU] (HU: Hounsfield Unit).
  • FIG. 14A is an image reconstructed from complete projection data using a filtered back projection method in normal CT, which is not interior CT.
  • FIG. 14B is an image reconstructed from interior CT projection data by the conventional method (3) (using a priori information that the boundaries of the ROI are piecewise uniform).
  • FIG. 14C is an image reconstructed from interior CT projection data by the conventional method (4) (using complete projection data in one direction using a priori information).
  • FIG. 14D shows an image reconstructed from projection data of IntelliCT using the image reconstruction method of Embodiment 1, but without using a priori information C of the sum of image values. In this case, not only the area around the ROI boundary is not accurately reconstructed, but also the image density is shifted to [90HU, 200HU].
  • FIG. 14E shows an image reconstructed from the projection data of IntelliCT using the a priori information C of the sum of image values by the image reconstruction method of the first embodiment. In this case, it can be seen that the inside of the ROI can be reconstructed at the same level as in FIGS. 14A, 14B, and 14C.
  • FIGS. 15A to 15E show the results of image reconstruction performed on abdominal CT images through simulation experiments. Except for FIG. 15D, the display range of image density is [-100HU, 300HU]. The experiment shown in FIG. 15 is a case where it is difficult to reconstruct an image by making the region of interest ROS small.
  • FIG. 15A is an image reconstructed from complete projection data using a filtered back projection method in normal CT, which is not interior CT.
  • FIG. 15B is an image reconstructed from interior CT projection data using the conventional method (3).
  • FIG. 15C is an image reconstructed from interior CT projection data using the conventional method (4).
  • FIG. 15D shows an image reconstructed from projection data of IntelliCT using the image reconstruction method of Embodiment 1, but without using a priori information C of the sum of image values. In this case, not only the area around the ROI boundary is not accurately reconstructed, but also the image density deviates from [310HU, 710HU].
  • FIG. 15E shows an image reconstructed from the projection data of IntelliCT using the a priori information C of the sum of image values by the image reconstruction method of the first embodiment. In this case, it can be seen that the inside of the ROI can be reconstructed at the same level as in FIGS. 15A, 15B, and 15C.
  • FIGS. 16A to 16C are results based on actual data measured using X-ray phase CT on a small polymer blend sample.
  • FIG. 16A is an image reconstructed from complete projection data in 522 directions by the filtered back projection method in normal sparse view CT, which is not interior CT.
  • FIG. 16B shows an image reconstructed from projection data in 46 directions of the sparse view interior CT using the image reconstruction method of the second embodiment, but without using the a priori information C of the sum of image values. In this case, the values deviate greatly and the entire image is black.
  • FIG. 16C is an image reconstructed from projection data in 46 directions of the sparse view interior CT by the image reconstruction method of the second embodiment using a priori information C of the sum of image values. In this case, it can be seen that the inside of the ROI can be reconstructed at a level comparable to that in FIG. 16A.
  • Embodiments of the present invention are applied to medical X-ray CT devices, nondestructive testing CT devices, material measurement CT devices, electron beam tomography devices, and the like.
  • X-ray CT device 100 Scan gantry part 101 X-ray source 102 Rotary disk 103 Collimator unit 104 Opening 105 Bed 106 X-ray detector 107 Data acquisition device 120 Operation console 121 Input device 122, 122A Image reconstruction device 123 Storage device 124 System control device 125 Display device 131 A priori information acquisition unit 132, 132A Projection data acquisition unit 133, 133A Image calculation unit

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Abstract

A method for reconstructing an interior CT image in which a region of interest in an object is irradiated with X-rays and an image of the region of interest in a cross section of the object is reconstructed, wherein the method includes: a projection data acquisition step in which a plurality of pieces of projection data are acquired for an occasion on which the region of interest of the object is irradiated with X-rays in a predetermined angular range in the circumferential direction of the object; and an image calculation step in which when matrices holding pixel information for an occasion on which X-rays pass through a cross section of the object in accordance with the irradiation angle serve as projection calculation matrices, a vector in which the plurality of pieces of projection data are arranged is denoted by b, a matrix in which a plurality of the projection calculation matrices corresponding to the projection data are arranged is denoted by A, and a vector in which the image values of the cross section of the object are arranged is denoted by x, Ax = b is solved under prior information C and an image of the region of interest is determined, said prior information C being the sum of the image values of an image of the cross section of the object.

Description

インテリアＣＴの画像再構成方法、画像再構成装置、及び、プログラムInterior CT image reconstruction method, image reconstruction device, and program
　本発明は、物体内部における物理量分布の線積分値を測定してデータ処理により物理量分布を画像生成する画像再構成方法に関し、特に、インテリアＣＴの画像再構成方法に関する。 The present invention relates to an image reconstruction method that measures line integral values of a physical quantity distribution inside an object and generates an image of the physical quantity distribution through data processing, and particularly relates to an image reconstruction method for interior CT.
　まず、インテリアＣＴ（Computed Tomography）と呼ばれるＣＴ撮影の方法について説明する。一般的に、ＣＴイメージングの多くの状況においては、物体内の小さな関心領域（ＲＯＩ：Region of Interest）だけの画像が欲しい場合が生じる。例えば、医療用ＣＴを用いた心臓病や乳がんの診断では、心臓や***を含む小さなＲＯＩの画像だけがあれば十分である。現在のＣＴ装置の構成方式やデータ収集法は、このようなＲＯＩだけの画像で十分な場合であっても、ＲＯＩを含む断面を完全に覆うＸ線ビームを照射して、ＲＯＩのみではなく、物体断面を通過する全ての直線上の投影データを測定するものになっている（図１Ａを参照）。これは、ＣＴ装置の画像再構成に用いられる計算手順であるフィルタ補正逆投影（ＦＢＰ；Filtered Back-Projection）法において、ＲＯＩ画像を生成するのにＲＯＩを通過しない直線上の投影データも必要になるためである。しかし、直感的には、ＲＯＩを通過しない直線上の投影データはＲＯＩの情報を全く含んでいないため、不必要なことが予想される。そこで、ＲＯＩだけにＸ線を照射して、ＲＯＩを通過する（全ての）直線上の投影データのみを測定してＲＯＩの画像のみを生成するＣＴ撮影の方法が、インテリアＣＴである（図１Ｂを参照）。 First, a CT imaging method called interior CT (Computed Tomography) will be explained. Generally, in many CT imaging situations, it may be desired to image only a small region of interest (ROI) within an object. For example, in diagnosing heart disease or breast cancer using medical CT, it is sufficient to have an image of a small ROI including the heart and breast. Current CT equipment configuration systems and data acquisition methods irradiate X-ray beams that completely cover the cross section including the ROI, even if an image of only the ROI is sufficient. Projection data on all straight lines passing through the cross section of the object is measured (see FIG. 1A). This is because in the filtered back-projection (FBP) method, which is a calculation procedure used for image reconstruction in CT equipment, projection data on a straight line that does not pass through the ROI is also required to generate the ROI image. This is to become. However, intuitively, projection data on a straight line that does not pass through the ROI does not include any information about the ROI, and therefore is expected to be unnecessary. Therefore, interior CT is a CT imaging method that irradiates only the ROI with X-rays and measures only the projection data on (all) straight lines passing through the ROI to generate only the image of the ROI (Figure 1B ).
　このインテリアＣＴには、不必要な投影データを無駄に測定する従来のＣＴと比較して、様々な長所がある。例えば、（１）ＲＯＩ外部の被曝量（試料損傷）の大幅な低減、（２）検出器サイズやＸ線ビーム幅の削減、（３）視野に収まらない大きい物体の撮影が可能になること、（４）物体の小視野だけにＸ線を照射して拡大撮影する高分解能ＣＴイメージングが可能になること等が挙げられる。 This interior CT has various advantages compared to conventional CT, which wastefully measures unnecessary projection data. For example, (1) the amount of radiation outside the ROI (sample damage) is significantly reduced, (2) the detector size and X-ray beam width are reduced, (3) it becomes possible to image large objects that do not fit within the field of view, (4) It becomes possible to perform high-resolution CT imaging in which only a small field of view of an object is irradiated with X-rays and photographed in an enlarged manner.
　一方、インテリアＣＴでは、ＲＯＩを通過しない直線上の投影データは測定されないため、一部が欠損した不完全投影データから画像再構成を行う手法が必要となる。より正確に、上記したインテリアＣＴにおける画像再構成問題の定義を述べると、以下のようになる。物体ｆ（ｘ，ｙ）と画像化の対象となるＲＯＩ　Ｓを考える（図１Ｂを参照）。そして、直線がＲＯＩ　Ｓを通過する投影データｐ（ｒ，θ）（ｒは動径、θは角度）のみが測定可能であるとする。ただし、簡単のため、平行ビームによる投影データ収集を想定している。この場合、直線がＲＯＩ　Ｓを通過しないｐ（ｒ，θ）は測定されないため、各角度θの投影データは、左右がトランケーションされて欠損することになる。このようなトランケーションされた投影データからＲＯＩ　Ｓにおいて画像ｆ（ｘ，ｙ）を正しく再構成する問題が、インテリアＣＴの画像再構成である。 On the other hand, in interior CT, projection data on a straight line that does not pass through the ROI is not measured, so a method of reconstructing an image from partially missing and incomplete projection data is required. More precisely, the definition of the image reconstruction problem in interior CT described above is as follows. Consider an object f(x, y) and an ROI S to be imaged (see FIG. 1B). It is assumed that only projection data p(r, θ) (r is the vector radius and θ is the angle) in which a straight line passes through the ROI S can be measured. However, for simplicity, it is assumed that projection data is collected using a parallel beam. In this case, since p(r, θ) where the straight line does not pass through the ROI S is not measured, the projection data for each angle θ will be truncated on the left and right and will be missing. The problem of correctly reconstructing the image f(x, y) in the ROI S from such truncated projection data is the image reconstruction of interior CT.
　この問題は長年多くの研究が行われてきており、以下に概略する。まず、非特許文献１では、Nattererは、インテリアＣＴの画像再構成は解が「一意」に定まらないことを数学的に証明し（ここで、一意とは、画像再構成の解が投影データから唯一に決まり数学的に正しい画像再構成が可能なことを指す）、この非一意性が知られていたため、多くの近似的な画像再構成法が研究されてきた。 This problem has been the subject of much research over the years, and is summarized below. First, in Non-Patent Document 1, Natterer mathematically proves that the solution for interior CT image reconstruction is not determined to be "unique" (here, unique means that the solution for image reconstruction is determined from projection data. Since this non-uniqueness has been known, many approximate image reconstruction methods have been studied.
　例えば、その代表的な手法として、（１）各方向投影データ左右の欠損部分を滑らかな関数で外挿してから画像再構成する手法、（２）不完全な投影データのまま逐次近似法により画像再構成を行う手法などが研究されたが、近似誤差によるシェーディングアーティファクトやカッピングアーティファクト等が発生して実用に至らなかった。 For example, typical methods include (1) a method in which the left and right missing portions of the projection data in each direction are extrapolated using a smooth function and then the image is reconstructed; (2) an image is reconstructed using the successive approximation method with incomplete projection data. Reconstruction methods have been studied, but shading artifacts and cupping artifacts occur due to approximation errors, so they have not been put to practical use.
　これらの先行研究に対して、２００７年になりようやく数学的に厳密な画像再構成法が発見され、インテリアＣＴにおける画像再構成の新しい方向性が生まれた。これらの厳密解法の重要なキーポイントを一言で要約すると、『インテリアＣＴの投影データのみでは厳密な画像再構成は不可能だが、物体に関するごく僅かな先験情報があれば数学的に厳密な画像再構成が可能になる』と述べることができる。 In contrast to these previous studies, a mathematically rigorous image reconstruction method was finally discovered in 2007, creating a new direction for image reconstruction in interior CT. To summarize the key points of these exact solution methods in one sentence, ``It is impossible to perform exact image reconstruction using interior CT projection data alone, but if there is very little a priori information about the object, it is possible to perform mathematically rigorous reconstruction.'' It can be stated that "image reconstruction becomes possible."
　上述した厳密解法の発展について述べると、まず、２００７年のYeらの論文（非特許文献２）、２００８年のKudoらの論文（非特許文献３）、２００８年のWangらの特許（特許文献１）は、ＲＯＩ　Ｓ内部の任意小領域Ｂ（先験情報領域）における画像値が既知という先験情報があれば、ＲＯＩ　Ｓの厳密な画像再構成が可能であることを証明した（方法１）。 To describe the development of the exact solution method mentioned above, first, the 2007 paper by Ye et al. (Non-patent Document 2), the 2008 paper by Kudo et al. 1) proved that strict image reconstruction of the ROI S is possible if there is a priori information that the image value in an arbitrary small region B (a priori information region) inside the ROI S is known (method 1). ).
　次に、２００９年のYuらの論文（非特許文献４）と２０１４年のWangらの特許（特許文献２）は、ＲＯＩ　Ｓ全体で画像値が区分的一様（完全な一定値を持つ有限個の領域で構成されていること）であれば、ＲＯＩ　Ｓの厳密な画像再構成が可能であることを証明した（方法２）。 Next, the 2009 paper by Yu et al. (Non-Patent Document 4) and the 2014 patent by Wang et al. (Method 2), it was proven that strict image reconstruction of the ROI S is possible (Method 2).
　更に、２０１７年の工藤らの特許（特許文献３）やKudoの論文（非特許文献５）は、Yuら、Wangらの手法において必要な先験情報を大幅に削減することに成功して、ＲＯＩ　Ｓ内部の任意小領域Ｂ（先験情報領域）において画像値が区分的一様（または区分的多項式）であれば、ＲＯＩ　Ｓの厳密な画像再構成が可能であることを証明し、また、ＲＯＩ　Ｓの縁のみに区分的一様な制約をかける実用的な方法を提案した（方法３）。 Furthermore, Kudo et al.'s patent (Patent Document 3) and Kudo's paper (Non-Patent Document 5) in 2017 succeeded in significantly reducing the required a priori information in the methods of Yu et al. and Wang et al. We prove that strict image reconstruction of ROI S is possible if the image values are piecewise uniform (or piecewise polynomial) in an arbitrary small region B (a priori information region) inside ROI S, and , we proposed a practical method that applies piecewise uniform constraints only to the edges of ROI S (Method 3).
　最後に、２０１７年の工藤らの現在出願中の特許出願（特許文献４）は、ファンビームＣＴにおいて、部分的な完全投影データを利用する厳密解法を考案した。すなわち、インテリアＣＴの投影データに加えて有限角度範囲Ｅ（いくら小さくても良い）のトランケーションなしの完全スキャンの投影データがあれば，ＲＯＩ　Ｓの厳密な画像再構成が可能であることを証明した（方法４）。 Finally, Kudo et al.'s currently pending patent application in 2017 (Patent Document 4) devised an exact solution method that utilizes partial complete projection data in fan beam CT. In other words, we proved that exact image reconstruction of ROI S is possible if we have complete scan projection data without truncation in a finite angular range E (no matter how small) in addition to interior CT projection data. (Method 4).
米国特許第７６９７６５８号明細書US Patent No. 7,697,658 米国特許第８８１１７００号明細書US Patent No. 8811700 特許第６７６０６１１号公報Patent No. 6760611 国際公開第２０１８／１７９９０５号International Publication No. 2018/179905
　しかしながら、上述のようにインテリアＣＴにおいて、画質劣化のない画像再構成を行うには、投影データの他に、物体に関する何らかの先験情報を利用したり（方法１、方法２、方法３）、余分な補足投影データを測定する必要がある（方法４）。これらの方法はかなり複雑であり、先験情報が獲得できない場合や、補足投影データを測定するように装置に変更を加えるのが困難な場合も多い。 However, as mentioned above, in interior CT, in order to perform image reconstruction without image quality deterioration, in addition to projection data, some a priori information about the object must be used (Method 1, Method 2, Method 3), or It is necessary to measure complementary projection data (Method 4). These methods are quite complex, and often a priori information is not available or it is difficult to modify the equipment to measure supplemental projection data.
　本発明は、このような課題を解決するためになされたものであり、インテリアＣＴにおいて、より簡便な先験情報を用いて、高精度な画像再構成を行うことを可能とする画像再構成法を提供することを目的とする。 The present invention was made to solve these problems, and is an image reconstruction method that enables highly accurate image reconstruction using simpler a priori information in interior CT. The purpose is to provide
　本発明の第１の態様は、物体の関心領域にＸ線を照射して、前記物体の断面の前記関心領域の画像を再構成するインテリアＣＴの画像再構成方法であって、前記物体の周方向において所定の角度の範囲で前記物体の前記関心領域にＸ線を照射した際の投影データを複数取得する投影データ取得ステップと、照射角度に応じてＸ線が前記物体の断面の通過する際の画素の情報をもつ行列を投影演算行列とするとき、複数の前記投影データを並べたベクトルをｂとし、前記投影データに対応する複数の前記投影演算行列を並べた行列をＡとし、前記物体の断面の画像値を並べたベクトルをｘとしたとき、前記先験情報Ｃの下でＡｘ＝ｂを解いて、前記関心領域の画像を求める画像算出ステップと、を含み、前記先験情報Ｃは、前記物体の断面の画像の画像値の総和である画像再構成方法である。 A first aspect of the present invention is an interior CT image reconstruction method for reconstructing an image of the region of interest in a cross section of the object by irradiating the region of interest of the object with X-rays, the method comprising: a projection data acquisition step of acquiring a plurality of projection data when the region of interest of the object is irradiated with X-rays in a predetermined angle range in a direction; and when the X-rays pass through a cross section of the object according to the irradiation angle. When a matrix having information on pixels is a projection calculation matrix, b is a vector in which a plurality of said projection data are arranged, A is a matrix in which a plurality of said projection calculation matrices corresponding to said projection data are arranged, and an image calculation step of solving Ax=b under the a priori information C to obtain an image of the region of interest, where x is a vector in which the image values of the cross sections are arranged; is an image reconstruction method that is a summation of image values of images of cross sections of the object.
　本発明の第２の態様は、物体の関心領域にＸ線を照射して、前記物体の断面の前記関心領域の画像を再構成するインテリアＣＴの画像再構成装置であって、前記物体の周方向において所定の角度の範囲で前記物体の前記関心領域にＸ線を照射した際の投影データを複数取得する投影データ取得部と、照射角度に応じてＸ線が前記物体の断面の通過する際の画素の情報をもつ行列を投影演算行列とするとき、複数の前記投影データを並べたベクトルをｂとし、前記投影データに対応する複数の前記投影演算行列を並べた行列をＡとし、前記物体の断面の画像値を並べたベクトルをｘとするとき、先験情報Ｃの下でＡｘ＝ｂを解いて、前記関心領域の画像を求める画像算出部と、を備え、前記先験情報Ｃは、前記物体の断面の画像の画像値の総和である画像再構成装置である。 A second aspect of the present invention is an interior CT image reconstruction apparatus that irradiates a region of interest of an object with X-rays to reconstruct an image of the region of interest in a cross section of the object, the apparatus comprising: a projection data acquisition unit that acquires a plurality of projection data when the region of interest of the object is irradiated with X-rays in a predetermined angular range in a direction; and when the X-rays pass through a cross section of the object according to the irradiation angle. When a matrix having information on pixels is a projection calculation matrix, b is a vector in which a plurality of said projection data are arranged, A is a matrix in which a plurality of said projection calculation matrices corresponding to said projection data are arranged, and an image calculation unit that solves Ax=b under a priori information C to obtain an image of the region of interest, where x is a vector in which the image values of the cross section are arranged, and the a priori information C is , an image reconstruction device that calculates the sum of image values of images of cross sections of the object.
　本発明の第３の態様は、コンピュータを、物体の関心領域にＸ線を照射して、前記物体の断面の前記関心領域の画像を再構成するインテリアＣＴの画像再構成装置として機能させるためのプログラムであって、前記コンピュータを、前記物体の周方向において所定の角度の範囲で前記物体の前記関心領域にＸ線を照射した際の投影データを複数取得する投影データ取得手段、照射角度に応じてＸ線が前記物体の断面の通過する際の画素の情報をもつ行列を投影演算行列とするとき、複数の前記投影データを並べたベクトルをｂとし、前記投影データに対応する複数の前記投影演算行列を並べた行列をＡとし、前記物体の断面の画像値を並べたベクトルをｘとするとき、先験情報Ｃの下でＡｘ＝ｂを解いて、前記関心領域の画像を求める画像算出手段、として機能させ、前記先験情報Ｃは、前記物体の断面の画像の画像値の総和であるプログラムである。 A third aspect of the present invention is to cause a computer to function as an image reconstruction device for interior CT that irradiates a region of interest of an object with X-rays and reconstructs an image of the region of interest of a cross section of the object. A projection data acquisition means for acquiring a plurality of projection data when the region of interest of the object is irradiated with X-rays in a predetermined angular range in the circumferential direction of the object; When a matrix having information on pixels when X-rays pass through the cross section of the object is a projection calculation matrix, b is a vector in which a plurality of the projection data are arranged, and a plurality of the projections corresponding to the projection data are Image calculation to obtain an image of the region of interest by solving Ax=b under a priori information C, where A is a matrix in which calculation matrices are arranged, and x is a vector in which image values of the cross section of the object are arranged. The a priori information C is a program that is the sum of image values of images of the cross section of the object.
　本発明によれば、インテリアＣＴにおいて、より簡便な先験情報を用いて、高精度な画像再構成を行うことを可能とする画像再構成法を提供することが可能となる。 According to the present invention, it is possible to provide an image reconstruction method that enables highly accurate image reconstruction using simpler a priori information in interior CT.
通常のＣＴとインテリアＣＴとの比較を表す概略図である。FIG. 2 is a schematic diagram showing a comparison between normal CT and interior CT. 通常のＣＴとインテリアＣＴとの比較を表す概略図である。FIG. 2 is a schematic diagram showing a comparison between normal CT and interior CT. Ｘ線ＣＴ装置１の全体構成を表す概略図である。1 is a schematic diagram showing the overall configuration of an X-ray CT apparatus 1. FIG. 投影データを表す模式図である。It is a schematic diagram showing projection data. 投影データを表す模式図である。It is a schematic diagram showing projection data. 第１実施形態に係るインテリアＣＴにおける画像再構成方法の原理を表す図である。FIG. 3 is a diagram illustrating the principle of an image reconstruction method in interior CT according to the first embodiment. 画像値の総和である先験情報Ｃの取得の例を示す図である。FIG. 6 is a diagram illustrating an example of acquiring a priori information C, which is the sum of image values. 物体全体と関心領域であるROI Sとの関係を示す図である。FIG. 3 is a diagram showing the relationship between the entire object and ROI S, which is a region of interest. 物体の断面の画素とＸ線がそれらを通過する際の様子を表す図である。FIG. 2 is a diagram showing pixels of a cross section of an object and how X-rays pass through them. 物体の断面の画素とＸ線がそれらを通過する際の様子を表す図である。FIG. 2 is a diagram showing pixels of a cross section of an object and how X-rays pass through them. 投影演算行列Ａと測定方程式Ａｘ＝ｂの例を示す図である。FIG. 3 is a diagram showing an example of a projection calculation matrix A and a measurement equation Ax=b. 第１実施形態に係る画像再構成装置１２２の機能構成の例を示す概略ブロック図である。FIG. 2 is a schematic block diagram showing an example of the functional configuration of an image reconstruction device 122 according to the first embodiment. 第１実施形態に係る画像再構成装置１２２の処理手順の例を示すフローチャートである。2 is a flowchart illustrating an example of a processing procedure of the image reconstruction device 122 according to the first embodiment. 反復法の一例であるＡＲＴ法の処理手順を示すフローチャートである。2 is a flowchart showing a processing procedure of the ART method, which is an example of an iterative method. 第２実施形態のスパースビューインテリアＣＴにおける画像再構成法の原理を表す図である。FIG. 7 is a diagram illustrating the principle of an image reconstruction method in sparse view interior CT according to the second embodiment. 第２実施形態に係る画像再構成装置１２２Ａの機能構成の例を示す概略ブロック図である。It is a schematic block diagram showing an example of the functional composition of image reconstruction device 122A concerning a 2nd embodiment. 第２実施形態に係る画像再構成装置１２２Ａの処理手順の例を示すフローチャートである。12 is a flowchart illustrating an example of a processing procedure of an image reconstruction device 122A according to a second embodiment. 頭部ＣＴ画像を用いて、第１実施形態の画像再構成法と従来の画像再構成法とで比較実験を行った結果を表す図である。FIG. 3 is a diagram showing the results of a comparative experiment between the image reconstruction method of the first embodiment and the conventional image reconstruction method using a head CT image. 頭部ＣＴ画像を用いて、第１実施形態の画像再構成法と従来の画像再構成法とで比較実験を行った結果を表す図である。FIG. 3 is a diagram showing the results of a comparative experiment between the image reconstruction method of the first embodiment and the conventional image reconstruction method using a head CT image. 頭部ＣＴ画像を用いて、第１実施形態の画像再構成法と従来の画像再構成法とで比較実験を行った結果を表す図である。FIG. 3 is a diagram showing the results of a comparative experiment between the image reconstruction method of the first embodiment and the conventional image reconstruction method using a head CT image. 頭部ＣＴ画像を用いて、第１実施形態の画像再構成法と従来の画像再構成法とで比較実験を行った結果を表す図である。FIG. 3 is a diagram showing the results of a comparative experiment between the image reconstruction method of the first embodiment and the conventional image reconstruction method using a head CT image. 頭部ＣＴ画像を用いて、第１実施形態の画像再構成法と従来の画像再構成法とで比較実験を行った結果を表す図である。FIG. 3 is a diagram showing the results of a comparative experiment between the image reconstruction method of the first embodiment and the conventional image reconstruction method using a head CT image. 腹部ＣＴ画像を用いて、第１実施形態の画像再構成法と従来の画像再構成法とで比較実験を行った結果を表す図である。FIG. 3 is a diagram showing the results of a comparative experiment between the image reconstruction method of the first embodiment and the conventional image reconstruction method using an abdominal CT image. 腹部ＣＴ画像を用いて、第１実施形態の画像再構成法と従来の画像再構成法とで比較実験を行った結果を表す図である。FIG. 3 is a diagram showing the results of a comparative experiment between the image reconstruction method of the first embodiment and the conventional image reconstruction method using an abdominal CT image. 腹部ＣＴ画像を用いて、第１実施形態の画像再構成法と従来の画像再構成法とで比較実験を行った結果を表す図である。FIG. 3 is a diagram showing the results of a comparative experiment between the image reconstruction method of the first embodiment and the conventional image reconstruction method using an abdominal CT image. 腹部ＣＴ画像を用いて、第１実施形態の画像再構成法と従来の画像再構成法とで比較実験を行った結果を表す図である。FIG. 3 is a diagram showing the results of a comparative experiment between the image reconstruction method of the first embodiment and the conventional image reconstruction method using an abdominal CT image. 腹部ＣＴ画像を用いて、第１実施形態の画像再構成法と従来の画像再構成法とで比較実験を行った結果を表す図である。FIG. 3 is a diagram showing the results of a comparative experiment between the image reconstruction method of the first embodiment and the conventional image reconstruction method using an abdominal CT image. ポリマーブレンド小片試料を用いて、第２実施形態の画像再構成法と従来の画像再構成法とで比較実験を行った結果を表す図である。FIG. 7 is a diagram showing the results of a comparative experiment between the image reconstruction method of the second embodiment and the conventional image reconstruction method using a polymer blend small piece sample. ポリマーブレンド小片試料を用いて、第２実施形態の画像再構成法と従来の画像再構成法とで比較実験を行った結果を表す図である。FIG. 7 is a diagram showing the results of a comparative experiment between the image reconstruction method of the second embodiment and the conventional image reconstruction method using a polymer blend small piece sample. ポリマーブレンド小片試料を用いて、第２実施形態の画像再構成法と従来の画像再構成法とで比較実験を行った結果を表す図である。FIG. 7 is a diagram showing the results of a comparative experiment between the image reconstruction method of the second embodiment and the conventional image reconstruction method using a polymer blend small piece sample.
　以下、図面を参照しながら本発明の実施形態を詳細に説明する。本実施形態では、医療用のＸ線ＣＴ装置を対象に説明するが、本発明は、ＰＥＴ（Positron Emission Tomographyや、ＳＰＥＣＴ（Single Photon Emission CT）、ＭＲＩ（Magnetic Resonance Imaging）、産業用及び工業用ＣＴ装置、材料計測用ＣＴ装置、電子線トモグラフィ装置等に適用可能である。 Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. In this embodiment, a medical X-ray CT device will be described, but the present invention also applies to PET (Positron Emission Tomography), SPECT (Single Photon Emission CT), MRI (Magnetic Resonance Imaging), industrial and It is applicable to a CT device, a CT device for material measurement, an electron beam tomography device, etc.
［Ｘ線ＣＴ装置］
　まず、図２を参照して本発明に係るＸ線ＣＴ装置１の全体構成について説明する。
　図２に示すように、Ｘ線ＣＴ装置１は、スキャンガントリ部１００、寝台１０５、及び操作卓１２０を備える。スキャンガントリ部１００は、被検体に対してＸ線を照射するとともに被検体を透過したＸ線を検出する装置である。操作卓１２０は、スキャンガントリ部１００の各部を制御するとともにスキャンガントリ部１００で計測した透過Ｘ線データを取得し、画像の生成を行う装置である。寝台１０５は、被検体（物体）を寝載し、スキャンガントリ部１００のＸ線照射範囲に被検体を搬入・搬出する装置である。 [X-ray CT device]
First, the overall configuration of the X-ray CT apparatus 1 according to the present invention will be explained with reference to FIG.
As shown in FIG. 2, the X-ray CT apparatus 1 includes a scan gantry section 100, a bed 105, and an operation console 120. The scan gantry unit 100 is a device that irradiates a subject with X-rays and detects the X-rays that have passed through the subject. The console 120 is a device that controls each part of the scan gantry section 100, acquires transmitted X-ray data measured by the scan gantry section 100, and generates an image. The bed 105 is a device on which a subject (object) is placed and transported into and out of the X-ray irradiation range of the scan gantry section 100.
　スキャンガントリ部１００は、Ｘ線源１０１、回転盤１０２、コリメータユニット１０３、Ｘ線検出器１０６、データ収集装置１０７、ガントリ制御装置１０８、寝台制御装置１０９、Ｘ線制御装置１１０、及びコリメータ制御装置１１１を備える。
　操作卓１２０は、入力装置１２１、画像再構成装置１２２、記憶装置１２３、システム制御装置１２４、及び表示装置１２５を備える。 The scan gantry unit 100 includes an X-ray source 101, a rotating disk 102, a collimator unit 103, an X-ray detector 106, a data acquisition device 107, a gantry control device 108, a bed control device 109, an X-ray control device 110, and a collimator control device. 111.
The console 120 includes an input device 121, an image reconstruction device 122, a storage device 123, a system control device 124, and a display device 125.
　スキャンガントリ部１００の回転盤１０２には開口部１０４が設けられ、開口部１０４を介してＸ線源１０１とＸ線検出器１０６とが対向配置される。開口部１０４に寝台１０５に載置された被検体が挿入される。回転盤１０２は、回転盤駆動装置から駆動伝達系を通じて伝達される駆動力によって被検体の周囲を回転する。回転盤駆動装置はガントリ制御装置１０８によって制御される。 An opening 104 is provided in the rotary disk 102 of the scan gantry section 100, and the X-ray source 101 and the X-ray detector 106 are arranged facing each other through the opening 104. A subject placed on a bed 105 is inserted into the opening 104 . The rotary disk 102 rotates around the subject by a driving force transmitted from a rotary disk drive device through a drive transmission system. The rotary disk drive is controlled by a gantry controller 108.
　Ｘ線源１０１は、Ｘ線制御装置１１０に制御されて所定の強度のＸ線を連続的または断続的に照射する。Ｘ線制御装置１１０は、操作卓１２０のシステム制御装置１２４により決定されたＸ線源電圧及びＸ線源電流に従って、Ｘ線源１０１に印加または供給するＸ線源電圧及びＸ線源電流を制御する。 The X-ray source 101 is controlled by the X-ray control device 110 and continuously or intermittently irradiates X-rays with a predetermined intensity. The X-ray control device 110 controls the X-ray source voltage and X-ray source current applied or supplied to the X-ray source 101 according to the X-ray source voltage and X-ray source current determined by the system control device 124 of the console 120. do.
　Ｘ線源１０１のＸ線照射口にはコリメータユニット１０３が設けられる。コリメータユニット１０３は、Ｘ線源１０１から照射されるＸ線の照射範囲を制限する機構であるコリメータやＸ線の線量分布を調整するＸ線補償フィルタを備える。コリメータの動作はコリメータ制御装置１１１により制御される。
　コリメータ制御装置１１１は、コリメータの動作を制御し、Ｘ線源１０１から照射されるＸ線の照射範囲を制御する装置である。 A collimator unit 103 is provided at the X-ray irradiation port of the X-ray source 101. The collimator unit 103 includes a collimator that is a mechanism that limits the irradiation range of X-rays emitted from the X-ray source 101, and an X-ray compensation filter that adjusts the dose distribution of X-rays. The operation of the collimator is controlled by a collimator control device 111.
The collimator control device 111 is a device that controls the operation of the collimator and controls the irradiation range of X-rays irradiated from the X-ray source 101.
　Ｘ線源１０１から照射され、コリメータユニット１０３を通過し、被検体を透過したＸ線はＸ線検出器１０６に入射する。 X-rays emitted from the X-ray source 101, passed through the collimator unit 103, and transmitted through the subject enter the X-ray detector 106.
　Ｘ線検出器１０６は、例えばシンチレータとフォトダイオードの組み合わせによって構成されるＸ線検出素子群を回転方向（チャネル方向）に例えば１０００個程度、回転軸方向（スライス方向）に例えば１～３２０個程度配列したものである。Ｘ線検出器１０６は、被検体を介してＸ線源１０１に対向するように配置される。Ｘ線検出器１０６はＸ線源１０１から照射されて被検体を透過したＸ線量を検出し、データ収集装置１０７に出力する。 The X-ray detector 106 includes, for example, a group of about 1000 X-ray detection elements in the rotation direction (channel direction) and about 1 to 320 X-ray detection elements in the rotation axis direction (slice direction), which are composed of a combination of a scintillator and a photodiode, for example. It is arranged. The X-ray detector 106 is arranged so as to face the X-ray source 101 through the subject. The X-ray detector 106 detects the amount of X-rays irradiated from the X-ray source 101 and transmitted through the subject, and outputs the detected amount to the data acquisition device 107 .
　データ収集装置１０７は、Ｘ線検出器１０６の個々のＸ線検出素子により検出されるＸ線量を収集し、デジタルデータに変換し、透過Ｘ線データとして操作卓１２０の画像再構成装置１２２に順次出力する。 The data collection device 107 collects the X-ray dose detected by each X-ray detection element of the X-ray detector 106, converts it into digital data, and sequentially sends it as transmitted X-ray data to the image reconstruction device 122 of the console 120. Output.
　画像再構成装置１２２は、データ収集装置１０７から入力された透過Ｘ線データを取得し、対数変換、感度補正等の前処理を行って再構成に必要な投影データを作成する。また画像再構成装置１２２は、投影データを用いてスキャノグラム像や断層像（再構成画像）等の画像を再構成する。また、画像再構成装置１２２は再構成された各スライスの断層像を積み上げてなるボリュームデータを生成してもよい。システム制御装置１２４は、画像再構成装置１２２によって生成した投影データ、スキャノグラム像、断層像、及びボリュームデータ等を表示装置１２５に表示するとともに、記憶装置１２３に記憶する。
　画像再構成装置１２２（１２２Ａ）の詳細は後述する。 The image reconstruction device 122 acquires the transmitted X-ray data input from the data acquisition device 107, performs preprocessing such as logarithmic transformation and sensitivity correction, and creates projection data necessary for reconstruction. The image reconstruction device 122 also reconstructs images such as scanogram images and tomographic images (reconstructed images) using the projection data. Further, the image reconstruction device 122 may generate volume data by stacking reconstructed tomographic images of each slice. The system control device 124 displays the projection data, scanogram image, tomographic image, volume data, etc. generated by the image reconstruction device 122 on the display device 125 and stores them in the storage device 123.
Details of the image reconstruction device 122 (122A) will be described later.
　システム制御装置１２４は、操作卓１２０及びスキャンガントリ部１００の各部を制御する装置である。
　画像再構成装置１２２及びシステム制御装置１２４は、ＣＰＵ（Ｃｅｎｔｒａｌ　Ｐｒｏｃｅｓｓｉｎｇ　Ｕｎｉｔ）、ＲＯＭ（Ｒｅａｄ　Ｏｎｌｙ　Ｍｅｍｏｒｙ）、ＲＡＭ（Ｒａｎｄｏｍ　Ａｃｃｅｓｓ　Ｍｅｍｏｒｙ）等を備えたコンピュータである。 The system control device 124 is a device that controls each part of the console 120 and the scan gantry section 100.
The image reconstruction device 122 and the system control device 124 are computers equipped with a CPU (Central Processing Unit), a ROM (Read Only Memory), a RAM (Random Access Memory), and the like.
　記憶装置１２３はデータ収集装置１０７で収集したデータ及び画像再構成装置１２２で作成された画像データ等を記憶する装置であり、具体的にはハードディスク等のデータ記録装置である。記憶装置１２３には、上述の透過Ｘ線データや画像データの他、Ｘ線ＣＴ装置１の機能を実現するためのプログラムやデータ等が予め記憶される。 The storage device 123 is a device that stores data collected by the data collection device 107 and image data created by the image reconstruction device 122, and is specifically a data recording device such as a hard disk. In addition to the above-described transmission X-ray data and image data, the storage device 123 stores in advance programs, data, etc. for realizing the functions of the X-ray CT apparatus 1.
　表示装置１２５は、液晶パネル、ＣＲＴモニタ等のディスプレイ装置と、ディスプレイ装置と連携して表示処理を実行するための論理回路で構成され、システム制御装置１２４に接続される。表示装置１２５は画像再構成装置１２２から出力される被検体画像、並びにシステム制御装置１２４が取り扱う種々の情報を表示する。 The display device 125 is composed of a display device such as a liquid crystal panel or a CRT monitor, and a logic circuit for performing display processing in cooperation with the display device, and is connected to the system control device 124. The display device 125 displays the subject image output from the image reconstruction device 122 and various information handled by the system control device 124.
　入力装置１２１は、被検体氏名、検査日時、検査条件等を入力するための装置であり、具体的にはキーボードやマウス等のポインティングデバイス、及び各種スイッチボタン等により構成される。入力装置１２１は、操作者によって入力される各種の指示や情報をシステム制御装置１２４に出力する。操作者は、表示装置１２５及び入力装置１２１を使用して対話的にＸ線ＣＴ装置１を操作する。入力装置１２１は表示装置１２５の表示画面と一体的に構成されるタッチパネル式の入力装置としてもよい。 The input device 121 is a device for inputting the subject's name, test date and time, test conditions, etc., and specifically includes a pointing device such as a keyboard and a mouse, various switch buttons, and the like. The input device 121 outputs various instructions and information input by the operator to the system control device 124. An operator interactively operates the X-ray CT apparatus 1 using the display device 125 and the input device 121. The input device 121 may be a touch panel type input device configured integrally with the display screen of the display device 125.
［投影データ］
　ここで、図３Ａ～図３Ｂを用いて投影データについて説明する。図３Ａは、平行ビーム方式の場合の投影データを示す図である。Ｘ線源が回転方向にθ回転した位置にあるとする。物体（被検体）のｚ軸の対象とする位置における断面の吸収係数分布（以下、画像値ともいう。）をｆ（ｘ，ｙ）とする。Ｘ線源から照射されたＸ線は、断面の透過した直線状の画素（ｘ，ｙ）の吸収係数分布ｆ（ｘ，ｙ）により積算して減弱され、Ｘ線検出器の軸上の位置ｒで、透過Ｘ線データとして検出される。画像再構成装置１２２が、この透過Ｘ線データに対して対数変換、感度補正等をおこなったものが、投影データｐ（ｒ，θ）である。
　また、図３Ｂのファンビーム方式でも同様である。
　なお、完全な投影データを取得する場合は、角度θの範囲は、平行ビーム方式では１８０度、ファンビーム方式では３６０度である。また、動径ｒは物体（又は関心領域）の一端から他端までである。 [Projection data]
Here, projection data will be explained using FIGS. 3A and 3B. FIG. 3A is a diagram showing projection data in the case of the parallel beam method. Assume that the X-ray source is at a position rotated by θ in the rotational direction. Let f(x, y) be the absorption coefficient distribution (hereinafter also referred to as image value) of a cross section of an object (subject) at a target position on the z-axis. The X-rays emitted from the X-ray source are accumulated and attenuated by the absorption coefficient distribution f(x,y) of the linear pixels (x,y) transmitted through the cross section, and the position on the axis of the X-ray detector is r, and is detected as transmitted X-ray data. The image reconstruction device 122 performs logarithmic transformation, sensitivity correction, etc. on this transmitted X-ray data, resulting in projection data p(r, θ).
The same applies to the fan beam method shown in FIG. 3B.
Note that when acquiring complete projection data, the range of the angle θ is 180 degrees in the parallel beam method and 360 degrees in the fan beam method. Further, the vector radius r is from one end of the object (or region of interest) to the other end.
［第１実施形態］
　次に、本願発明の第１実施形態について説明する。第１実施形態は、通常のインテリアＣＴにおける画像再構成方法である。まず、図４～図７を用いて、第１実施形態のインテリアＣＴにおける画像再構成法の原理を説明する。以下、被検体のことを物体とも言う。 [First embodiment]
Next, a first embodiment of the present invention will be described. The first embodiment is an image reconstruction method for normal interior CT. First, the principle of the image reconstruction method in interior CT of the first embodiment will be explained using FIGS. 4 to 7. Hereinafter, the subject will also be referred to as an object.
　図４のように、本実施形態の画像再構成法では、物体の対象とする断面の画像を考え、その中に関心領域ＲＯＩ　Ｓが含まれるとする。画像には、吸収係数分布に相当する画像値ｆ（ｘ，ｙ）が与えられている。サポートΩは、物体を含むように設定される物体の存在領域で、サポートΩの外では画像値は０とする。本実施形態の画像再構成法では、インテリアＣＴは、回転方向に所定の角度の範囲（例えば３６０°）でＸ線源から物体の関心領域ＳにＸ線を照射し、検出器を介して投影データを取得する。例えば、投影データを数百から数千個程度取得する。前述したように、インテリアＣＴでは、投影データだけで画像の再構成をすると解が一意に定まらない。 As shown in FIG. 4, in the image reconstruction method of this embodiment, an image of a target cross section of an object is considered, and a region of interest ROI S is assumed to be included in the image. The image is given an image value f(x,y) corresponding to the absorption coefficient distribution. The support Ω is an object existence area that is set to include the object, and the image value is 0 outside the support Ω. In the image reconstruction method of this embodiment, interior CT irradiates X-rays from an X-ray source to a region of interest S of an object in a predetermined angular range (for example, 360°) in the rotation direction, and projects the X-rays through a detector. Get data. For example, several hundred to several thousand pieces of projection data are acquired. As described above, in interior CT, if an image is reconstructed using only projection data, a solution cannot be determined uniquely.
　そこで、本実施形態の画像再構成法では、先験情報として、物体の断面の画像値の総和を使用する。
Figure JPOXMLDOC01-appb-M000001
 　ここで、Ωは、サポート（物体の存在領域）である。ｆ（ｘ，ｙ）は、物体の断面の画像の画像値である。Ｃは、ｆ（ｘ，ｙ）をサポートΩの領域で積分した画像値の総和である。なお、Ｃは、関心領域Ｓの内部だけでなく、物体の断面全体の画像値の総和であることに注意する。 Therefore, in the image reconstruction method of this embodiment, the sum of image values of the cross section of the object is used as a priori information.
Figure JPOXMLDOC01-appb-M000001
 Here, Ω is the support (the area where the object exists). f(x,y) is an image value of an image of a cross section of the object. C is the sum of image values obtained by integrating f(x, y) over the region of support Ω. Note that C is the sum of image values not only for the inside of the region of interest S but also for the entire cross section of the object.
　先験情報Ｃは、例えば次のように獲得される。
１．図５に示すように、一方向（回転方向の１つの角度）から物体の断面全体を含む完全投影データを取得し、その総和を先験情報Ｃとする。
　画像値の総和Ｃのみしか使用しないため、関心領域Ｓに対して投影データを取得したインテリアＣＴと異なる装置で取得した投影データであってもよい。また、関心領域Ｓに対する投影データと解像度が異なる投影データであっても、位置がずれている投影データであってもよい。また、角度はどの方向から測定した投影データであってもよく、雑音が多く低ＳＮ比である投影データであってもよい。 The a priori information C is obtained, for example, as follows.
1. As shown in FIG. 5, complete projection data including the entire cross section of the object is acquired from one direction (one angle in the rotational direction), and the sum of the data is defined as a priori information C.
Since only the sum C of image values is used, the projection data for the region of interest S may be obtained using a different device from the interior CT that obtained the projection data. Further, the projection data may have a different resolution from the projection data for the region of interest S, or the projection data may be out of position. Further, the angle may be projection data measured from any direction, and may be projection data that is noisy and has a low signal-to-noise ratio.
２．インテリアＣＴで関心領域Ｓに対して投影データを取得する時刻とは異なる時刻に撮影された撮影画像から、式（１）により先験情報Ｃを算出する。また、動いている物体でも画像値の総和はあまり変わらないことから、動画撮影の場合、他時間のフレーム画像から式（１）により先験情報Ｃを算出することも可能である。 2. A priori information C is calculated using equation (1) from a photographed image taken at a time different from the time when projection data is acquired for the region of interest S in interior CT. In addition, since the sum of image values does not change much even with a moving object, in the case of video shooting, it is also possible to calculate the a priori information C using equation (1) from frame images taken at other times.
３．インテリアＣＴによる撮影の前に、低ＳＮ比・低解像度・短測定時間などの悪条件（低品質）で簡単に画像撮影（プリスキャン）を行い、その再構成画像ｆ（ｘ，ｙ）から画像値の総和Ｃを求める。
　画像値の総和Ｃのみしか使用しないため、プリスキャンは、インテリアＣＴと異なる装置で撮影されたものであっても、解像度が異なっていても、位置がずれていても、雑音が多く低ＳＮ比であってもよい。また、プリスキャンは、時間変化が小さい被写体であれば、投影データを取得する時刻とは異なる時刻に行ってもよい。 3. Before imaging with interior CT, images are easily captured (prescan) under adverse conditions (low quality) such as low SN ratio, low resolution, and short measurement time, and images are generated from the reconstructed image f(x, y). Find the total sum C of the values.
Since only the sum of image values C is used, pre-scanning is noisy and has a low signal-to-noise ratio, even if the image was taken with a different device than interior CT, has a different resolution, or is in a different position. It may be. Furthermore, if the subject is subject to small temporal changes, the prescan may be performed at a different time from the time at which the projection data is acquired.
　このように、先験情報Ｃは、前述の従来の方法（１）～（４）と比較して、スカラー値１つであるのではるかに情報が少なく獲得しやすい。また、先験情報Ｃは、画像の合計値Ｃ（スカラー値）だけであるので、先験情報としては最小のものに近いと考えられる。 In this way, compared to the conventional methods (1) to (4) described above, the a priori information C is one scalar value, so it is much less information and easier to obtain. Further, since the a priori information C is only the total value C (scalar value) of the image, it is considered to be close to the minimum a priori information.
　本実施形態の画像再構成法は、以下の条件を連立させて反復法により解を求め、関心領域の画像（画像値）を求める。
　まず、物体の断面の画像値を並べたベクトルをｘとし（各要素をｘｉとする）、そのうち関心領域Ｓの内部の画像値を並べたベクトルをｘＲＯＩとし、物体の断面のうち関心領域の外部の画像値を並べたベクトルをｘＥＸＴとする（なお、文中ではベクトルの矢印記号は省略する）。
Figure JPOXMLDOC01-appb-M000002
 In the image reconstruction method of this embodiment, a solution is obtained by an iterative method using the following conditions simultaneously, and an image (image value) of the region of interest is obtained.
First, let x be a vector in which the image values of the cross section of the object are arranged (each element is x i ), and let the vector in which the image values inside the region of interest S are arranged be x ROI . Let x EXT be a vector in which the external image values of are arranged (note that the arrow symbol of the vector is omitted in the text).
Figure JPOXMLDOC01-appb-M000002
　先験情報Ｃにより、サポートΩの内部（物体の内部）の画像値の総和はＣである。
Figure JPOXMLDOC01-appb-M000003
 　サポートΩの外部（物体の外部）の画像値は０とする。
Figure JPOXMLDOC01-appb-M000004
 Based on the a priori information C, the sum of image values inside the support Ω (inside the object) is C.
Figure JPOXMLDOC01-appb-M000003
 The image value outside the support Ω (outside the object) is set to 0.
Figure JPOXMLDOC01-appb-M000004
　回転方向に所定の角度の範囲で関心領域ＳにＸ線を照射し、取得した各投影データをベクトルで表しｂｉとする。また、照射角度に応じてＸ線が物体の断面の通過する際の画素の情報をもつ行列を投影演算行列（後述する）とし、投影データｂｉに対応する投影演算行列をＡｉとする。そして、ベクトルｂｉを１列に並べたベクトルをｂとし、行列Ａｉを１列に並べた行列をＡとするとき、測定方程式は、式（４）のように表される。
Figure JPOXMLDOC01-appb-M000005
 The region of interest S is irradiated with X-rays within a predetermined angular range in the rotational direction, and each acquired projection data is expressed as a vector and designated as b i . Further, a matrix having information on pixels when X-rays pass through a cross section of an object according to the irradiation angle is defined as a projection calculation matrix (described later), and a projection calculation matrix corresponding to projection data b i is defined as A i . Then, when b is a vector in which the vectors b i are arranged in one column, and A is a matrix in which the matrix A i is arranged in one column, the measurement equation is expressed as in equation (4).
Figure JPOXMLDOC01-appb-M000005
　本実施形態の画像再構成法は、式（２）、（３）、（４）を連立させて反復法により解となるベクトルｘを求める。求めたベクトルｘのうち、関心領域の画像（画像値）ｘＲＯＩは高精度で再構成される。
　画像再構成法が用いる反復法は、ＡＲＴ（Algebraic Reconstruction Technique）法、ＳＩＲＴ（Simultaneous Iterative Reconstruction Technique）法、統計的画像再構成法（Transmission Maximum Likelihood他）など、ＣＴ分野で知られるどのような反復法でも（サポートの外部で画像ｆ（ｘ，ｙ）は０、画像値の総和Ｃの制約を毎反復後に課すように修正して）使用可能である。なお、反復法で解く際のベクトルｘの初期値は特に限定されない。 In the image reconstruction method of this embodiment, equations (2), (3), and (4) are simultaneously applied to obtain a vector x that becomes a solution by an iterative method. Of the obtained vector x, the image (image value) x ROI of the region of interest is reconstructed with high precision.
The iterative method used in the image reconstruction method can be any of the iterative methods known in the CT field, such as the ART (Algebraic Reconstruction Technique) method, the SIRT (Simultaneous Iterative Reconstruction Technique) method, and the statistical image reconstruction method (Transmission Maximum Likelihood, etc.). It is also possible to use the method (modified to impose the constraint that the image f(x, y) is 0 outside the support and the sum of the image values C after every iteration). Note that the initial value of the vector x when solving by the iterative method is not particularly limited.
　ここで、図６Ａ～図６Ｃ及び図７を用いて、投影演算行列Ａと測定方程式Ａｘ＝ｂの簡単な例を説明する。図６Ａのように、物体の存在領域であるサポートΩがあり、その中に物体が含まれ、物体の中に関心領域Ｓがあるとする。この場合の関心領域Ｓの画素は、ｘ１～ｘ７である。また、物体（の断面）の画素は、関心領域を含んでｘ１～ｘ２１である。したがって、ｘ＝［ｘ１，ｘ２，・・・，ｘ２１］Ｔであり、ｘＲＯＩ＝［ｘ１，ｘ２，・・・，ｘ７］Ｔであり、ｘＥＸＴ＝［ｘ８，ｘ９，・・・，ｘ２１］Ｔである（Ｔは転置を表す）。 Here, a simple example of the projection calculation matrix A and the measurement equation Ax=b will be explained using FIGS. 6A to 6C and FIG. 7. As shown in FIG. 6A, it is assumed that there is a support Ω that is the region where the object exists, that the object is included therein, and that there is a region of interest S inside the object. The pixels of the region of interest S in this case are x 1 to x 7 . Furthermore, the pixels of (the cross section of) the object are x 1 to x 21 including the region of interest. Therefore, x = [x 1 , x 2 , ..., x 21 ] T , x ROI = [x 1 , x 2 , ..., x 7 ] T , and x EXT = [x 8 , x 9 ,..., x 21 ] T (T represents transposition).
　図６Ｂのように、３本のＸ線ｌ１，ｌ２，ｌ３を考え、Ｘ線が軸に対して角度０°で照射されたとする。このとき、Ｘ線ｌ１は、画素ｘ１１，ｘ１２，ｘ１，ｘ２，ｘ１３を通過し、これらの画像値を積算した値（に基づく値）が投影データとして取得される。Ｘ線ｌ２は、画素ｘ１４，ｘ３，ｘ４，ｘ５，ｘ１５を通過し、これらの画像値を積算した値（に基づく値）が投影データとして取得される。Ｘ線ｌ３は、画素ｘ１６，ｘ６，ｘ７，ｘ１７，ｘ１８を通過し、これらの画像値を積算した値（に基づく値）が投影データとして取得される。この際のＸ線が通過する画素（の位置）の情報と物体の画素の情報ｘ＝［ｘ１，ｘ２，・・・，ｘ２１］Ｔから投影演算行列Ａ１を定めることができる。また、このときの投影データをｂ１とする。 As shown in FIG. 6B, three X-rays l 1 , l 2 , and l 3 are considered, and it is assumed that the X-rays are irradiated at an angle of 0° with respect to the axis. At this time, the X-ray l 1 passes through the pixels x 11 , x 12 , x 1 , x 2 , x 13 , and a value (based on) obtained by integrating these image values is acquired as projection data. The X-ray l 2 passes through the pixels x 14 , x 3 , x 4 , x 5 , x 15 , and a value (based on) obtained by integrating these image values is acquired as projection data. The X-ray l 3 passes through the pixels x 16 , x 6 , x 7 , x 17 , and x 18 , and a value (based on) obtained by integrating these image values is acquired as projection data. At this time, the projection calculation matrix A 1 can be determined from the information on (the position of) the pixel through which the X-ray passes and the information on the pixel of the object x=[x 1 , x 2 , . . . , x 21 ] T . Further, the projection data at this time is assumed to be b1 .
　また、図６Ｃのように、３本のＸ線ｌ１，ｌ２，ｌ３が軸に対して角度９０°で照射されたとする。このとき、Ｘ線ｌ１は、画素ｘ１９，ｘ６，ｘ３，ｘ１２，ｘ８を通過し、これらの画像値を積算した値（に基づく値）が投影データとして取得される。Ｘ線ｌ２は、画素ｘ２０，ｘ７，ｘ４，ｘ１，ｘ９を通過し、これらの画像値を積算した値（に基づく値）が投影データとして取得される。Ｘ線ｌ３は、画素ｘ２１，ｘ１７，ｘ５，ｘ２，ｘ１０を通過し、これらの画像値を積算した値（に基づく値）が投影データとして取得される。この際のＸ線が通過する画素（の位置）の情報と物体の画素の情報ｘ＝［ｘ１，ｘ２，・・・，ｘ２１］Ｔから投影演算行列Ａ２を定めることができる。また、このときの投影データをｂ２とする。 Further, as shown in FIG. 6C, assume that three X-rays l 1 , l 2 , l 3 are irradiated at an angle of 90° with respect to the axis. At this time, the X-ray l 1 passes through the pixels x 19 , x 6 , x 3 , x 12 , and x 8 , and a value (based on) obtained by integrating these image values is acquired as projection data. The X-ray l 2 passes through pixels x 20 , x 7 , x 4 , x 1 , and x 9 , and a value (based on) obtained by integrating these image values is acquired as projection data. The X-ray l 3 passes through the pixels x 21 , x 17 , x 5 , x 2 , and x 10 , and a value (based on) obtained by integrating these image values is acquired as projection data. At this time, the projection calculation matrix A 2 can be determined from the information on the pixels (positions) through which the X-rays pass and the information on the pixels of the object x=[x 1 , x 2 , . . . , x 21 ] T . Further, the projection data at this time is assumed to be b2 .
　投影データがｂ１とｂ２の２つのみの場合、ｂ１とｂ２を１列に並べてベクトルｂとし、対応する投影演算行列Ａ１とＡ２を１列に並べて行列Ａとすると、測定方程式Ａｘ＝ｂは、図７に示すようになる。この場合の右辺のｂ（ｂ１，ｂ２）は実際には投影データである。なお、図中の行列Ａの要素は１となっているが１には限られない。また行列Ａの空白の要素は０である。 If there are only two projection data, b 1 and b 2 , then b 1 and b 2 are arranged in one column to form a vector b, and the corresponding projection calculation matrices A 1 and A 2 are arranged in one column to form a matrix A. The equation Ax=b becomes as shown in FIG. In this case, b (b 1 , b 2 ) on the right side is actually projection data. Note that although the element of matrix A in the figure is 1, it is not limited to 1. Furthermore, blank elements of matrix A are 0.
　図８は、第１実施形態に係る画像再構成装置１２２の機能構成の例を示す概略ブロック図である。画像再構成装置１２２は、先験情報取得部１３１と、投影データ取得部１３２と、画像算出部１３３とを備える。なお、画像再構成装置１２２は、図２に示したようにＸ線ＣＴ装置１の一部として備えられてもよいし、別体としてＸ線ＣＴ装置１に接続されてもよい。また、画像再構成装置１２２は単体で動作し、ネットワークを介して外部サーバや記憶装置等から必要な情報を取得してもよい。 FIG. 8 is a schematic block diagram showing an example of the functional configuration of the image reconstruction device 122 according to the first embodiment. The image reconstruction device 122 includes an a priori information acquisition section 131, a projection data acquisition section 132, and an image calculation section 133. Note that the image reconstruction device 122 may be provided as a part of the X-ray CT apparatus 1 as shown in FIG. 2, or may be connected to the X-ray CT apparatus 1 as a separate body. Further, the image reconstruction device 122 may operate alone and obtain necessary information from an external server, storage device, etc. via a network.
　先験情報取得部１３１は、物体の断面の画像の画像値の総和を先験情報Ｃとして取得する。先験情報Ｃは次の式で算出される。
Figure JPOXMLDOC01-appb-M000006
 　ここで、Ωは、サポート（物体の存在領域）である。ｆ（ｘ，ｙ）は、物体の断面の画像の画像値である。Ｃは、ｆ（ｘ，ｙ）をサポートΩの領域で積分した画像値の総和である。なお、Ｃは、関心領域Ｓの内部だけでなく、物体の断面全体の画像値の総和であることに注意する。 The a priori information acquisition unit 131 acquires, as a priori information C, the sum of image values of images of the cross section of the object. A priori information C is calculated using the following formula.
Figure JPOXMLDOC01-appb-M000006
 Here, Ω is the support (the area where the object exists). f(x,y) is an image value of an image of a cross section of the object. C is the sum of image values obtained by integrating f(x, y) over the region of support Ω. Note that C is the sum of image values not only for the inside of the region of interest S but also for the entire cross section of the object.
　先験情報取得部１３１は、一方向（回転方向の１つの角度）から物体の断面全体を含む完全投影データを取得し、その総和を先験情報Ｃとして算出してもよい。また、先験情報取得部１３１は、物体を含む撮影画像から式（５）により先験情報Ｃを算出してもよい。また、先験情報取得部１３１は、悪条件（低品質）で簡単にプリスキャンした画像から式（５）により先験情報Ｃを算出してもよい。また、先験情報取得部１３１は、記憶装置１２３等に記憶してある式（５）の値を先験情報Ｃとして取得してもよい。 The a priori information acquisition unit 131 may acquire complete projection data including the entire cross section of the object from one direction (one angle in the rotational direction), and calculate the sum as the a priori information C. Further, the a priori information acquisition unit 131 may calculate the a priori information C from the captured image including the object using equation (5). Further, the a priori information acquisition unit 131 may calculate the a priori information C using equation (5) from an image simply prescanned under bad conditions (low quality). Further, the a priori information acquisition unit 131 may obtain the value of equation (5) stored in the storage device 123 or the like as the a priori information C.
　投影データ取得部１３２は、物体の周方向において所定の角度の範囲（例えば３６０°）で物体の関心領域にＸ線を照射した際の投影データを複数取得する。例えば、投影データ取得部１３２は、投影データを数百から数千個程度取得する。なお、投影データ取得部１３２は、Ｘ線ＣＴ装置１で撮影しながら取得された投影データを用いてもよいし、予め記憶装置１２３に記憶しておいた投影データを取得してもよい。 The projection data acquisition unit 132 acquires a plurality of projection data when a region of interest of the object is irradiated with X-rays in a predetermined angular range (for example, 360°) in the circumferential direction of the object. For example, the projection data acquisition unit 132 acquires approximately several hundred to several thousand pieces of projection data. Note that the projection data acquisition unit 132 may use projection data acquired while imaging with the X-ray CT apparatus 1, or may acquire projection data stored in the storage device 123 in advance.
　画像算出部１３３は、照射角度に応じてＸ線が物体の断面の通過する際の画素の情報をもつ行列を投影演算行列とするとき、複数の投影データｂｉを並べたベクトルをｂとし、投影データｂｉに対応して複数の投影演算行列Ａｉを並べた行列をＡとし、物体の断面の画像値を並べたベクトルをｘとするとき、先験情報Ｃの下でＡｘ＝ｂを解いて、関心領域の画像を求める。
　具体的には、画像算出部１３３は、物体の断面の画像値を並べたベクトルをｘとし（各要素をｘｉとする）、そのうち関心領域Ｓの内部の画像値を並べたベクトルをｘＲＯＩとし、物体の断面のうち関心領域の外部の画像値を並べたベクトルをｘＥＸＴとする。
Figure JPOXMLDOC01-appb-M000007
 When the image calculation unit 133 sets a matrix having information of pixels when the X-ray passes through the cross section of the object according to the irradiation angle as a projection calculation matrix, b is a vector in which a plurality of projection data b i are arranged, When A is a matrix in which a plurality of projection calculation matrices A i are arranged corresponding to projection data b i , and x is a vector in which image values of a cross section of an object are arranged, Ax = b under a priori information C. Solve to obtain an image of the region of interest.
Specifically, the image calculation unit 133 defines a vector in which the image values of the cross section of the object are arranged as x (each element is x i ), and a vector in which the image values inside the region of interest S are arranged as x ROI. Let x EXT be a vector in which image values outside the region of interest in the cross section of the object are arranged.
Figure JPOXMLDOC01-appb-M000007
　画像算出部１３３は、サポートΩの内部（物体の内部）の画像値の総和をＣとする。
Figure JPOXMLDOC01-appb-M000008
 　画像算出部１３３は、サポートΩの外部（物体の外部）の画像値を０とする。
Figure JPOXMLDOC01-appb-M000009
 The image calculation unit 133 sets C as the sum of image values inside the support Ω (inside the object).
Figure JPOXMLDOC01-appb-M000008
 The image calculation unit 133 sets the image value outside the support Ω (outside the object) to 0.
Figure JPOXMLDOC01-appb-M000009
　画像算出部１３３は、投影データ取得部１３２が取得した各投影データをベクトルｂｉとし、投影データｂｉに対応する投影演算行列をＡｉとする。そして、画像算出部１３３は、ベクトルｂｉを１列に並べたベクトルをｂとし、行列Ａｉを１列に並べた行列をＡとするとき、測定方程式を式（４）のように立式する。
Figure JPOXMLDOC01-appb-M000010
 The image calculation unit 133 sets each projection data acquired by the projection data acquisition unit 132 as a vector b i , and sets the projection calculation matrix corresponding to the projection data b i as A i . Then, the image calculation unit 133 calculates the measurement equation by formulating the measurement equation as shown in equation (4), where b is a vector in which the vectors b i are arranged in one column, and A is a matrix in which the matrix A i is arranged in one column. do.
Figure JPOXMLDOC01-appb-M000010
　画像算出部１３３は、式（６）、（７）、（８）を連立させて反復法により解となるベクトルｘを求め、ｘの中のｘＲＯＩを関心領域の画像とする。 The image calculation unit 133 calculates a vector x that is a solution by simultaneous equations (6), (7), and (8) by an iterative method, and sets x ROI in x as an image of the region of interest.
　次に、図９及び図１０を参照して、第１実施形態に係る画像再構成装置１２２の動作を説明する。図９は、第１実施形態に係る画像再構成装置１２２の処理手順の例を示すフローチャートである。
　まず、先験情報取得部１３１は、物体の断面の画像の画像値の総和を先験情報Ｃとして取得する（ステップＳ１０１）。 Next, the operation of the image reconstruction device 122 according to the first embodiment will be described with reference to FIGS. 9 and 10. FIG. 9 is a flowchart illustrating an example of a processing procedure of the image reconstruction device 122 according to the first embodiment.
First, the a priori information acquisition unit 131 acquires the sum of image values of images of a cross section of an object as a priori information C (step S101).
　次に、投影データ取得部１３２は、物体の周方向において所定の角度の範囲で物体の関心領域にＸ線を照射した際の投影データｂｉを複数取得する（ステップＳ１０２）。 Next, the projection data acquisition unit 132 acquires a plurality of projection data b i when the region of interest of the object is irradiated with X-rays within a predetermined angular range in the circumferential direction of the object (step S102).
　次に、画像算出部１３３は、照射角度に応じてＸ線が物体の断面の通過する際の画素の情報をもつ行列を投影演算行列とするとき、複数の投影データｂｉを並べたベクトルをｂとし、投影データｂｉに対応して複数の投影演算行列Ａｉを並べた行列をＡとし、物体の断面の画像値を並べたベクトルをｘとするとき、測定方程式Ａｘ＝ｂを立式する（ステップＳ１０３）。 Next, the image calculation unit 133 calculates a vector in which a plurality of projection data b b, A is a matrix in which a plurality of projection calculation matrices A i are arranged corresponding to projection data b i , and x is a vector in which image values of a cross section of an object are arranged, then the measurement equation Ax=b can be expressed as (Step S103).
　次に、画像算出部１３３は、先験情報Ｃの下で反復法によりＡｘ＝ｂを解いて、解のｘＲＯＩを関心領域の画像とする（ステップＳ１０４）。 Next, the image calculation unit 133 solves Ax=b using an iterative method under the a priori information C, and sets the x ROI of the solution as the image of the region of interest (step S104).
　図１０は、画像算出部１３３の行う反復法の一例であるＡＲＴの処理手順の例を示すフローチャートである。求める画像ｘをベクトルｘ＝（ｘ１，ｘ２，・・・，ｘＪ）Ｔとし、投影データをベクトルｂ＝（ｂ１，ｂ２，・・・，ｂＩ）Ｔとし、投影演算行列Ａを上の行から順にベクトルａｉ Ｔ（１≦ｉ≦Ｉ）とする。 FIG. 10 is a flowchart illustrating an example of the processing procedure of ART, which is an example of the iterative method performed by the image calculation unit 133. The image x to be sought is vector x = (x 1 , x 2 , ..., x J ) T , the projection data is vector b = (b 1 , b 2 , ..., b I ) T , and the projection calculation matrix is Let A be a vector a i T (1≦i≦I) in order from the top row.
　まず、画像算出部１３３は、ベクトルｘの初期値ｘ（０）を任意に設定する（ステップＳ２０１）。
　次に、画像算出部１３３は、ｋ（＝０，１，２，・・・）について所定回メイン反復を行う（ステップＳ２０２）。
　次に、画像算出部１３３は、テンポラリベクトルｘ（ｋ，１）にｘ（ｋ）を代入して（ステップＳ２０３）、ｉについてサブ反復を、投影データの要素数であるＩ回行う（ステップＳ２０４）。 First, the image calculation unit 133 arbitrarily sets the initial value x (0) of the vector x (step S201).
Next, the image calculation unit 133 performs main repetition for k (=0, 1, 2, . . . ) a predetermined number of times (step S202).
Next, the image calculation unit 133 substitutes x (k) into the temporary vector x (k, 1) (step S203), and performs sub-iteration I times for i, which is the number of elements of the projection data (step S204). ).
　次に、画像算出部１３３は、投影データの値ｂｉと現在のｘ（ｋ，ｉ）の投影演算行列の中のベクトルａｉ Ｔによる投影値との差分を係数とする正規化したベクトルａｉを現在のｘ（ｋ，ｉ）に加えて中間ベクトルｘ（ｋ，ｉ＋１／２）とする（ステップＳ２０５）。 Next, the image calculation unit 133 calculates a normalized vector a whose coefficient is the difference between the value b i of the projection data and the projection value by the vector a i T in the projection calculation matrix of the current x (k, i) . Add i to the current x (k, i) to obtain an intermediate vector x (k, i+1/2) (step S205).
　次に、画像算出部１３３は、先験情報Ｃを用いて、Ｃ（画像値の総和）と中間ベクトルｘ（ｋ，ｉ＋１／２）の画像値の総和との差を、サポートΩ内の画素数で割った値を、中間ベクトルｘ（ｋ，ｉ＋１／２）の要素の値に加えて、更新用ベクトルｘ（ｋ，ｉ＋１）の要素の値とする。ただし、画像算出部１３３は、サポートΩに含まれない画素に対しては、更新用ベクトルｘ（ｋ，ｉ＋１）の要素の値は０とする。（ステップＳ２０６）。 Next, using the a priori information C, the image calculation unit 133 calculates the difference between C (the sum of image values) and the sum of the image values of the intermediate vector The value divided by the number is added to the value of the element of the intermediate vector x (k, i+1/2) , and is set as the value of the element of the update vector x (k, i+1) . However, the image calculation unit 133 sets the value of the element of the update vector x (k, i+1) to 0 for pixels that are not included in the support Ω. (Step S206).
　次に、画像算出部１３３は、サブ反復が終了したら、ベクトルｘ（ｋ＋１）を更新用ベクトルｘ（ｋ，Ｉ＋１）で更新する（ステップＳ２０７）。
　画像算出部１３３は、メイン反復が終了したら、ベクトルｘ＝ｘ（ｋ＋１）を算出したとして、処理を終了する。
　以上で、図９及び図１０の説明は終了である。 Next, when the sub-iteration is completed, the image calculation unit 133 updates the vector x (k+1) with the update vector x (k, I+1) (step S207).
When the main iteration ends, the image calculation unit 133 concludes that the vector x=x (k+1) has been calculated and ends the process.
This is the end of the explanation of FIGS. 9 and 10.
　以上説明したように、先験情報取得部１３１は、物体の断面の画像の画像値の総和を先験情報Ｃとして取得し、投影データ取得部１３２は、物体の周方向において所定の角度の範囲で物体の関心領域にＸ線を照射した際の投影データを複数取得し、画像算出部１３３は、投影データのベクトルをｂとし、投影演算行列をＡとし、物体の断面の画像値を並べたベクトルをｘとするとき、先験情報Ｃの下でＡｘ＝ｂを解いて、関心領域の画像を求める。 As explained above, the a priori information acquisition unit 131 acquires the sum of image values of the cross-sectional images of the object as the a priori information C, and the projection data acquisition unit 132 acquires the sum of the image values of the cross-sectional images of the object as the a priori information C, and the projection data acquisition unit 132 acquires the sum of the image values of the images of the cross section of the object as the a priori information C. A plurality of projection data are obtained when the region of interest of the object is irradiated with X-rays, and the image calculation unit 133 sets the vector of the projection data to b, the projection calculation matrix to A, and arranges the image values of the cross section of the object. When the vector is x, Ax=b is solved under a priori information C to obtain an image of the region of interest.
　これにより、画像再構成装置１２２は、インテリアＣＴにおいて、より簡便（超簡便）な先験情報を用いて、高精度な画像再構成を行うことができる。
　また、画像再構成装置１２２の用いる先験情報Ｃは、前述の従来の方法（１）～（４）と比較して、スカラー値１つであるのではるかに情報が少なく獲得しやすい。そのため、画像再構成装置１２２は、非常に実用的で使いやすい。また、先験情報Ｃは、画像の合計値Ｃ（スカラー値）だけであるので、先験情報としては最小のものに近いと考えられる。 Thereby, the image reconstruction device 122 can perform highly accurate image reconstruction using simpler (ultra-simple) a priori information in interior CT.
Further, the a priori information C used by the image reconstruction device 122 is a single scalar value compared to the conventional methods (1) to (4) described above, so it is much less information and easier to obtain. Therefore, the image reconstruction device 122 is very practical and easy to use. Further, since the a priori information C is only the total value C (scalar value) of the image, it is considered to be close to the minimum a priori information.
［第２実施形態］
　次に、本願発明の第２実施形態について説明する。第２実施形態は、スパースビューインテリアＣＴにおける画像再構成方法である。スパースビュー（sparse view）ＣＴとは、Ｘ線の投影方向数を削減して撮影を行うＣＴのことである。図１１を用いて、第２実施形態のスパースビューインテリアＣＴにおける画像再構成法の原理を説明する。 [Second embodiment]
Next, a second embodiment of the present invention will be described. The second embodiment is an image reconstruction method in sparse view interior CT. Sparse view CT is CT that performs imaging by reducing the number of X-ray projection directions. The principle of the image reconstruction method in sparse view interior CT of the second embodiment will be explained using FIG. 11.
　図１１のように、本実施形態の画像再構成法でも、物体の対象とする断面の画像を考え、その中に関心領域ＲＯＩ　Ｓが含まれるとする。画像には、吸収分布係数に相当する画像値ｆ（ｘ，ｙ）が与えられている。サポートΩは、物体を含むように設定される物体の存在領域で、サポートΩの外では画像値は０とする。本実施形態の画像再構成法では、インテリアＣＴは、回転方向に所定の角度の範囲（例えば３６０°）において所定の間隔で疎にＸ線源から物体の関心領域ＳにＸ線を照射し、検出器を介して投影データを取得する。例えば、投影データを８０個、６４個、又は４６個程度取得する。前述したように、スパースビューインテリアＣＴでも、投影データだけで画像の再構成をすると解が一意に定まらず高精度の画像が得られない。 As shown in FIG. 11, the image reconstruction method of this embodiment also considers an image of a target cross section of an object, and assumes that the region of interest ROIS is included in the image. An image value f(x,y) corresponding to an absorption distribution coefficient is given to the image. The support Ω is an object existence area that is set to include the object, and the image value is 0 outside the support Ω. In the image reconstruction method of this embodiment, the interior CT irradiates the region of interest S of the object with X-rays from an X-ray source sparsely at predetermined intervals in a predetermined angular range (for example, 360°) in the rotation direction, Obtain projection data via a detector. For example, approximately 80, 64, or 46 pieces of projection data are acquired. As described above, even in sparse view interior CT, if an image is reconstructed using only projection data, the solution will not be uniquely determined and a highly accurate image will not be obtained.
　そこで、本実施形態の画像再構成法では、先験情報として、物体の断面の画像値の総和を使用する。
Figure JPOXMLDOC01-appb-M000011
 　ここで、Ωは、サポート（物体の存在領域）である。ｆ（ｘ，ｙ）は、物体の断面の画像の画像値である。Ｃは、ｆ（ｘ，ｙ）をサポートΩの領域で積分した画像値の総和である。なお、Ｃは、関心領域Ｓの内部だけでなく、物体の断面全体の画像値の総和であることに注意する。 Therefore, in the image reconstruction method of this embodiment, the sum of image values of the cross section of the object is used as a priori information.
Figure JPOXMLDOC01-appb-M000011
 Here, Ω is the support (the area where the object exists). f(x,y) is an image value of an image of a cross section of the object. C is the sum of image values obtained by integrating f(x, y) over the region of support Ω. Note that C is the sum of image values not only for the inside of the region of interest S but also for the entire cross section of the object.
　先験情報Ｃの獲得の方法は、第１実施形態で説明したものと同様である。先験情報Ｃは、前述の従来の方法（１）～（４）と比較して、スカラー値１つであるのではるかに情報が少なく獲得しやすい。また、先験情報Ｃは、画像の合計値Ｃ（スカラー値）だけであるので、先験情報としては最小のものに近いと考えられる。 The method of acquiring the a priori information C is the same as that described in the first embodiment. Compared to the conventional methods (1) to (4) described above, the a priori information C is a single scalar value, so it contains much less information and is easier to obtain. Further, since the a priori information C is only the total value C (scalar value) of the image, it is considered to be close to the minimum a priori information.
　本実施形態の画像再構成法は、以下の条件を連立させて反復法により解を求め、その中でＴＶ（Total Variation）ノルムが最小の解を関心領域の画像（画像値）として求める。
　まず、物体の断面の画像値を並べたベクトルをｘとし（各要素をｘｉとする）、ベクトルｘＲＯＩとベクトルｘＥＸＴを第１実施形態と同様に次のように定める。
Figure JPOXMLDOC01-appb-M000012
 In the image reconstruction method of this embodiment, a solution is obtained by an iterative method using the following conditions simultaneously, and among them, the solution with the smallest TV (Total Variation) norm is obtained as an image (image value) of the region of interest.
First, a vector in which image values of a cross section of an object are arranged is set to x (each element is set to x i ), and a vector x ROI and a vector x EXT are determined as follows in the same manner as in the first embodiment.
Figure JPOXMLDOC01-appb-M000012
　先験情報Ｃにより、サポートΩの内部（物体の内部）の画像値の総和はＣである。
Figure JPOXMLDOC01-appb-M000013
 　サポートΩの外部（物体の外部）の画像値は０とする。
Figure JPOXMLDOC01-appb-M000014
 Based on the a priori information C, the sum of image values inside the support Ω (inside the object) is C.
Figure JPOXMLDOC01-appb-M000013
 The image value outside the support Ω (outside the object) is set to 0.
Figure JPOXMLDOC01-appb-M000014
　回転方向に所定の角度の範囲において所定の間隔で疎に関心領域ＳにＸ線を照射し、取得した各投影データをベクトルで表しｂｉとする。また、照射角度に応じてＸ線が物体の断面を通過する際の画素の情報をもつ行列を投影演算行列とし、投影データｂｉに対応する投影演算行列をＡｉとする。そして、ベクトルｂｉを１列に並べたベクトルをｂとし、行列Ａｉを１列に並べた行列をＡとするとき、測定方程式は、式（４）のように表される。
Figure JPOXMLDOC01-appb-M000015
 The region of interest S is sparsely irradiated with X-rays at predetermined intervals within a predetermined angular range in the rotational direction, and each acquired projection data is represented by a vector and is denoted by b i . Further, a matrix having information on pixels when X-rays pass through a cross section of an object according to the irradiation angle is defined as a projection calculation matrix, and a projection calculation matrix corresponding to projection data b i is defined as A i . Then, when b is a vector in which the vectors b i are arranged in one column, and A is a matrix in which the matrix A i is arranged in one column, the measurement equation is expressed as in equation (4).
Figure JPOXMLDOC01-appb-M000015
　本実施形態の画像再構成法は、式（９）、（１０）、（１１）を連立させて反復法により解となるベクトルｘを求める。ただし、スパースビューインテリアＣＴの場合は、上記３つの式を同時に満たす解を求めても解が無数に存在して高精度の画像が再構成できない。そこで、式（１２）で表されるＴＶノルムが最小となるようなｘを求める。
Figure JPOXMLDOC01-appb-M000016
 このＴＶノルムは、ｘを２次元画像と見た際の水平方向差分と垂直方向差分の大きさに基づく値を計算する。そして、画像再構成法は、求めたｘのｘＲＯＩを関心領域の画像とする。関心領域の画像ｘＲＯＩは高精度で再構成される。
　なお、第２実施形態の画像再構成法が用いる反復法は、第１実施形態で例示したものと同様である。また、反復法で解く際のベクトルｘの初期値は特に限定されない。 In the image reconstruction method of this embodiment, equations (9), (10), and (11) are simultaneously applied to obtain a vector x that is a solution by an iterative method. However, in the case of sparse-view interior CT, even if solutions that simultaneously satisfy the above three equations are sought, there are countless solutions and a highly accurate image cannot be reconstructed. Therefore, x is determined such that the TV norm expressed by equation (12) is minimized.
Figure JPOXMLDOC01-appb-M000016
 This TV norm is calculated as a value based on the magnitude of the horizontal difference and the vertical difference when x is viewed as a two-dimensional image. Then, in the image reconstruction method, the x ROI of the obtained x is used as the image of the region of interest. The image of the region of interest x ROI is reconstructed with high accuracy.
Note that the iterative method used in the image reconstruction method of the second embodiment is the same as that exemplified in the first embodiment. Further, the initial value of the vector x when solving by the iterative method is not particularly limited.
　図１２は、第２実施形態に係る画像再構成装置１２２Ａの機能構成の例を示す概略ブロック図である。画像再構成装置１２２Ａは、先験情報取得部１３１と、投影データ取得部１３２Ａと、画像算出部１３３Ａとを備える。なお、画像再構成装置１２２Ａは、図２に示したようにＸ線ＣＴ装置１の一部として備えられてもよいし、別体としてＸ線ＣＴ装置１に接続されてもよい。また、画像再構成装置１２２Ａは単体で動作し、ネットワークを介して外部サーバや記憶装置等から必要な情報を取得してもよい。
　先験情報取得部１３１は、第１実施形態の画像再構成装置１２２の先験情報取得部１３１と同様であるので説明を省略する。 FIG. 12 is a schematic block diagram showing an example of the functional configuration of an image reconstruction device 122A according to the second embodiment. The image reconstruction device 122A includes an a priori information acquisition section 131, a projection data acquisition section 132A, and an image calculation section 133A. Note that the image reconstruction device 122A may be provided as a part of the X-ray CT apparatus 1 as shown in FIG. 2, or may be connected to the X-ray CT apparatus 1 as a separate body. Further, the image reconstruction device 122A may operate alone and obtain necessary information from an external server, storage device, etc. via a network.
The a priori information acquisition unit 131 is the same as the a priori information acquisition unit 131 of the image reconstruction device 122 of the first embodiment, so a description thereof will be omitted.
　投影データ取得部１３２Ａは、物体の周方向において所定の角度の範囲（例えば３６０°）において所定の間隔で疎に物体の関心領域にＸ線を照射した際の投影データを複数取得する。例えば、投影データ取得部１３２はＡ、投影データを８０個、６４個、又は４６個程度取得する。なお、投影データ取得部１３２Ａは、Ｘ線ＣＴ装置１で撮影しながら取得された投影データを用いてもよいし、予め記憶装置１２３に記憶しておいた投影データを取得してもよい。 The projection data acquisition unit 132A acquires a plurality of projection data when the region of interest of the object is sparsely irradiated with X-rays at predetermined intervals in a predetermined angular range (for example, 360°) in the circumferential direction of the object. For example, the projection data acquisition unit 132 acquires about 80, 64, or 46 pieces of A projection data. Note that the projection data acquisition unit 132A may use projection data acquired while imaging with the X-ray CT apparatus 1, or may acquire projection data stored in the storage device 123 in advance.
　画像算出部１３３Ａは、照射角度に応じてＸ線が物体の断面の通過する際の画素の情報をもつ行列を投影演算行列とするとき、複数の投影データｂｉを並べたベクトルをｂとし、投影データｂｉに対応して複数の投影演算行列Ａｉを並べた行列をＡとし、物体の断面の画像値を並べたベクトルをｘとするとき、先験情報Ｃの下でＡｘ＝ｂの解をＴＶノルムが最小となるように求めて関心領域の画像とする。
　具体的には、画像算出部１３３Ａは、物体の断面の画像値を並べたベクトルをｘとし（各要素をｘｉとする）、ベクトルｘＲＯＩとベクトルｘＥＸＴを次のように定める。
Figure JPOXMLDOC01-appb-M000017
 When the image calculation unit 133A sets a matrix having information on pixels when the X-ray passes through the cross section of the object according to the irradiation angle as a projection calculation matrix, b is a vector in which a plurality of projection data b i are arranged, When A is a matrix in which a plurality of projection calculation matrices A i are arranged corresponding to projection data b i , and x is a vector in which image values of a cross section of an object are arranged, then under a priori information C, Ax=b. A solution is obtained so that the TV norm is minimized, and an image of the region of interest is obtained.
Specifically, the image calculation unit 133A sets a vector in which the image values of the cross section of the object are arranged as x (each element is x i ), and determines the vector x ROI and the vector x EXT as follows.
Figure JPOXMLDOC01-appb-M000017
　画像算出部１３３Ａは、サポートΩの内部（物体の内部）の画像値の総和をＣとする。
Figure JPOXMLDOC01-appb-M000018
 　画像算出部１３３Ａは、サポートΩの外部（物体の外部）の画像値を０とする。
Figure JPOXMLDOC01-appb-M000019
 The image calculation unit 133A sets C as the sum of image values inside the support Ω (inside the object).
Figure JPOXMLDOC01-appb-M000018
 The image calculation unit 133A sets the image value outside the support Ω (outside the object) to 0.
Figure JPOXMLDOC01-appb-M000019
　画像算出部１３３Ａは、投影データ取得部１３２が取得した各投影データをベクトルｂｉとし、投影データｂｉに対応する投影演算行列をＡｉとする。そして、画像算出部１３３Ａは、ベクトルｂｉを１列に並べたベクトルをｂとし、行列Ａｉを１列に並べた行列をＡとするとき、測定方程式を式（１５）のように立式する。
Figure JPOXMLDOC01-appb-M000020
 The image calculation unit 133A sets each projection data acquired by the projection data acquisition unit 132 as a vector b i , and sets the projection calculation matrix corresponding to the projection data b i as A i . Then, the image calculation unit 133A calculates the measurement equation by formulating the measurement equation as shown in equation (15), where b is a vector in which the vectors b i are arranged in one column, and A is a matrix in which the matrix A i is arranged in one column. do.
Figure JPOXMLDOC01-appb-M000020
　画像算出部１３３Ａは、式（１３）、（１４）、（１５）を連立させて、反復法により式（１６）で表されるＴＶノルムが最小となるようなベクトルｘを求める。
Figure JPOXMLDOC01-appb-M000021
 そして、画像算出部１３３Ａは、求めたｘのｘＲＯＩを関心領域の画像とする。 The image calculation unit 133A combines equations (13), (14), and (15), and uses an iterative method to find a vector x that minimizes the TV norm expressed by equation (16).
Figure JPOXMLDOC01-appb-M000021
 Then, the image calculation unit 133A sets the x ROI of x as the image of the region of interest.
　次に、図１３を参照して、第２実施形態に係る画像再構成装置１２２Ａの動作を説明する。図１３は、第２実施形態に係る画像再構成装置１２２Ａの処理手順の例を示すフローチャートである。
　まず、先験情報取得部１３１は、物体の断面の画像の画像値の総和を先験情報Ｃとして取得する（ステップＳ３０１）。 Next, with reference to FIG. 13, the operation of the image reconstruction device 122A according to the second embodiment will be described. FIG. 13 is a flowchart illustrating an example of the processing procedure of the image reconstruction device 122A according to the second embodiment.
First, the a priori information acquisition unit 131 acquires the sum of image values of images of a cross section of an object as a priori information C (step S301).
　次に、投影データ取得部１３２Ａは、物体の周方向において所定の角度の範囲において所定の間隔で物体の関心領域にＸ線を照射した際の投影データｂｉを複数取得する（ステップＳ３０２）。 Next, the projection data acquisition unit 132A acquires a plurality of projection data b i when the region of interest of the object is irradiated with X-rays at predetermined intervals in a predetermined angular range in the circumferential direction of the object (step S302).
　次に、画像算出部１３３Ａは、照射角度に応じてＸ線が物体の断面の通過する際の画素の情報をもつ行列を投影演算行列とするとき、複数の投影データｂｉを並べたベクトルをｂとし、投影データｂｉに対応して複数の投影演算行列Ａｉを並べた行列をＡとし、物体の断面の画像値を並べたベクトルをｘとするとき、測定方程式Ａｘ＝ｂを立式する（ステップＳ３０３）。 Next, when the projection calculation matrix is a matrix having information on pixels when the X-ray passes through the cross section of the object according to the irradiation angle, the image calculation unit 133A calculates a vector in which a plurality of projection data b i are arranged. b, A is a matrix in which a plurality of projection calculation matrices A i are arranged corresponding to projection data b i , and x is a vector in which image values of a cross section of an object are arranged, then the measurement equation Ax=b can be expressed as (Step S303).
　次に、画像算出部１３３Ａは、先験情報Ｃの下で反復法によりＡｘ＝ｂの解ｘをＴＶノルムが最小となるように求める。画像算出部１３３Ａは、反復法には例えばＡＲＴ法を使い、その処理手順は、図１０と同様である。そして、画像算出部１３３Ａは、求めたｘのｘＲＯＩを関心領域の画像とする（ステップＳ３０４）。
　以上で、図１３の説明は終了である。 Next, the image calculation unit 133A uses an iterative method under the a priori information C to find a solution x for Ax=b such that the TV norm is minimized. The image calculation unit 133A uses, for example, the ART method as the iterative method, and the processing procedure is the same as that in FIG. 10. Then, the image calculation unit 133A sets the obtained x ROI of x as the image of the region of interest (step S304).
This concludes the explanation of FIG. 13.
　以上説明したように、先験情報取得部１３１は、物体の断面の画像の画像値の総和を先験情報Ｃとして取得し、投影データ取得部１３２Ａは、物体の周方向の所定の角度の範囲において所定の間隔で物体の関心領域にＸ線を照射した際の投影データを複数取得し、画像算出部１３３Ａは、投影データのベクトルをｂとし、投影演算行列をＡとし、物体の断面の画像値を並べたベクトルをｘとするとき、先験情報Ｃの下でＡｘ＝ｂの解ｘをＴＶノルムが最小となるように求めて関心領域の画像とする。 As explained above, the a priori information acquisition unit 131 acquires the sum of image values of cross-sectional images of the object as the a priori information C, and the projection data acquisition unit 132A acquires a predetermined angular range in the circumferential direction of the object. , a plurality of projection data obtained when the region of interest of the object is irradiated with X-rays at predetermined intervals is acquired, and the image calculation unit 133A sets the vector of the projection data to b, the projection calculation matrix to A, and generates an image of the cross section of the object. When a vector in which values are arranged is x, a solution x of Ax=b is obtained under a priori information C so that the TV norm is minimized, and is used as an image of the region of interest.
　これにより、画像再構成装置１２２Ａは、スパースビューインテリアＣＴにおいて、より簡便（超簡便）な先験情報を用いて、高精度な画像再構成を行うことができる。特に、通常のインテリアＣＴよりも難しいスパースビューインテリアＣＴにおいても高精度な画像再構成を行うことができる。
　また、画像再構成装置１２２Ａの用いる先験情報Ｃは、前述の従来の方法（１）～（４）と比較して、スカラー値１つであるのではるかに情報が少なく獲得しやすい。そのため、画像再構成装置１２２Ａは、非常に実用的で使いやすい。また、先験情報Ｃは、画像の合計値Ｃ（スカラー値）だけであるので、先験情報としては最小のものに近いと考えられる。 Thereby, the image reconstruction device 122A can perform highly accurate image reconstruction using simpler (ultra-simple) a priori information in sparse view interior CT. In particular, highly accurate image reconstruction can be performed even in sparse-view interior CT, which is more difficult than normal interior CT.
Further, the a priori information C used by the image reconstruction device 122A is a single scalar value compared to the conventional methods (1) to (4) described above, so it is much less information and easier to obtain. Therefore, the image reconstruction device 122A is very practical and easy to use. Further, since the a priori information C is only the total value C (scalar value) of the image, it is considered to be close to the minimum a priori information.
［第１実施形態のシミュレーション実験による再構成例］
　続いて、第１実施形態の画像再構成装置１２２（画像再構成法）で行ったシミュレーション実験による再構成例を示す。 [Example of reconstruction based on simulation experiment of first embodiment]
Next, a reconstruction example based on a simulation experiment conducted using the image reconstruction device 122 (image reconstruction method) of the first embodiment will be shown.
　図１４Ａ～図１４Ｅは、頭部ＣＴ画像においてシミュレーション実験による画像再構成を行った結果である。図１４Ｄを除き、画像濃度の表示範囲は［－２０ＨＵ，９０ＨＵ］である（単位ＨＵ：Hounsfield Unit）。 FIGS. 14A to 14E show the results of image reconstruction performed on head CT images through simulation experiments. Except for FIG. 14D, the display range of image density is [-20HU, 90HU] (HU: Hounsfield Unit).
　図１４Ａは、インテリアＣＴではない通常のＣＴにおいて完全投影データから、フィルタ補正逆投影法により再構成した画像である。図１４Ｂは、インテリアＣＴの投影データから、従来技術の方法（３）（ＲＯＩの境界が区分的に一様であるという先験情報を用いる）により再構成した画像である。図１４Ｃは、インテリアＣＴの投影データから、従来技術の方法（４）（１方向の完全投影データを先験情報を用いる）により再構成した画像である。 FIG. 14A is an image reconstructed from complete projection data using a filtered back projection method in normal CT, which is not interior CT. FIG. 14B is an image reconstructed from interior CT projection data by the conventional method (3) (using a priori information that the boundaries of the ROI are piecewise uniform). FIG. 14C is an image reconstructed from interior CT projection data by the conventional method (4) (using complete projection data in one direction using a priori information).
　図１４Ｄは、インテリＣＴの投影データから、実施形態１の画像再構成法であるが、画像値の総和の先験情報Ｃを用いずに再構成した画像である。この場合、ＲＯＩの境界あたりが正確に再構成されていないのに加えて、画像濃度も［９０ＨＵ，２００ＨＵ］とずれている。一方、図１４Ｅは、インテリＣＴの投影データから、実施形態１の画像再構成法で、画像値の総和の先験情報Ｃを用いて再構成した画像である。この場合、ＲＯＩの内部は、図１４Ａ、図１４Ｂ、図１４Ｃと同程度のレベルで再構成できていることが分かる。 FIG. 14D shows an image reconstructed from projection data of IntelliCT using the image reconstruction method of Embodiment 1, but without using a priori information C of the sum of image values. In this case, not only the area around the ROI boundary is not accurately reconstructed, but also the image density is shifted to [90HU, 200HU]. On the other hand, FIG. 14E shows an image reconstructed from the projection data of IntelliCT using the a priori information C of the sum of image values by the image reconstruction method of the first embodiment. In this case, it can be seen that the inside of the ROI can be reconstructed at the same level as in FIGS. 14A, 14B, and 14C.
　図１５Ａ～図１５Ｅは、腹部ＣＴ画像においてシミュレーション実験による画像再構成を行った結果である。図１５Ｄを除き、画像濃度の表示範囲は［－１００ＨＵ，３００ＨＵ］である。図１５の実験は、関心領域ＲＯＳを小さくして画像再構成が難しい場合である。 FIGS. 15A to 15E show the results of image reconstruction performed on abdominal CT images through simulation experiments. Except for FIG. 15D, the display range of image density is [-100HU, 300HU]. The experiment shown in FIG. 15 is a case where it is difficult to reconstruct an image by making the region of interest ROS small.
　図１５Ａは、インテリアＣＴではない通常のＣＴにおいて完全投影データから、フィルタ補正逆投影法により再構成した画像である。図１５Ｂは、インテリアＣＴの投影データから、従来技術の方法（３）により再構成した画像である。図１５Ｃは、インテリアＣＴの投影データから、従来技術の方法（４）により再構成した画像である。 FIG. 15A is an image reconstructed from complete projection data using a filtered back projection method in normal CT, which is not interior CT. FIG. 15B is an image reconstructed from interior CT projection data using the conventional method (3). FIG. 15C is an image reconstructed from interior CT projection data using the conventional method (4).
　図１５Ｄは、インテリＣＴの投影データから、実施形態１の画像再構成法であるが、画像値の総和の先験情報Ｃを用いずに再構成した画像である。この場合、ＲＯＩの境界あたりが正確に再構成されていないのに加えて、画像濃度も［３１０ＨＵ，７１０ＨＵ］とずれている。一方、図１５Ｅは、インテリＣＴの投影データから、実施形態１の画像再構成法で、画像値の総和の先験情報Ｃを用いて再構成した画像である。この場合、ＲＯＩの内部は、図１５Ａ、図１５Ｂ、図１５Ｃと同程度のレベルで再構成できていることが分かる。 FIG. 15D shows an image reconstructed from projection data of IntelliCT using the image reconstruction method of Embodiment 1, but without using a priori information C of the sum of image values. In this case, not only the area around the ROI boundary is not accurately reconstructed, but also the image density deviates from [310HU, 710HU]. On the other hand, FIG. 15E shows an image reconstructed from the projection data of IntelliCT using the a priori information C of the sum of image values by the image reconstruction method of the first embodiment. In this case, it can be seen that the inside of the ROI can be reconstructed at the same level as in FIGS. 15A, 15B, and 15C.
［第２実施形態のシミュレーション実験による再構成例］
　続いて、第２実施形態の画像再構成装置１２２Ａ（画像再構成法）で行ったシミュレーション実験による再構成例を示す。
　図１６Ａ～図１６Ｃは、ポリマーブレンド小片試料をＸ線位相ＣＴで測定した実データに基づく結果である。 [Example of reconstruction based on simulation experiment of second embodiment]
Next, a reconstruction example based on a simulation experiment conducted using the image reconstruction device 122A (image reconstruction method) of the second embodiment will be shown.
FIGS. 16A to 16C are results based on actual data measured using X-ray phase CT on a small polymer blend sample.
　図１６Ａは、インテリアＣＴではない通常のスパースビューＣＴにおいて、５２２方向の完全投影データから、フィルタ補正逆投影法により再構成した画像である。図１６Ｂは、スパースビューインテリアＣＴの４６方向の投影データから、実施形態２の画像再構成法であるが、画像値の総和の先験情報Ｃを用いずに再構成した画像である。この場合、値が大きくずれており全体が黒くなっている。一方、図１６Ｃは、スパースビューインテリアＣＴの４６方向の投影データから、実施形態２の画像再構成法で、画像値の総和の先験情報Ｃを用いて再構成した画像である。この場合、ＲＯＩの内部は、図１６Ａと同程度のレベルで再構成できていることが分かる。 FIG. 16A is an image reconstructed from complete projection data in 522 directions by the filtered back projection method in normal sparse view CT, which is not interior CT. FIG. 16B shows an image reconstructed from projection data in 46 directions of the sparse view interior CT using the image reconstruction method of the second embodiment, but without using the a priori information C of the sum of image values. In this case, the values deviate greatly and the entire image is black. On the other hand, FIG. 16C is an image reconstructed from projection data in 46 directions of the sparse view interior CT by the image reconstruction method of the second embodiment using a priori information C of the sum of image values. In this case, it can be seen that the inside of the ROI can be reconstructed at a level comparable to that in FIG. 16A.
　以上、本発明の実施形態について図面を参照して詳述してきたが、具体的な構成は本実施形態に限られるものではなく、本発明の要旨を逸脱しない範囲の設計変更等も含まれる。 Although the embodiments of the present invention have been described above in detail with reference to the drawings, the specific configuration is not limited to the present embodiments, and may include design changes without departing from the gist of the present invention.
　本発明の実施形態は、医療用Ｘ線ＣＴ装置、非破壊検査用ＣＴ装置、材料計測用ＣＴ装置、電子線トモグラフィ装置等に適用される。 Embodiments of the present invention are applied to medical X-ray CT devices, nondestructive testing CT devices, material measurement CT devices, electron beam tomography devices, and the like.
　１　　　　　　　　Ｘ線ＣＴ装置
　１００　　　　　　スキャンガントリ部
　１０１　　　　　　Ｘ線源
　１０２　　　　　　回転盤
　１０３　　　　　　コリメータユニット
　１０４　　　　　　開口部
　１０５　　　　　　寝台
　１０６　　　　　　Ｘ線検出器
　１０７　　　　　　データ収集装置
　１２０　　　　　　操作卓
　１２１　　　　　　入力装置
　１２２、１２２Ａ　画像再構成装置
　１２３　　　　　　記憶装置
　１２４　　　　　　システム制御装置
　１２５　　　　　　表示装置
　１３１　　　　　　先験情報取得部
　１３２、１３２Ａ　投影データ取得部
　１３３、１３３Ａ　画像算出部 1 X-ray CT device 100 Scan gantry part 101 X-ray source 102 Rotary disk 103 Collimator unit 104 Opening 105 Bed 106 X-ray detector 107 Data acquisition device 120 Operation console 121 Input device 122, 122A Image reconstruction device 123 Storage device 124 System control device 125 Display device 131 A priori information acquisition unit 132, 132A Projection data acquisition unit 133, 133A Image calculation unit

Claims (9)

  1. 　物体の関心領域にＸ線を照射して、前記物体の断面の前記関心領域の画像を再構成するインテリアＣＴの画像再構成方法であって、
    　前記物体の周方向において所定の角度の範囲で前記物体の前記関心領域にＸ線を照射した際の投影データを複数取得する投影データ取得ステップと、
    　照射角度に応じてＸ線が前記物体の断面の通過する際の画素の情報をもつ行列を投影演算行列とするとき、複数の前記投影データを並べたベクトルをｂとし、前記投影データに対応する複数の前記投影演算行列を並べた行列をＡとし、前記物体の断面の画像値を並べたベクトルをｘとしたとき、先験情報Ｃの下でＡｘ＝ｂを解いて、前記関心領域の画像を求める画像算出ステップと、を含み、
    　前記先験情報Ｃは、前記物体の断面の画像の画像値の総和である画像再構成方法。     An image reconstruction method for interior CT in which an image of the region of interest of a cross section of the object is reconstructed by irradiating a region of interest of an object with X-rays, the method comprising:
    a projection data acquisition step of acquiring a plurality of projection data when the region of interest of the object is irradiated with X-rays in a predetermined angular range in the circumferential direction of the object;
    When a projection calculation matrix is a matrix having information on pixels when X-rays pass through the cross section of the object according to the irradiation angle, b is a vector in which a plurality of the projection data are arranged, and b corresponds to the projection data. When A is a matrix in which a plurality of projection calculation matrices are arranged, and x is a vector in which image values of cross sections of the object are arranged, Ax=b is solved under a priori information C to obtain an image of the region of interest. an image calculation step of determining
    In the image reconstruction method, the a priori information C is a sum of image values of images of a cross section of the object.
  2. 　前記ベクトルｘにおいて、前記物体の外部の画像値は０である
    　請求項１に記載の画像再構成方法。     The image reconstruction method according to claim 1, wherein in the vector x, an image value outside the object is 0.
  3. 　前記画像算出ステップは、反復法によりＡｘ＝ｂを解く
    　請求項１に記載の画像再構成方法。     The image reconstruction method according to claim 1, wherein the image calculation step solves Ax=b by an iterative method.
  4. 　前記反復法において、毎反復ごとに前記先験情報Ｃを用いて前記ベクトルｘを補正する
    　請求項３に記載の画像再構成方法。     The image reconstruction method according to claim 3, wherein in the iterative method, the vector x is corrected using the a priori information C every iteration.
  5. 　前記先験情報Ｃは、前記周方向の１つの角度における前記物体の断面の投影データの総和である
    　請求項１に記載の画像再構成方法。     The image reconstruction method according to claim 1, wherein the a priori information C is a sum of projection data of a cross section of the object at one angle in the circumferential direction.
  6. 　前記先験情報Ｃは、前記投影データを撮影するより前にプリスキャンを行って再構成された画像から求めた画像値の総和である
    　請求項１に記載の画像再構成方法。     The image reconstruction method according to claim 1, wherein the a priori information C is a sum of image values obtained from images reconstructed by performing pre-scanning before photographing the projection data.
  7. 　前記投影データ取得ステップは、前記所定の角度の範囲において所定の間隔で前記投影データを複数取得し、
    　前記画像算出ステップは、前記先験情報Ｃの下でＡｘ＝ｂの解ｘを所定のノルムが最小となるように求めて前記関心領域の画像とする
    　請求項１に記載の画像再構成方法。     The projection data acquisition step acquires a plurality of projection data at predetermined intervals within the predetermined angle range;
    2. The image reconstruction method according to claim 1, wherein the image calculation step calculates a solution x of Ax=b under the a priori information C such that a predetermined norm is minimized and uses it as an image of the region of interest.
  8. 　物体の関心領域にＸ線を照射して、前記物体の断面の前記関心領域の画像を再構成するインテリアＣＴの画像再構成装置であって、
    　前記物体の周方向において所定の角度の範囲で前記物体の前記関心領域にＸ線を照射した際の投影データを複数取得する投影データ取得部と、
    　照射角度に応じてＸ線が前記物体の断面の通過する際の画素の情報をもつ行列を投影演算行列とするとき、複数の前記投影データを並べたベクトルをｂとし、前記投影データに対応する複数の前記投影演算行列を並べた行列をＡとし、前記物体の断面の画像値を並べたベクトルをｘとするとき、先験情報Ｃの下でＡｘ＝ｂを解いて、前記関心領域の画像を求める画像算出部と、を備え、
    　前記先験情報Ｃは、前記物体の断面の画像の画像値の総和である画像再構成装置。     An interior CT image reconstruction device that irradiates a region of interest of an object with X-rays to reconstruct an image of the region of interest of a cross section of the object,
    a projection data acquisition unit that acquires a plurality of projection data when the region of interest of the object is irradiated with X-rays in a predetermined angular range in the circumferential direction of the object;
    When a projection calculation matrix is a matrix having information on pixels when X-rays pass through the cross section of the object according to the irradiation angle, b is a vector in which a plurality of the projection data are arranged, and b corresponds to the projection data. When A is a matrix in which a plurality of projection calculation matrices are arranged, and x is a vector in which image values of cross sections of the object are arranged, Ax=b is solved under a priori information C to obtain an image of the region of interest. an image calculation unit that calculates
    The image reconstruction device is an image reconstruction device in which the a priori information C is a sum of image values of images of a cross section of the object.
  9. 　コンピュータを、物体の関心領域にＸ線を照射して、前記物体の断面の前記関心領域の画像を再構成するインテリアＣＴの画像再構成装置として機能させるためのプログラムであって、前記コンピュータを、
    　前記物体の周方向において所定の角度の範囲で前記物体の前記関心領域にＸ線を照射した際の投影データを複数取得する投影データ取得手段、
    　照射角度に応じてＸ線が前記物体の断面の通過する際の画素の情報をもつ行列を投影演算行列とするとき、複数の前記投影データを並べたベクトルをｂとし、前記投影データに対応する複数の前記投影演算行列を並べた行列をＡとし、前記物体の断面の画像値を並べたベクトルをｘとするとき、先験情報Ｃの下でＡｘ＝ｂを解いて、前記関心領域の画像を求める画像算出手段、として機能させ、
    　前記先験情報Ｃは、前記物体の断面の画像の画像値の総和であるプログラム。     A program for causing a computer to function as an image reconstruction device for interior CT that irradiates a region of interest of an object with X-rays to reconstruct an image of the region of interest of a cross section of the object, the computer comprising:
    projection data acquisition means for acquiring a plurality of projection data when the region of interest of the object is irradiated with X-rays in a predetermined angular range in the circumferential direction of the object;
    When a projection calculation matrix is a matrix having information on pixels when X-rays pass through the cross section of the object according to the irradiation angle, b is a vector in which a plurality of the projection data are arranged, and b corresponds to the projection data. When A is a matrix in which a plurality of projection calculation matrices are arranged, and x is a vector in which image values of cross sections of the object are arranged, Ax=b is solved under a priori information C to obtain an image of the region of interest. function as an image calculation means to obtain
    A program in which the a priori information C is a sum of image values of images of cross sections of the object.
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Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH10248835A (en) * 1997-03-12 1998-09-22 Hitachi Medical Corp Irradiation range limiting type x-ray ct device
JPH11332862A (en) * 1998-05-27 1999-12-07 Hitachi Medical Corp X-ray ct apparatus
JP2002017716A (en) * 2000-04-28 2002-01-22 Ge Medical Systems Global Technology Co Llc Method and device for multi-slice ct scanning for region of interest
US20180185001A1 (en) * 2017-01-05 2018-07-05 Pusan National University Industry-University Cooperation Foundation Apparatus and method for k-edge based interior tomography image processing
WO2018179905A1 (en) * 2017-03-27 2018-10-04 国立大学法人筑波大学 Interior ct image generation method
CN109717886A (en) * 2017-10-30 2019-05-07 上海交通大学 A kind of CT scanning method of low radiation dose

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH10248835A (en) * 1997-03-12 1998-09-22 Hitachi Medical Corp Irradiation range limiting type x-ray ct device
JPH11332862A (en) * 1998-05-27 1999-12-07 Hitachi Medical Corp X-ray ct apparatus
JP2002017716A (en) * 2000-04-28 2002-01-22 Ge Medical Systems Global Technology Co Llc Method and device for multi-slice ct scanning for region of interest
US20180185001A1 (en) * 2017-01-05 2018-07-05 Pusan National University Industry-University Cooperation Foundation Apparatus and method for k-edge based interior tomography image processing
WO2018179905A1 (en) * 2017-03-27 2018-10-04 国立大学法人筑波大学 Interior ct image generation method
CN109717886A (en) * 2017-10-30 2019-05-07 上海交通大学 A kind of CT scanning method of low radiation dose

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