CN111487265A - Cone beam CT hardening artifact correction method combined with projection consistency - Google Patents

Cone beam CT hardening artifact correction method combined with projection consistency Download PDF

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CN111487265A
CN111487265A CN202010449765.9A CN202010449765A CN111487265A CN 111487265 A CN111487265 A CN 111487265A CN 202010449765 A CN202010449765 A CN 202010449765A CN 111487265 A CN111487265 A CN 111487265A
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李磊
闫镔
韩玉
席晓琦
孙奎奎
朱林林
孙艳敏
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Information Engineering University of PLA Strategic Support Force
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Abstract

The invention provides a cone beam CT hardening artifact correction method combining projection consistency. The method comprises the following steps: reconstructing the multi-energy projection logarithmic data to obtain a CT image, segmenting the CT image, and performing binarization to obtain a binarization image model; establishing a re-projection coordinate system according to parameters of a cone-beam CT imaging system during actual scanning, re-projecting the binary image model onto a flat panel detector, and performing intersection calculation on the X-ray and the binary image model through the corresponding relation between the binary image model and the virtual detector to obtain the length of the ray passing through an object; performing polynomial fitting according to the length of the ray passing through the object and the logarithmic data of the multi-energy projection to obtain a hardening artifact correction model; correcting the log-quantized data of the multi-energy projection according to the hardening artifact correction model to obtain equivalent log-quantized data of the single-energy projection; and reconstructing according to the equivalent monoenergetic projection logarithmic data to obtain a corrected CT image. The invention does not need any precondition and is suitable for various detectors.

Description

Cone beam CT hardening artifact correction method combined with projection consistency
Technical Field
The invention relates to the technical field of beam hardening correction of flat panel detectors, in particular to a cone beam CT hardening artifact correction method combining projection consistency.
Background
In Computed Tomography (CT) techniques, the energy is E0Strength of I0According to beer's law, the intensity I after passing through an object with length l is known as: i ═ I0exp (- [ integral ] u (x, y, z) dl); wherein u (x, y, z) is a section of the object to be measured at E0In the case of a distribution function of linear attenuation coefficients. Single energy projection logarithmic data pmComprises the following steps:
Figure BDA0002507264180000011
the amount is distributed in (E)max,Emin) In the range, the linear attenuation coefficient is a function of energy, and the energy spectrum distribution is S (E), which can be obtained from beer's law
Figure BDA0002507264180000012
Multi-energy projection logarithmic data ppComprises the following steps:
Figure BDA0002507264180000013
from ppThe expression (c) indicates that the larger l is, the larger ppThe larger, but not linear relationship between the two. Let ppG (l), g being a ray hardening model, from which the derivation can be derived to discuss the increase and decrease of this function, g' (l) being a monotonically decreasing function with respect to l, i.e. p increases with lpThe magnitude of the increase becomes smaller. Because low-energy photons in the ray beam are attenuated more quickly than high-energy photons, the energy distribution of the ray beam is different when the ray beam passes through objects with different thicknesses, and the attenuation coefficient u corresponding to the average energy of the ray beam is not a constant any more, but is reduced along with the increase of the thickness of the object passing through. True logarithmized projection data p due to ray hardening effectspAnd in reconstructionSet logarithmic projection data pmDifferent expressions are provided for linear attenuation coefficient u (x, y, z, E), the data is not linear relation with the crossing length, and p is used in the reconstruction processpIn place of pmTherefore, an artifact is caused in the reconstructed image, and the artifact caused by the multi-energy X-ray is a hardening artifact which is represented by that the gray value of the center of the reconstructed image of the single-material object is smaller than that of the edge and is in a cup shape. The hardening artifacts severely degrade the CT image quality and therefore need to be corrected.
For the hardening artifact correction, there are many correction methods, mainly polynomial fitting method (Huangkurton et al. cone beam CT beam hardening correction method based on slice profile reprojection [ J ]. Instrument Proc. 2008.029 (009): 1873 1871871877), Monte Carlo correction method, iterative correction method, etc. The polynomial fitting method has the advantages that polynomial coefficients are easy to calculate, the thought is simple and easy to accept, and the correction effect is good under certain conditions. This method is currently the most commonly used calibration method in view of its effectiveness and simplicity. However, the polynomial fitting method has the effect of amplifying noise, amplifies noise in an image while correcting beam hardening, and is good for a single material of an object to be detected, but a phantom made of the same material as the object to be detected is required, and the method is not flexible in practical application. The Monte Carlo method is also called statistical simulation method, is a very important numerical calculation method guided by probability statistical theory, and the core of the method is a random sampling method. The method is applied on the premise that the material of the object to be detected must be known. The iterative method is a process of recurrently recursing new values by using old values of variables. One advantage of iterative based methods is that physical effects such as beam hardening can be merged into the forward projection process, so that the beam hardening can be taken into account in the reconstruction process for the purpose of eliminating artifacts. However, due to the reasons of large calculation amount, slow reconstruction speed, low parallelism and the like of the iterative reconstruction algorithm, the iterative reconstruction algorithm is still in a research stage at present and is not widely applied in practical application.
Disclosure of Invention
In order to solve the problems of poor flexibility and large calculation amount due to the requirement of precondition (for example, a film with the same material as the detected object is required, and the material of the detected object is required to be known in advance) in the existing correction method, the invention provides a cone beam CT hardening artifact correction method combining projection consistency.
The invention provides a cone beam CT hardening artifact correction method combining projection consistency, which comprises the following steps:
step 1: reconstructing according to the multi-energy projection logarithmic data to obtain a CT image, carrying out image segmentation on the CT image, and carrying out binarization on a contour image obtained after segmentation to obtain a binarization image model of an object solid region;
step 2: establishing a re-projection coordinate system according to parameters of a cone-beam CT imaging system during actual scanning, re-projecting the binary image model onto a flat panel detector, and performing intersection calculation on the X-ray and the binary image model through the corresponding relation between the binary image model and the virtual detector to obtain the length of the ray passing through an object;
and step 3: performing polynomial fitting according to the length of the ray passing through the object and the logarithmic data of the multi-energy projection to obtain a hardening artifact correction model;
and 4, step 4: correcting the multi-energy projection logarithmic data according to the hardening artifact correction model to obtain equivalent mono-energy projection logarithmic data;
and 5: and reconstructing according to the equivalent monoenergetic projection logarithmic data to obtain a corrected CT image.
Further, step 2 specifically comprises:
firstly, determining a projection point C of a reconstructed point (X, y, z) on a central plane, and then respectively making auxiliary lines CA and CD perpendicular to an X axis and a central ray SO from the point C to obtain a geometric relationship:
Figure BDA0002507264180000031
FA＝xtanβ，CF＝y-xtanβ
CE＝CF×cosβ＝-xsinβ+ycosβ
Figure BDA0002507264180000032
and because:
Figure BDA0002507264180000033
a＝R×tanγ
therefore, the horizontal position a (x, y, β) of the ray on the virtual detector is:
Figure BDA0002507264180000034
the vertical position b (x, y, z, β) of the ray on the virtual detector is then obtained as:
Figure BDA0002507264180000035
wherein, O represents the position of a rotation center, (X, Y, z) represents the coordinates of a reconstructed point, S represents the position of an X-ray source, SO ' is a central ray of a conical X-ray, SK represents a ray passing through the reconstructed point, K ' represents the projection of the K point on the central plane of a flat panel detector, the reconstructed point of K ' is M, U is the length of SM, β is the included angle between the central ray and the Y axis, K is the cone angle of the ray SK, gamma is the included angle between SK ' and the central ray SO ', E, F are the intersection points of the central ray SO, CD and CA, A, D are points on the X axis, and R represents the distance from the X-ray source to the center of an object.
Further, step 4 comprises:
step 4.1: the transmission thickness X of an experimental substance and X-rays corresponding to the experimental substance are given, and the experimental substance is scanned to obtain the transmission intensity I of the X-rayspCorresponding ray and data y:
x＝[x1x2…xn]T
y＝ln(I0/IP)＝[y1y2…yn]T
step 4.2: according to the transmission thickness x and the ray sum data y, adopting a curve y as axbFitting the ray and the data y, and estimating parameters a ' and b ' of a and b in the curve by using least square fitting '：
Figure BDA0002507264180000041
Figure BDA0002507264180000042
Step 4.3: calculating the equivalent transmission thickness x according to a 'and b' obtained by fitting estimationeq：
Figure BDA0002507264180000043
Step 4.4: according to the equivalent transmission thickness xeqObtaining a fitting equation of the equivalent beam and the beer law;
step 4.5: substituting the log data of the multi-energy projection into the fitting curve obtained in the step 4.2
Figure BDA0002507264180000044
Obtaining a penetration thickness x1 corresponding to the log-quantized data of the multi-energy projection, and then substituting the penetration thickness x1 into the fitting equation of the equivalent beam and the beer's law obtained in the step 4.4 to obtain the log-quantized data of the equivalent mono-energy projection corresponding to the log-quantized data of the multi-energy projection.
The invention has the beneficial effects that:
the cone beam CT hardening artifact correction method combined with projection consistency provided by the invention utilizes a relation curve between the length of a ray penetrating object and a multi-energy projection value, and then carries out beam hardening correction on the fitted relation of the curve, firstly carries out pretreatment on a reconstructed image of original projection, and carries out image segmentation to obtain image segmentation information; then, a re-projection coordinate system is established according to parameters of a cone-beam CT imaging system during actual scanning, and the corresponding relation between the length of a ray passing through an object and the projection gray scale is obtained through intersection calculation of re-projection of the ray and a binary image model onto a flat panel detector; and finally, fitting a beam hardening curve and correcting beam hardening artifacts, and optimizing by using a data consistency condition. The method does not need precondition (for example, a body film with the same material as the detected object is not needed, and the material of the detected object is not needed to be known in advance), and the needed hardening correction parameters are obtained by calculating the projection image, so the method is applicable to various detectors, and compared with an iterative reconstruction algorithm, the method has small calculation amount and can simply and effectively eliminate the beam hardening artifact of cone beam CT.
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Fig. 1 is a schematic flowchart of a cone-beam CT hardening artifact correction method in combination with projection consistency according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a scanning structure according to an embodiment of the present invention;
FIG. 3 is a schematic view of a circular scanning geometry provided in accordance with an embodiment of the present invention;
FIG. 4 is an image before beam hardening artifact correction provided by embodiments of the present invention;
fig. 5 is an image after beam hardening artifact correction by the method of the present invention according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly described below with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example 1
As shown in fig. 1, an embodiment of the present invention provides a method for correcting cone-beam CT hardening artifacts in combination with projection consistency, the method comprising the following steps:
s101: reconstructing according to the multi-energy projection logarithmic data to obtain a CT image, carrying out image segmentation on the CT image, and carrying out binarization on a contour image obtained after segmentation to obtain a binarization image model of an object solid region;
s102: establishing a re-projection coordinate system according to parameters of a cone-beam CT imaging system during actual scanning, re-projecting the binary image model onto a flat panel detector, and performing intersection calculation on the X-ray and the binary image model through the corresponding relation between the binary image model and the virtual detector to obtain the length of the ray passing through an object;
s103: performing polynomial fitting according to the length of the ray passing through the object and the logarithmic data of the multi-energy projection to obtain a hardening artifact correction model;
s104: correcting the multi-energy projection logarithmic data according to the hardening artifact correction model to obtain equivalent mono-energy projection logarithmic data;
s105: and reconstructing according to the equivalent monoenergetic projection logarithmic data to obtain a corrected CT image.
The cone beam CT hardening artifact correction method combined with projection consistency provided by the embodiment of the invention does not need any precondition (for example, a body film made of the same material as the detected object is not needed, and the material of the detected object is not needed to be known in advance), and the required hardening correction parameters are obtained by calculating the projection image, so that the method is suitable for various detectors, and compared with an iterative reconstruction algorithm, the method provided by the invention has the advantages that the calculated amount is small, and the beam hardening artifact of the cone beam CT can be simply and effectively eliminated.
Example 2
On the basis of the foregoing embodiment 1, an embodiment of the present invention further provides a cone-beam CT hardening artifact correction method in combination with projection consistency, including the following steps:
s201: reconstructing according to the multi-energy projection logarithmic data to obtain a CT image, carrying out image segmentation on the CT image, and carrying out binarization on a contour image obtained after segmentation to obtain a binarization image model of an object solid region;
specifically, in image segmentation, the finer the segmentation of the reconstructed CT image, the better the segmentation, at least the approximate contour of the object to be measured should be segmented. The reconstructed CT image generates a volume data, and the binarization is performed to obtain information represented by each individual data, and after the binarization, the information of each individual data can be clearly obtained, for example, 0 represents air and 1 represents an object. The physical area is the area where the object is located.
S202: establishing a re-projection coordinate system according to parameters of a cone-beam CT imaging system during actual scanning, re-projecting the binary image model onto a flat panel detector, and performing intersection calculation on the X-ray and the binary image model through the corresponding relation between the binary image model and the virtual detector to obtain the length of the ray passing through an object;
specifically, the step of re-projecting the binarized image model onto a flat panel detector to obtain a corresponding relationship between the binarized image model and a virtual detector includes:
the scanning structure of the circular trajectory FDK reconstruction algorithm is shown in FIG. 2, wherein O represents the rotation center position, and (X, Y, Z) represents the coordinates of a point to be reconstructed, and for convenience of representation and calculation, a virtual detector is introduced at the position of the O point, and an object to be scanned is located at the scanning center position.
The circular scanning geometry is shown in fig. 3, where C is the projection point of the reconstructed point of coordinates (X, y, z) on the central plane, SO is the central ray, and the following geometry can be obtained by drawing auxiliary lines CA and CD from C, perpendicular to the X axis and SO, respectively:
Figure BDA0002507264180000071
FA＝xtanβ，CF＝y-xtanβ
CE＝CF×cosβ＝-xsinβ+ycosβ
Figure BDA0002507264180000072
and because:
Figure BDA0002507264180000073
a＝R×tanγ
therefore, the horizontal position a (x, y, β) of the ray on the virtual detector is:
Figure BDA0002507264180000074
the vertical position b (x, y, z, β) of the ray on the virtual detector is then obtained as:
Figure BDA0002507264180000075
specifically, the corresponding relationship between the binarized image model and the virtual detector can be obtained by deduction according to the above formula, so that the number of binarized image model elements corresponding to a single virtual detector element can be obtained, and can be expressed as the number of binarized image models penetrated by X-rays, that is, the length of the object penetrated by the X-rays.
S203: performing polynomial fitting according to the length of the ray passing through the object and the logarithmic data of the multi-energy projection to obtain a hardening artifact correction model;
s204: correcting the multi-energy projection logarithmic data according to the hardening artifact correction model to obtain equivalent mono-energy projection logarithmic data;
specifically, in the calibration process, a set of beams and data y of the transmission thickness X is determined through experiments, and a relationship curve between the X-ray beams and data y and the transmission thickness X, namely the X-ray beams and the fitted curve, is obtained after fitting. Then, the equivalent transmission thickness is fitted by using the X-ray beam and the fitting curve, so that a fitting equation of the equivalent beam and the beer law is obtained. And finally, reconstructing to effectively eliminate the influence of the hardening of the X-ray beam. As an implementable manner, this step comprises the following sub-steps:
s2041: the transmission thickness X of an experimental substance and X-rays corresponding to the experimental substance are given, and the experimental substance is scanned to obtain the transmission intensity I of the X-rayspCorresponding ray and data y:
x＝[x1x2…xn]T
y＝ln(I0/IP)＝[y1y2…yn]T
wherein n represents the number of X-ray penetrating object parts different from 0;
s2042: according to the transmission thickness x and the ray sum data y, adopting a curve y as axbFitting the ray and the data y, and estimating parameters a 'and b' of a and b in the curve by using least square fitting:
Figure BDA0002507264180000081
Figure BDA0002507264180000082
specifically, the curve y ═ ax is usedbThe method of fitting the ray and data y is: taking logarithm on two sides
lgy＝lga+blgx
Then a ', b' can be estimated using a least squares fit:
Figure BDA0002507264180000083
Figure BDA0002507264180000084
s2043: calculating the equivalent transmission thickness x according to a 'and b' obtained by fitting estimationeq：
Figure BDA0002507264180000085
Specifically, the X-ray beam and the fitted curve may be fitted with the fitting equation:
Figure BDA0002507264180000086
to fit. Correspondingly, the transmission thickness x of the polychromatic beam sum is to be modified to the equivalent transmission of the monochromatic beam sumThe transmission thickness X is the equivalent transmission thickness X, which is known from Bell's law, and the attenuation coefficient and beam sum value of the X-ray equivalent to the monochromatic ray are guaranteedeqI.e. equivalent beam and beer's law should be expressed as y-uxeqThus, x can be obtainedeq。
S2044: according to the equivalent transmission thickness xeqObtaining a fitting equation of the equivalent beam and the beer law;
s2045: substituting the log data of the multi-energy projection into the fitting curve obtained in step S2042
Figure BDA0002507264180000087
Then, the penetration thickness x1 corresponding to the log-quantized data of the multi-energy projection is obtained, and the penetration thickness x1 is substituted into the fitting equation of the equivalent beam and the beer' S law obtained in the step S2046, so as to obtain the log-quantized data of the equivalent mono-energy projection corresponding to the log-quantized data of the multi-energy projection.
S205: and reconstructing according to the equivalent monoenergetic projection logarithmic data to obtain a corrected CT image.
In order to verify the effectiveness of the cone beam CT hardening artifact correction method provided by the present invention, the present invention further provides fig. 4 and 5: FIG. 4 is a reconstructed image that has not been corrected using the method of the present invention; fig. 5 is a reconstructed image corrected by the method of the present invention. As shown in fig. 4, it can be seen that there is a serious cupping artifact on the image and the beam hardening phenomenon is serious. As shown in FIG. 5, after the correction by the method of the present invention, the present invention can achieve a good effect of removing the cupping artifact caused by beam hardening, and compared with the conventional correction method, the present invention can correct the cupping artifact more thoroughly and has a good effect of correcting the hardening artifact.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (3)

1. A method for cone beam CT hardening artifact correction in conjunction with projection consistency, comprising:
step 1: reconstructing according to the multi-energy projection logarithmic data to obtain a CT image, carrying out image segmentation on the CT image, and carrying out binarization on a contour image obtained after segmentation to obtain a binarization image model of an object solid region;
step 2: establishing a re-projection coordinate system according to parameters of a cone-beam CT imaging system during actual scanning, re-projecting the binary image model onto a flat panel detector, and performing intersection calculation on the X-ray and the binary image model through the corresponding relation between the binary image model and the virtual detector to obtain the length of the ray passing through an object;
and step 3: performing polynomial fitting according to the length of the ray passing through the object and the logarithmic data of the multi-energy projection to obtain a hardening artifact correction model;
and 4, step 4: correcting the multi-energy projection logarithmic data according to the hardening artifact correction model to obtain equivalent mono-energy projection logarithmic data;
and 5: and reconstructing according to the equivalent monoenergetic projection logarithmic data to obtain a corrected CT image.
2. The method according to claim 1, wherein step 2 is specifically:
firstly, determining a projection point C of a reconstructed point (X, y, z) on a central plane, and then respectively making auxiliary lines CA and CD perpendicular to an X axis and a central ray SO from the point C to obtain a geometric relationship:
Figure FDA0002507264170000011
FA＝x tanβ，CF＝y-x tanβ
CE＝CF×cosβ＝-x sinβ+y cosβ
Figure FDA0002507264170000012
and because:
Figure FDA0002507264170000013
a＝R×tanγ
therefore, the horizontal position a (x, y, β) of the ray on the virtual detector is:
Figure FDA0002507264170000014
the vertical position b (x, y, z, β) of the ray on the virtual detector is then obtained as:
Figure FDA0002507264170000021
wherein, O represents the position of a rotation center, (X, Y, z) represents the coordinates of a reconstructed point, S represents the position of an X-ray source, SO ' is a central ray of a conical X-ray, SK represents a ray passing through the reconstructed point, K ' represents the projection of the K point on the central plane of a flat panel detector, the reconstructed point of K ' is M, U is the length of SM, β is the included angle between the central ray and the Y axis, K is the cone angle of the ray SK, gamma is the included angle between SK ' and the central ray SO ', E, F are the intersection points of the central ray SO, CD and CA, A, D are points on the X axis, and R represents the distance from the X-ray source to the center of an object.
3. The method of claim 1, wherein step 4 comprises:
step 4.1: the transmission thickness X of an experimental substance and X-rays corresponding to the experimental substance are given, and the experimental substance is scanned to obtain the transmission intensity I of the X-rayspCorresponding ray and data y:
x＝[x1x2… xn]T
y＝ln(I0/IP)＝[y1y2… yn]T
wherein n represents the number of X-ray penetrating object parts different from 0;
step 4.2: according to the transmission thickness x and the ray sum data y, adopting a curve y as axbFitting the ray and the data y, and estimating parameters a 'and b' of a and b in the curve by using least square fitting:
Figure FDA0002507264170000022
Figure FDA0002507264170000023
step 4.3: calculating the equivalent transmission thickness x according to a 'and b' obtained by fitting estimationeq：
Figure FDA0002507264170000024
Step 4.4: according to the equivalent transmission thickness xeqObtaining a fitting equation of the equivalent beam and the beer law;
step 4.5: substituting the log data of the multi-energy projection into the fitting curve obtained in the step 4.2
Figure FDA0002507264170000025
Obtaining a penetration thickness x1 corresponding to the log-quantized data of the multi-energy projection, and then substituting the penetration thickness x1 into the fitting equation of the equivalent beam and the beer's law obtained in the step 4.4 to obtain the log-quantized data of the equivalent mono-energy projection corresponding to the log-quantized data of the multi-energy projection.
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张益海: "X射线工业CT能谱测量与射线硬化校正研究", 《中国优秀硕士学位论文全文数据库 信息科技辑》 *
彭光含 等: "X射线TICT中射束硬化拟合校正研究", 《光电工程》 *

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