CN111161182A - MR structure information constrained non-local mean guided PET image partial volume correction method - Google Patents

MR structure information constrained non-local mean guided PET image partial volume correction method Download PDF

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CN111161182A
CN111161182A CN201911374012.XA CN201911374012A CN111161182A CN 111161182 A CN111161182 A CN 111161182A CN 201911374012 A CN201911374012 A CN 201911374012A CN 111161182 A CN111161182 A CN 111161182A
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高园园
路利军
阳维
冯前进
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Southern Medical University
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Abstract

A PET image partial volume correction method of non-local mean guidance constrained by MR structure information restrains an NLM search range through the MR structure information, and can avoid excessive dependence of the generated PET image on the MR image while utilizing the MR structure information, thereby improving the quality of the PET image. The method utilizes the MR structure information to carry out partial volume correction on the PET image, improves the precision and the efficiency of partial volume correction on the PET image, utilizes the MR structure area to restrain the search window of the NLM, reduces the excessive dependence of the PET correction result image on the MR image, and improves the accuracy of the PET correction image.

Description

MR structure information constrained non-local mean guided PET image partial volume correction method
Technical Field
The invention relates to the technical field of medical image processing, in particular to a PET image partial volume correction method based on MR structure information constraint and non-local mean guidance.
Background
Positron Emission Tomography (PET) is an important imaging tool for clinical diagnosis and research at the molecular level. Due to insufficient spatial resolution of the detector, the partial volume effect is more obvious compared with an MRI/CT imaging device. Partial volume effects can blur images, distort lesions, degrade image quality, and affect clinical diagnosis and quantitative assessment. PET partial volume correction methods can be divided into two main categories: corrected during reconstruction and corrected during post-reconstruction. Each type of method can be further classified into voxel level and region-of-interest level correction methods.
The partial volume correction of the post-PET reconstruction procedure at the region of interest level is mainly to restore the true radioactivity of the regions, which are assumed to have the same activity in each region. Typically, these regions of interest are acquired by segmenting anatomical images that are well registered with the PET images. The Geometric Transfer Matrix (GTM) is to convolve the obtained binary image of the region of interest with a Point Spread Function (PSF) of PET to obtain a region spread function, and calculate the region spread function to obtain a transfer matrix, thereby correcting the region activity. A Voxel-Based (RBV) correction method is an improvement of a GTM algorithm and is also a typical algorithm Based on MR segmentation, however, the method has high requirements on the registration and segmentation accuracy of a PET image and an anatomical image, and meanwhile, the Region activity needs to be assumed to be consistent, and errors of the registration and segmentation can cause the image quality to be reduced, so that certain limitations and complexity exist. Compared with a post-reconstruction correction method based on a region of interest, the voxel level post-reconstruction correction method does not need to assume that the activities in the region are consistent, and can correct a single voxel. Performing an iterative deconvolution process on the native PET image corrects every voxel of the image, but the correction process introduces a high level of noise. In order to suppress the increase of noise, the existing iterative deconvolution methods guided by median priors and wavelet filters have the effect, but the deconvolution algorithms have Gibbs artifacts. There has been a great interest in PET partial volume correction methods based on anatomical prior guidance, however, existing anatomical prior guidance partial volume correction methods such as RBV methods have a problem that the dependency on the anatomical structure is too high, and a small change in segmentation or registration may cause a large difference in the result.
Therefore, it is necessary to provide a MR structure information constrained non-local mean-guided PET image partial volume correction method to overcome the deficiencies of the prior art.
Disclosure of Invention
The invention aims to avoid the defects of the prior art and provide a PET image partial volume correction method of non-local mean guidance constrained by MR structure information, which can constrain the NLM search range by the MR structure information, avoid the excessive dependence of the generated PET image on the MR image while utilizing the MR structure information and improve the PET image quality.
The above object of the present invention is achieved by the following technical means.
Providing a PET image partial volume correction method of non-local mean guidance constrained by MR structure information, which comprises the following specific steps; the method specifically comprises the following steps of,
the method comprises the following steps that (1) PET and MR image data of the same target object are synchronously acquired through a PET device and an MRI device respectively, a PET image and an MR image of the target object are synchronously acquired, and the system resolution of a detector in the PET imaging device is acquired simultaneously;
step (2) constructing a model based on partial volume correction of the PET image under the PWLS framework according to the PET image data acquired in the step (1);
step (3) registering the MR image and the PET image acquired in the step (1);
step (4), introducing non-local mean prior constrained by the MR image into the PET partial volume correction model to construct an NLMA-based PET partial volume correction model;
and (5) adopting a Gaussian Seidel combined late-step algorithm GS + OLS to carry out iterative optimization on the objective function obtained in the step (4) to obtain a corrected PET image.
Preferably, the system resolution of the detector in the MR imaging apparatus is obtained in step (1) by the full width at half maximum of the image after point source reconstruction.
Preferably, the PET image partial volume correction model based on the PWLS framework constructed in step (2) specifically includes:
Figure BDA0002340429200000031
wherein g (x) represents the PET image detected by the PET imaging device in the step (1), i.e. the degraded image with partial volume effect, f is the PET ideal image corresponding to the object, H is the system matrix, Hf represents the point spread function of the ideal image and the system to perform deconvolution operation, R (x) is the regular term, β is the regular parameter,
Figure BDA0002340429200000041
XTrepresents the transpose matrix of X and D is a gaussian weighting matrix.
Preferably, step (3) obtains the registered MR image by using a rigid registration method.
Preferably, in the partial volume correction of the PET image with MR image constraint non-local mean value prior obtained in the step (4),
the prior model based on non-local means is:
Figure BDA0002340429200000042
wherein
Figure BDA0002340429200000047
Representing a positive potential function, selecting
Figure BDA0002340429200000043
Representing a reference image, x is an image to be solved, j is the pixel position of the image, the value range is the image size, NjRepresenting a search window centered on pixel j, k being the position of the image pixel within the search window range, k being in the range 1-21.
Weight coefficient
Figure BDA0002340429200000048
Determined by the similarity of the blocks of pixels surrounding the two pixels to be compared, which is defined as
Figure BDA0002340429200000044
Wherein
Figure BDA0002340429200000045
For an image block centered on pixel j,
Figure BDA0002340429200000046
calculating a squared value of the weighted Euclidean distance, wherein a is a weighting coefficient, b is a super coefficient, the value range is 1000-plus 5000, N is a search window, and N isjIs a search window centered on pixel j.
Preferably, the MR anatomical structure information in step (4) is introduced into an NLM canonical term (we call it NLMA), and the search window of the non-local mean is constrained by using each anatomical structure of the MR, so that the calculation of the non-local mean is limited to a specific tissue range;
the canonical function of NLMA is:
Figure BDA0002340429200000051
wherein
Figure BDA0002340429200000052
Is a tag function defined as
Figure BDA0002340429200000053
RjFor tissue regions, x, to which pixels j in the structural image belongkIs the PET image value of the k-th pixel, NjRepresenting a search window centered on pixel j.
Preferably, in the step (5), a Gaussian Seidel (GS) is combined with a late step algorithm (OSL) to optimize the objective function to obtain a corrected image;
the GS + OSL iterative expression with NLMA constraint term is:
Figure BDA0002340429200000054
wherein h isiIs the i-th column value, f, of the system matrix HiW is the weight coefficient of NLM method for the ith row of image to be corrected, and is calculated according to the current image,
Figure BDA0002340429200000055
is assumed to be a constant value and n is the number of iteration steps.
Preferably, k is in the range of 1 to 21,
Figure BDA0002340429200000056
the value is 4 × 4 to 10 × 10, and N is 16 × 16 to 30 × 30.
Preferably, the value range of b is 1000-.
Preferably, the first and second liquid crystal materials are,
Figure BDA0002340429200000061
the values are 7 × 7 and N is 21 × 21.
According to the PET image partial volume correction method based on the MR structure information constraint and non-local mean guidance, the NLM search range is constrained through the MR structure information, excessive dependence of the generated PET image on the MR image can be avoided while the MR structure information is utilized, and the PET image quality is improved.
The invention utilizes MR structure information to carry out partial volume correction of the PET image, and improves the precision and efficiency of partial volume correction of the PET image. The structural region of the MR is utilized to constrain the search window of the NLM, so that the excessive dependence of the PET correction result image on the MR image is reduced, and the accuracy of the PET correction image is improved.
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The invention is further illustrated by means of the attached drawings, the content of which is not in any way limiting.
FIG. 1 is a flow chart of the PVC algorithm of the MR structure information constrained non-local mean-guided PET image partial volume correction method of the invention.
Fig. 2 is a diagrammatic illustration of the present invention NLMA.
Fig. 3 is simulation image data used in the experiment in embodiment 2 of the present invention.
Figure 4 corrected PET image results obtained with different PVCs.
Fig. 5 compares the quantization results of different methods for two regions, GM (left) and WM (right).
FIG. 6 comparison of the quantification results of the different methods for two areas GM (left) and WM (right).
Fig. 7 is a quantitative comparison of the effect of different registration deviations of 1mm (left), 2mm (middle), and 4mm (right) on different algorithms for GM regions.
Detailed Description
The invention is further described with reference to the following examples.
Example 1.
A partial volume correction method of a non-local mean-guided PET image constrained by MR structure information is disclosed as shown in figure 1, and comprises the following specific steps:
the method comprises the following steps that (1) PET and MR image data of the same target object are synchronously acquired through a PET device and an MRI device respectively, a PET image and an MR image of the target object are synchronously acquired, and the system resolution of a detector in the PET imaging device is acquired simultaneously;
step (2) constructing a model based on partial volume correction of the PET image under the PWLS framework according to the PET image data acquired in the step (1);
step (3) registering the MR image and the PET image acquired in the step (1);
step (4), introducing non-local mean prior constrained by the MR image into the PET partial volume correction model to construct an NLMA-based PET partial volume correction model;
and (5) adopting a Gaussian Seidel combined late-step algorithm GS + OLS to carry out iterative optimization on the objective function obtained in the step (4) to obtain a corrected PET image.
Specifically, the system resolution of a detector in the MR imaging equipment is obtained through the full width at half maximum of an image after point source reconstruction in the step (1).
Specifically, the PET image partial volume correction model based on the PWLS framework constructed in step (2) specifically includes:
Figure BDA0002340429200000071
Figure BDA0002340429200000081
wherein g (x) represents the PET image detected by the PET imaging device in the step (1), i.e. the degraded image with partial volume effect, f is the PET ideal image corresponding to the object, H is the system matrix, Hf represents the point spread function of the ideal image and the system to perform deconvolution operation, R (x) is the regular term, β is the regular parameter,
Figure BDA0002340429200000082
XTrepresents the transpose matrix of X and | D is a gaussian weighting matrix.
Specifically, the step (3) specifically adopts a rigid registration method to obtain the registered MR image.
Specifically, in the partial volume correction of the PET image with MR image constraint non-local mean value prior obtained in the step (4),
the prior model based on non-local means is:
Figure BDA0002340429200000083
wherein
Figure BDA0002340429200000084
Representing a positive potential function, here we choose
Figure BDA0002340429200000085
Representing a reference image, x is an image to be solved, j is the pixel position of the image, the value range is the image size, NjThe invention represents a search window with a pixel j as the center, wherein N is 21 multiplied by 21, k is the position of the image pixel in the search window range, and the range is 1-21.
Weight coefficient
Figure BDA0002340429200000086
Determined by the similarity of the blocks of pixels around the two compared pixels, which is defined as:
Figure BDA0002340429200000091
wherein
Figure BDA0002340429200000092
For an image block centered on pixel j, the value is 7 x 7 in this embodiment,
Figure BDA0002340429200000093
the squared value of the weighted Euclidean distance is calculated, a is a weighting coefficient, b is a super coefficient, the value range is 1000-plus 5000, N is a search window, the value is set to be 21 multiplied by 21, and N is set to be a search windowjIs a search window centered on pixel j. N may also be selected according to the purpose of practical use, for example, N is 16 × 16, 30 × 30, 20 × 20, or 25 × 25.
Figure BDA0002340429200000094
Meanwhile, the value can be selected according to the purpose of practical use, and is 4 × 4, 5 × 5, 6 × 6, 10 × 10 or 8 × 8.
Specifically, the MR anatomical structure information in the step (4) is introduced into an NLM regular term, and each anatomical structure of the MR is utilized to constrain a search window of the non-local mean value, so that the calculation of the non-local mean value is only limited in a specific tissue range;
the canonical function of NLMA is:
Figure BDA0002340429200000095
wherein
Figure BDA0002340429200000096
Is a tag function defined as
Figure BDA0002340429200000097
RjFor the tissue region to which the pixel j in the structural image belongsDomain, xkIs the PET image value of the k-th pixel, NjRepresenting a search window centered on pixel j.
Specifically, the MR anatomical structure information in the step (4) is defined as NLMA after being introduced into the NLM regular term;
a schematic of NLMA is shown in fig. 2:
in FIG. 2 xi，xj，xkIs the gray value of the corresponding pixel point in the PET image, Ai，Aj，AkFor gray values from the same tissue structure in the corresponding MR image, P is the matching image block, N is the search window, WijAnd WikIs the weight coefficient of j, k to i.
Specifically, in the step (5), a Gaussian Seidel (GS) is combined with a late step algorithm (OSL) to optimize the objective function to obtain a corrected image;
the GS + OSL iterative expression with NLMA constraint term is:
Figure BDA0002340429200000101
wherein h isiIs the i-th column value, f, of the system matrix HiW is the weight coefficient of NLM method for the ith row of image to be corrected, and is calculated according to the current image,
Figure BDA0002340429200000102
is assumed to be a constant value and n is the number of iteration steps.
According to the PET image partial volume correction method based on the MR structure information constraint and non-local mean guidance, the NLM search range is constrained through the MR structure information, excessive dependence of the generated PET image on the MR image can be avoided while the MR structure information is utilized, and the PET image quality is improved.
The technical scheme of the invention is as follows: firstly, the PET image partial volume correction is carried out by utilizing the MR structure information, and the precision and the efficiency of the PET image partial volume correction are improved.
And secondly, the structural region of the MR is utilized to constrain the search window of the NLM, so that the excessive dependence of the PET correction result image on the MR image is reduced, and the accuracy of the PET correction image is improved.
Example 2.
A MR structure information constrained non-local mean-guided PET image portion volume correction method, corrected according to the method described in embodiment 1.
Fig. 3 is simulation image data used in the experiment of example 2, which is derived from real human PET data, wherein fig. 3(a) is an ideal PET image corresponding to a real target, and the size is 128 × 128. Fig. 3(c) shows an MR simulation image, which is divided into 6 different brain regions. Fig. 3(d) MR simulation images with segmentation errors obtained using the SPM12 tool, also containing 6 different brain regions.
For the PET simulation image, after attenuation correction, homogenization correction and reduction of photon count in the projection domain, an uncorrected PET image is obtained through MLEM iteration 240 times of post-reconstruction, as shown in fig. 3 (b). For NLM and NLMA methods, the size of the search window set by the invention is 21 × 21, and the size of the image block is 7 × 7.
FIG. 4 is a comparison of the results of PET corrected images. The two comparative correction methods are respectively a non-local mean algorithm (NLM method for short) without introducing MR information and the method of the invention (NLMA method for short), and the image results are compared under the condition of reaching the same noise level. As can be seen from the figure, the PET image obtained by the NLMA method provided by the invention has a visual effect closer to a real phantom image.
Where fig. 4(a) is a true PET image, where fig. 4(B) is an uncorrected PET image, fig. 4(C) is an NLM correction result, and fig. 4(D) is an NLMA correction result.
Fig. 5 shows the quantization results. As can be seen from the figure, the NLMA method proposed by the present invention has a higher noise-deviation ratio than the NLM method.
The PET image partial volume correction method based on the MR structure information constraint and non-local mean guidance can utilize the MR anatomical structure information to constrain a non-local mean algorithm, inhibit PET image noise, avoid excessive dependence of the correction image on an MR image, realize correction of PET partial volume, improve image quality and better improve diagnosis efficiency of clinical PET.
Example 3.
A method for correcting the partial volume of a PET image by MR structure information constraint non-local mean guidance has the same other characteristics as the embodiment 1 or 2, except that verification is carried out according to the embodiment 2, in order to verify the influence of the segmentation deviation of the MR image on the method of the invention, two MR segmentation images are compared as the experiment of structure prior, and the related results are as follows.
For the PET simulation image, an uncorrected PET image is obtained by attenuation correction, homogenization correction, and reduction of photon count in the projection domain, as shown in fig. 3 (b). The RBV algorithm is an algorithm that extends the GTM algorithm to pixels, is based on MR segmentation, and is also a typical algorithm that uses MR information for partial volume correction, and this method is selected in this implementation 2 to be compared with the method of the present invention. Fig. 6 is a comparison of the quantization results.
Compared with other methods, the PET image partial volume correction method based on the MR structure information constrained non-local mean guidance has low requirements on the MR image segmentation precision, is slightly influenced by the segmentation precision, and has relatively high corrected image quality.
In order to verify the influence of the registration deviation of the MR image and the PET image on the method of the invention, the correction results under different deviations are compared, and the correlation results are obtained as follows.
The registration deviation is obtained by axial translation of the MR image, and the translation amplitude is 1.0mm-4.0 mm. For the PET simulation image, an uncorrected PET image is obtained by attenuation correction, homogenization correction, and reduction of photon count in the projection domain, as shown in fig. 3 (b).
Fig. 7 is a comparison of the quantification results.
Therefore, the PET image partial volume correction method based on the MR structure information constraint and non-local mean guidance has strong registration deviation resistance, improves the PET correction image quality, and does not depend on MR images excessively.
Finally, it should be noted that the above embodiments are only used for illustrating the technical solutions of the present invention and not for limiting the protection scope of the present invention, and although the present invention is described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions can be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention.

Claims (9)

1. A MR structural information constrained non-local mean-guided PET image partial volume correction method, characterized by: the method specifically comprises the following steps of,
the method comprises the following steps that (1) PET and MR image data of the same target object are synchronously acquired through a PET device and an MRI device respectively, a PET image and an MR image of the target object are synchronously acquired, and the system resolution of a detector in the PET imaging device is acquired simultaneously;
step (2) constructing a model based on partial volume correction of the PET image under the PWLS framework according to the PET image data acquired in the step (1);
step (3) registering the MR image and the PET image acquired in the step (1);
step (4), introducing non-local mean prior constrained by the MR image into the PET partial volume correction model to construct an NLMA-based PET partial volume correction model;
and (5) adopting a Gaussian Seidel combined late step algorithm to carry out iterative optimization on the objective function obtained in the step (4) to obtain a corrected PET image.
2. The MR structure information constrained non-local mean-guided PET image portion volume correction method according to claim 1, characterized in that: and (1) acquiring the system resolution of the detector in the MR imaging equipment through the full width at half maximum of the image after point source reconstruction.
3. The MR structure information constrained non-local mean-guided PET image portion volume correction method according to claim 2, characterized in that: the PET image partial volume correction model based on the PWLS framework constructed in the step (2) specifically comprises the following steps:
Figure FDA0002340429190000011
wherein g (x) represents the PET image detected by the PET imaging device in the step (1), i.e. the degraded image with partial volume effect, f is the PET ideal image corresponding to the object, H is the system matrix, Hf represents the point spread function of the ideal image and the system to perform deconvolution operation, R (x) is the regular term, β is the regular parameter,
Figure FDA0002340429190000021
XTrepresents the transpose matrix of X and D is a gaussian weighting matrix.
4. The MR structure information constrained non-local mean-guided PET image portion volume correction method according to claim 3, characterized in that: and (3) specifically, a rigid registration method is adopted to obtain the MR image after registration.
5. The MR structure information constrained non-local mean-guided PET image portion volume correction method according to claim 4, characterized in that: in the partial volume correction of the PET image with MR image constraint non-local mean value prior obtained in the step (4),
the prior model based on non-local means is:
Figure FDA0002340429190000022
wherein
Figure FDA0002340429190000023
Representing a positive potential function, selecting
Figure FDA0002340429190000024
Figure FDA0002340429190000025
Representing a reference image, j being the pixel position of the image, the range of values being the image size, NjRepresenting a search window centered on pixel j, k being the position of the image pixel within the search window;
weight coefficient
Figure FDA0002340429190000027
Determined by the similarity of the blocks of pixels around the two pixels to be compared, which is defined as:
Figure FDA0002340429190000026
Figure FDA0002340429190000031
wherein
Figure FDA0002340429190000032
For the image block centered on j,
Figure FDA0002340429190000033
the squared value of the weighted euclidean distance is calculated. Wherein
Figure FDA0002340429190000034
For an image block centered on pixel j,
Figure FDA0002340429190000035
calculating a squared value of the weighted Euclidean distance, wherein a is a weighting coefficient, b is a super coefficient, N is a search window, and N isjIs a search window centered on pixel j.
6. The MR structure information constrained non-local mean-guided PET image portion volume correction method according to claim 5, characterized in that: in the step (4), MR anatomical structure information is introduced into an NLM regular term, and each anatomical structure of MR is utilized to constrain a search window of a non-local mean value, so that the calculation of the non-local mean value is limited in a specific tissue range;
the canonical function of NLMA is:
Figure FDA0002340429190000036
wherein
Figure FDA0002340429190000037
Is a tag function defined as
Figure FDA0002340429190000038
RjFor tissue regions, x, to which pixels j in the structural image belongkIs the PET image value of the k-th pixel, NjRepresenting a search window centered on pixel j.
7. The MR structure information constrained non-local mean-guided PET image portion volume correction method according to claim 6, characterized in that: in the step (5), a Gaussian Seidel combined delay one-step algorithm is adopted to optimize the objective function to obtain a corrected image;
the iterative expression of the Gauss Seidel combined later-step algorithm with the NLMA constraint term is as follows:
Figure FDA0002340429190000041
wherein h isiIs the i-th column value, f, of the system matrix HiW is the weight coefficient of the NLM method for the image to be corrected in the ith column, and is calculated according to the current image,
Figure FDA0002340429190000042
is assumed to be a constant value and n is the number of iteration steps.
8. The MR structure information constrained non-local mean guided PET image portion volume correction method of claim 7,the method is characterized in that: k is in the range of 1 to 21,
Figure FDA0002340429190000043
the value is 4 × 4 to 10 × 10, and N is 16 × 16 to 30 × 30.
9. The MR structure information constrained non-local mean-guided PET image portion volume correction method according to claim 8, characterized in that: the value range of b is 1000-5000,
Figure FDA0002340429190000044
the values are 7 × 7 and N is 21 × 21.
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