CN108596995A - A kind of PET-MRI maximum a posteriori joint method for reconstructing - Google Patents

Abstract

A PET‑MRI maximum posterior joint reconstruction method, comprising the steps of: one, collecting PET data and MRI data of an object; two, constructing a mathematical statistical model of PET‑MRI joint reconstruction; three, in the mathematical statistical model, using the Reconstruct the correlation of PET and MRI images and design a cross prior model; 4. Combine the cross prior model of PET and MRI designed in step 3, and use the maximum a posteriori method to combine the mathematical statistics model of PET and MRI images constructed in step 2 Reconstruction to obtain an optimization equation with a constrained objective function; fifth, perform iterative calculation on the optimized equation with a constrained objective function obtained in step 4, and simultaneously obtain PET and MRI reconstructed images. The invention can simultaneously reconstruct PET and MRI images, suppress PET image noise, reduce MRI artifacts, improve the quantization level of reconstructed images, and better assist clinical diagnosis.

Description

A PET-MRI maximum a posteriori joint reconstruction method

technical field

The invention relates to the technical field of PET and MRI image processing of medical images, in particular to a PET-MRI maximum a posteriori joint reconstruction method.

Background technique

MRI provides high-resolution structural information of soft tissues, and PET provides information on human metabolic functions. Traditionally, PET and MRI reconstructions were performed independently, or MRI structural similarities were used to guide PET reconstruction.

With the emergence and development of PET-MRI system, the concept of PET-MRI joint reconstruction was proposed. In recent years, the PET-MRI integrated system has been continuously developed and gradually applied in clinical practice. The PET-MRI integrated system can make PET anatomical positioning accurately by means of MRI, which reduces the radiation dose and harm to the human body compared with PET/CT. The PET-MRI integrated system can collect PET and MRI data at the same time, and obtain PET and MRI data with high registration. The quality of PET and MRI image reconstruction can be improved by effectively utilizing the correlation between PET and MRI data.

Due to the longer MRI acquisition time, fast MRI usually acquires less MRI data, resulting in undersampled k-space data. In the case of undersampling, the reconstructed MRI image will produce a large number of artifacts, seriously affecting the image quality. Due to its own characteristics, the resolution of PET is low, so that the noise of the reconstructed image is obvious. Utilizing the anatomical similarity between PET and MRI, PET-MRI can be jointly reconstructed to enhance structural information, reduce noise and artifacts, and improve the quality of PET and MRI image reconstruction.

In PET-MRI reconstruction, the prior model plays an extremely critical role in whether the structural similarity and common feature information of PET and MRI images can be effectively used. PET and MRI images not only have common edge feature information, but also have their own independent features. In the reconstruction process, the joint prior function should not only effectively utilize common edge features to improve image quality, but also maintain the integrity of independent features.

M.J. Ehrhardt et al. used joint total variation and level set methods for joint reconstruction of PET-MRI based on structural similarity. It is demonstrated by simulation phantoms that reconstructed images using level set priors outperform joint total variational priors. However, PET and MRI images obtained through level set prior reconstruction have feature interlacing, which increases image artifacts and seriously affects image quality.

Therefore, it is necessary to provide a PET-MRI maximum a posteriori joint reconstruction method to solve the shortcomings of the existing technology.

Contents of the invention

The purpose of the present invention is to provide a PET-MRI maximum a posteriori joint reconstruction method. The method can simultaneously reconstruct PET and MRI images, suppress PET image noise, reduce MRI artifacts, and improve the quantization level of reconstructed images.

Above-mentioned purpose of the present invention is achieved through the following technical measures:

A PET-MRI maximum a posteriori joint reconstruction method is provided, which comprises the following steps: step 1, collecting PET data and MRI data of an object;

Step 2, constructing a mathematical statistical model of PET-MRI joint reconstruction through the PET data and MRI data collected in step 1;

Step 3, in the mathematical statistical model of step 2, use the correlation between the PET image to be reconstructed and the MRI image to be reconstructed to design a cross prior model;

Step 4, combined with the cross-a priori model of step 3, the maximum a posteriori method is used to jointly reconstruct the mathematical statistical model of step 2, and an optimization equation with a constrained objective function is obtained;

In step five, iteratively calculate the optimization equation with the constrained objective function obtained in step four, and simultaneously obtain PET reconstructed images and MRI reconstructed images.

Preferably, the above-mentioned step 1 specifically collects PET projection data and MRI k-space data of the subject through an imaging device, and obtains a system matrix type of the imaging device's probability distribution of PET projections.

Preferably, the above step two specifically includes:

Step 2.1, among the PET projection data of the collected object, the PET projection data is f={f _j }, and the PET projection data meets expectations as The independent Poisson distribution of , the relationship between the PET projection data and the tracer distribution u = {u _j } is as follows:

in Represents the system matrix, n _j is the number of pixels of the PET image, n _i is the number of PET data, and each element P _ij represents the geometric probability that the photon emitted from the PET image pixel j is detected by the detector pair i;

In step 2.2, construct a mathematical statistical model for PET-MRI joint reconstruction as follows:

g＝Fv+ε,ε～N(0,σ ² )...Formula II;

The noise in the MRI k-space data is regarded as additive white Gaussian noise, where g is the MRI k-space undersampling data, v is the MRI image to be reconstructed, F is the MRI undersampling Fourier transform operator, ε represents Gaussian noise with variance ^σ2 .

Preferably, the above step three is specifically: designing a cross prior model using the correlation between the PET image to be reconstructed and the MRI image to be reconstructed, the form of the cross prior model is as follows:

Among them, the function and _ψx can be expressed in the form as follows,

in β is smooth coefficient, μ and η are functions and the weight parameters in ψ _x , u is the PET image to be reconstructed, v is the MRI image to be reconstructed,

For different variables u and v, the weight parameters in the function are represented by μ _u , μ _v , η _u , η _v , and μ _u , μ _v , η _u or η _v are correspondingly represented, which are used for the image in the calculation process Gradient information is weighted.

Preferably, the above-mentioned step 4 specifically uses the maximum a posteriori method to jointly reconstruct the mathematical statistical model of step 2 to obtain an optimization equation with a constrained objective function:

Among them, f is the projection data of PET, λ and α are weight parameters; λ and α are used to adjust the ratio of fidelity item and prior item.

Preferably, the Gatto derivative of the cross-priority model in the above step 3 is expressed as follows:

Among them, κ ₁ (u, v) is the diffusion coefficient of the projection data of PET, and κ ₂ (u, v) is the diffusion coefficient of the k-space data of MRI, respectively obtained by calculation, as follows:

Preferably, the above step five specifically uses the L-BFGS-B algorithm to iteratively calculate the optimization equation with the constrained objective function obtained in step four, and obtain PET reconstructed images and MRI reconstructed images simultaneously.

Preferably, the above-mentioned step five is specifically:

Step 5.1 Define the initial values of the PET image to be reconstructed and the MRI image to be reconstructed as u ₀ and v ₀ respectively,

Step 5.2 makes N=1, enters step 5.3,

Step 5.3 makes M=N, and M is the current number of iterations;

Step 5.4 Substitute u ₀ and v ₀ into the L-BFGS-B algorithm to iterate, and calculate estimated values u _n and v _n ;

Step 5.5 Judging the current iteration number M and calculating the estimated values u _n and v _n , if u _n meets the noise requirement and v _n meets the artifact requirement, go to step 5.6; otherwise go to step 5.7;

Step 5.6 set u _n =u ₀ , v _n =v _{0 set} N=N+1 and enter step 5.3;

Step 5.7 uses the currently obtained u _n and v _n as reconstructed PET and MRI images respectively.

A kind of PET-MRI maximum a posteriori joint reconstruction method of the present invention comprises the following steps: one, the PET data and MRI data of collection object; Two, construct the mathematical statistical model of PET-MRI joint reconstruction; Three, in the mathematical statistical model , using the correlation of PET and MRI images to be reconstructed to design a cross prior model; 4. Combining the cross prior model of PET and MRI designed in step 3, using the maximum a posteriori method for the mathematical statistics of PET and MRI images constructed in step 2 The model is jointly reconstructed to obtain an optimization equation with a constrained objective function; fifth, perform iterative calculation on the optimized equation with a constrained objective function obtained in step 4, and simultaneously obtain PET and MRI reconstruction images. The invention can simultaneously reconstruct PET and MRI images, suppress PET image noise, reduce MRI artifacts, improve the quantization level of reconstructed images, and better assist clinical diagnosis.

Description of drawings

The present invention will be further described by using the accompanying drawings, but the content in the accompanying drawings does not constitute any limitation to the present invention.

Fig. 1 is a flowchart of a PET-MRI maximum a posteriori joint reconstruction method of the present invention.

(a) in Fig. 2 is the PET image of the resolution phantom and the projection data of PET adopted in the embodiment 1 of a kind of PET-MRI maximum a posteriori joint reconstruction method, (b) in Fig. 2 is a kind of PET - The resolution phantom MRI image and the MRI undersampling data of Radial20 and the MRI undersampling data of Lines2 used in the MRI maximum a posteriori joint reconstruction method in Embodiment 1.

FIG. 3 is a PET-MRI maximum a posteriori joint reconstruction method used in Embodiment 2 of the brain PET image, MRI image, PET projection data and MRI undersampling data of Spiral20.

Fig. 4 is a PET-MRI maximum a posteriori joint reconstruction method through different methods to jointly reconstruct PET projection data and Radial20 undersampling MRI data to obtain the resolution phantom PET and MRI reconstructed images.

Fig. 5 is a PET-MRI maximum a posteriori joint reconstruction method through different methods to jointly reconstruct PET projection data and Lines2 MRI undersampling data to obtain the resolution phantom PET and MRI reconstructed images.

Fig. 6 is a PET-MRI maximum a posteriori joint reconstruction method through different methods to jointly reconstruct PET projection data and MRI undersampling data of Spiral20 to reconstruct PET and MRI images of the brain.

Detailed ways

The technical solution of the present invention will be further described in conjunction with the following examples.

Example 1.

A PET-MRI maximum a posteriori joint reconstruction method, as shown in Figures 1, 2, 4 and 5, includes the following steps in turn:

Step 1, collecting PET data and MRI data of the subject;

Step 2, constructing a mathematical statistical model of PET-MRI joint reconstruction through the PET data and MRI data collected in step 1;

Step 3, in the mathematical statistical model of step 2, use the correlation between the PET image to be reconstructed and the MRI image to be reconstructed to design a cross prior model;

Step 4, combined with the cross-a priori model of step 3, the maximum a posteriori method is used to jointly reconstruct the mathematical statistical model of step 2, and an optimization equation with a constrained objective function is obtained;

In step five, iteratively calculate the optimization equation with the constrained objective function obtained in step four, and simultaneously obtain PET reconstructed images and MRI reconstructed images.

The first step is to collect the PET projection data of the object and the k-space data of the MRI through the imaging device, and obtain the system matrix type of the PET projection probability distribution of the imaging device.

Step two specifically includes:

Step 2.1, among the PET projection data of the collected object, the PET projection data is f={f _j }, and the PET projection data meets expectations as The independent Poisson distribution of , the relationship between the PET projection data and the tracer distribution u = {u _j } is as follows:

in Represents the system matrix, n _j is the number of pixels of the PET image, n _i is the number of PET data, and each element P _ij represents the geometric probability that the photon emitted from the PET image pixel j is detected by the detector pair i;

In step 2.2, construct a mathematical statistical model for PET-MRI joint reconstruction as follows:

g＝Fv+ε,ε～N(0,σ ² )...Formula II;

The noise in the MRI k-space data is regarded as additive white Gaussian noise, where g is the MRI k-space undersampling data, v is the MRI image to be reconstructed, F is the MRI undersampling Fourier transform operator, ε represents Gaussian noise with variance ^σ2 .

Step three is specifically: using the correlation between the PET image to be reconstructed and the MRI image to be reconstructed to design a cross prior model, the form of the cross prior model is as follows:

Among them, the function and _ψx can be expressed in the form as follows,

in β is smooth coefficient, μ and η are functions and the weight parameters in ψ _x , u is the PET image to be reconstructed, v is the MRI image to be reconstructed,

For different variables u and v, the weight parameters in the function are represented by μ _u , μ _v , η _u , η _v , and μ _u , μ _v , η _u or η _v are correspondingly represented, which are used for the image in the calculation process Gradient information is weighted.

Step 4 is specifically to use the maximum a posteriori method to jointly reconstruct the mathematical statistical model of step 2, and obtain the optimization equation with constrained objective function:

Among them, f is the projection data of PET, λ and α are weight parameters; λ and α are used to adjust the ratio of fidelity item and prior item.

The Gatto derivative of the cross-prior model in step 3 is expressed as follows:

Among them, κ ₁ (u, v) is the diffusion coefficient of the projection data of PET, and κ ₂ (u, v) is the diffusion coefficient of the k-space data of MRI, respectively obtained by calculation, as follows:

Step five is specifically to use the L-BFGS-B algorithm to iteratively calculate the optimization equation with the constrained objective function obtained in step four, and obtain PET reconstructed images and MRI reconstructed images simultaneously.

Step five is specifically:

Step 5.1 Define the initial values of the PET image to be reconstructed and the MRI image to be reconstructed as u ₀ and v ₀ respectively,

Step 5.2 makes N=1, enters step 5.3,

Step 5.3 makes M=N, and M is the current number of iterations;

Step 5.4 Substitute u ₀ and v ₀ into the L-BFGS-B algorithm to iterate, and calculate estimated values u _n and v _n ;

Step 5.5 Judging the current iteration number M and calculating the estimated values u _n and v _n , if u _n meets the noise requirement and v _n meets the artifact requirement, go to step 5.6; otherwise go to step 5.7;

Step 5.6 set u _n =u ₀ , v _n =v _{0 set} N=N+1 and enter step 5.3;

Step 5.7 uses the currently obtained u _n and v _n as reconstructed PET and MRI images respectively.

The acquisition object of the present embodiment is a resolution phantom, and Fig. 4 and Fig. 5 have shown the resolution phantom PET and the MRI reconstructed image obtained by joint reconstruction of PET and Radial20 and Lines2 subsampling MRI data by different methods, and M.J.Ehrhardt etc. Compared with the images reconstructed by the maximum a posteriori reconstruction method based on the joint total variation (JTV) and linear level set (LPLS) prior proposed by people, the PET and MRI images reconstructed by the method of the present invention are clearer and can be reconstructed synchronously PET and MRI images, suppress PET image noise, reduce MRI artifacts, and improve the quantification level of reconstructed images.

Table 1 shows the normalized root mean square error (normalized root mean square error) of the reconstructed images of the resolution phantom PET and MRI obtained by different methods after optimizing the parameters α, β, γ, μ _u , μ _v , η _u , η _v , NRMSE) quantitative indicators.

Table 1 The normalized root mean square error NRMSE (%) of different reconstruction methods of the resolution phantom

It can be seen from Table 1 that the normalized root mean square error of the image reconstructed by the PET-MRI maximum a posteriori joint reconstruction method proposed by the present invention is the smallest. The above analysis shows that the method of the present invention can more effectively improve the quantization level of the reconstructed image compared with the reconstruction of the JTV and LPLS methods.

A kind of PET-MRI maximum a posteriori joint reconstruction method of the present invention comprises the following steps: one, the PET data and MRI data of collection object; Two, construct the mathematical statistical model of PET-MRI joint reconstruction; Three, in the mathematical statistical model , using the correlation of PET and MRI images to be reconstructed to design a cross prior model; 4. Combining the cross prior model of PET and MRI designed in step 3, using the maximum a posteriori method for the mathematical statistics of PET and MRI images constructed in step 2 The model is jointly reconstructed to obtain an optimization equation with a constrained objective function; fifth, perform iterative calculation on the optimized equation with a constrained objective function obtained in step 4, and simultaneously obtain PET and MRI reconstruction images. The invention can simultaneously reconstruct PET and MRI images, suppress PET image noise, reduce MRI artifacts, improve the quantization level of reconstructed images, and better assist clinical diagnosis.

Example 2.

A PET-MRI maximum a posteriori joint reconstruction method, other features are the same as in Embodiment 1, the difference is that the acquisition object in this implementation is the brain, and the reconstruction images of PET and MRI are shown in Figures 3 and 6.

In order to verify the effect of the method of the present invention, Figure 6 shows the brain PET and MRI reconstruction images obtained by joint reconstruction of PET and Spiral20 undersampling MRI data by different methods, and the joint total variation (JTV) based on the joint total variation (JTV) proposed by M.J.Ehrhardt et al. Compared with the images reconstructed by the linear level set (LPLS) prior maximum a posteriori reconstruction method, the PET and MRI images reconstructed by the method of the present invention are clearer, can simultaneously reconstruct PET and MRI images, suppress PET image noise, and reduce MRI artifacts, improving the quantification of reconstructed images.

Table 2 _lists the _normalized root mean square _error ( _NRMSE )Quantitative indicators.

Table 2 The normalized root mean square error NRMSE (%) of different reconstruction methods of the brain

The above analysis from Table 2 shows that the normalized root mean square error of the image reconstructed by the PET-MRI maximum a posteriori joint reconstruction method proposed by the present invention is the smallest. The above analysis shows that the method of the present invention can more effectively improve the quantization level of the reconstructed image compared with the reconstruction of the JTV and LPLS methods.

A kind of PET-MRI maximum a posteriori joint reconstruction method of the present invention comprises the following steps: one, the PET data and MRI data of collection object; Two, construct the mathematical statistical model of PET-MRI joint reconstruction; Three, in the mathematical statistical model , using the correlation of PET and MRI images to be reconstructed to design a cross prior model; 4. Combining the cross prior model of PET and MRI designed in step 3, using the maximum a posteriori method for the mathematical statistics of PET and MRI images constructed in step 2 The model is jointly reconstructed to obtain an optimization equation with a constrained objective function; fifth, perform iterative calculation on the optimized equation with a constrained objective function obtained in step 4, and simultaneously obtain PET and MRI reconstruction images. The invention can simultaneously reconstruct PET and MRI images, suppress PET image noise, reduce MRI artifacts, improve the quantization level of reconstructed images, and better assist clinical diagnosis.

Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than limit the protection scope of the present invention. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that Modifications or equivalent replacements are made to the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention.

Claims (8)

1. a PET-MRI maximum a posteriori joint reconstruction method, is characterized in that: comprises the following steps successively: Step 1, collecting PET data and MRI data of the subject; Step 2, constructing a mathematical statistical model of PET-MRI joint reconstruction through the PET data and MRI data collected in step 1; Step 3, in the mathematical statistical model of step 2, use the correlation between the PET image to be reconstructed and the MRI image to be reconstructed to design a cross prior model; Step 4, combined with the cross-a priori model of step 3, the maximum a posteriori method is used to jointly reconstruct the mathematical statistical model of step 2, and an optimization equation with a constrained objective function is obtained; In step five, iteratively calculate the optimization equation with the constrained objective function obtained in step four, and simultaneously obtain PET reconstructed images and MRI reconstructed images. 2. a kind of PET-MRI maximum a posteriori joint reconstruction method according to claim 1, it is characterized in that: described step one is specifically the projection data of the PET of collecting object by imaging equipment and the k-space data of MRI, and obtain Systematic matrix type of imaging device with respect to PET projection probability distribution. 3. A kind of PET-MRI maximum a posteriori joint reconstruction method according to claim 2, is characterized in that: described step 2 specifically comprises: Step 2.1, among the PET projection data of the collected object, the PET projection data is f={f _j }, and the PET projection data meets expectations as The independent Poisson distribution of , the relationship between the PET projection data and the tracer distribution u = {u _j } is as follows: in Represents the system matrix, n _j is the number of pixels of the PET image, n _i is the number of PET data, and each element P _ij is expressed as the geometric probability that the photon emitted from the PET image pixel j is detected by the detector pair i; In step 2.2, construct a mathematical statistical model for PET-MRI joint reconstruction as follows: g＝Fv+ε,ε～N(0,σ ² )...Formula II; The noise in the MRI k-space data is regarded as additive white Gaussian noise, where g is the MRI k-space undersampling data, v is the MRI image to be reconstructed, F is the MRI undersampling Fourier transform operator, ε represents Gaussian noise with variance ^σ2 . 4. A kind of PET-MRI maximum a posteriori joint reconstruction method according to claim 3, it is characterized in that: described step 3 is specifically: Utilize the correlation design cross prior model of PET image to be reconstructed and MRI image to be reconstructed , the form of the cross prior model is as follows: Among them, the function and _ψx can be expressed in the form as follows, in β is smooth coefficient, μ and η are functions and the weight parameters in ψ _x , u is the PET image to be reconstructed, v is the MRI image to be reconstructed, For different variables u and v, the weight parameters in the function are represented by μ _u , μ _v , η _u , η _v , and μ _u , μ _v , η _u or η _v are correspondingly represented, which are used for the image in the calculation process Gradient information is weighted. 5. A kind of PET-MRI maximum a posteriori joint reconstruction method according to claim 4, it is characterized in that: said step 4 specifically adopts the maximum a posteriori method to carry out joint reconstruction to the mathematical statistical model of step 2, obtains band constraint The optimization equation for the objective function: Among them, f is the projection data of PET, λ and α are weight parameters; λ and α are used to adjust the ratio of fidelity item and prior item. 6. a kind of PET-MRI maximum a posteriori joint reconstruction method according to claim 5, is characterized in that: in described step 3, the Gatto derivative of cross prior model is expressed as follows: Among them, κ ₁ (u, v) is the diffusion coefficient of the projection data of PET, and κ ₂ (u, v) is the diffusion coefficient of the k-space data of MRI, respectively obtained by calculation, as follows: 7. A kind of PET-MRI maximum a posteriori joint reconstruction method according to claim 6, is characterized in that: described step 5 is specifically the optimization equation of the band constraint objective function that adopts L-BFGS-B algorithm to step 4 to obtain Iterative calculation is performed to obtain PET reconstruction images and MRI reconstruction images simultaneously. 8. A kind of PET-MRI maximum a posteriori joint reconstruction method according to claim 7, is characterized in that: described step five is specifically: Step 5.1 Define the initial values of the PET image to be reconstructed and the MRI image to be reconstructed as u ₀ and v ₀ respectively, Step 5.2 sets N=1, enters step 5.3; Step 5.3 makes M=N, and M is the current number of iterations; Step 5.4 Substitute u ₀ and v ₀ into the L-BFGS-B algorithm to iterate, and calculate estimated values u _n and v _n ; Step 5.5 Judging the current iteration number M and calculating the estimated values u _n and v _n , if u _n meets the noise requirement and v _n meets the artifact requirement, go to step 5.6; otherwise go to step 5.7; Step 5.6 set u _n =u ₀ , v _n =v _{0 set} N=N+1 and enter step 5.3; Step 5.7 uses the currently obtained u _n and v _n as reconstructed PET and MRI images respectively.