Multi-excitation diffusion kurtosis imaging method based on convex set projection and joint reconstruction

Abstract

The invention discloses a multi-excitation diffusion kurtosis imaging method based on convex set projection and joint reconstruction, and relates to the technical field of magnetic resonance imaging. The method comprises the following steps: carrying out data acquisition; merging the multi-excitation original k space data of which the b value is 0; performing inverse Fourier transform to obtain a corresponding image, and calculating to obtain corresponding coil sensitivity information; performing parallel reconstruction; extracting DKI image phase information; calculating an initial DKI image, and multiplying the initial DKI image by corresponding phase information and coil sensitivity information; performing Fourier transform on the DKI image to a k space; performing data projection operation on the new k space data; performing inverse Fourier transform on the projected k space data to an image domain; the projected DKI images are combined; performing data fitting to obtain a DKI tensor; and performing total variation de-noising on the DKI tensor obtained by fitting to obtain a de-noised DKI tensor. According to the method, joint reconstruction is carried out by using the correlation between DKI images, and meanwhile, the influence of noise on reconstruction is reduced by adopting total variation denoising.

Description

Technical Field

[0001] The present invention relates to the technical field of magnetic resonance imaging, and in particular, to a multi-excitation diffusion kurtosis imaging method based on projection onto convex sets and joint reconstruction. Background Art

[0002] Diffusion kurtosis imaging (DKI) is a new type of magnetic resonance imaging technology. DKI introduces a kurtosis tensor on the basis of traditional diffusion tensor imaging (DTI) to characterize the non-Gaussian characteristics of the diffusion motion of water molecules in tissues. By acquiring DKI images with multiple b-values and multiple diffusion encoding directions, and performing data fitting according to the DKI signal model, a DKI tensor can be obtained, and then DKI quantization parameters can be calculated, including fractional anisotropy (FA), mean diffusivity (MD), axial diffusivity (AD), radial diffusivity (RD), kurtosis fractional anisotropy (KFA), mean kurtosis (MK), axial kurtosis (AK), and radial kurtosis (RK). These rich quantization parameters provide more information for disease prevention, diagnosis, and treatment.

[0003] In clinical practice, single-shot echo planar imaging (ss-EPI) technology is often used to acquire DKI data. However, the ss-EPI technology is vulnerable to the influence of the inhomogeneity of the main magnetic field of magnetic resonance, resulting in large geometric distortion of the image and low image resolution. In recent years, multishot echo planar imaging (ms-EPI) technology has developed rapidly. It overcomes the shortcomings of the ss-EPI technology and can reduce the geometric distortion of the image while obtaining high-resolution images. However, ms-EPI is sensitive to motion. Even a slight physiological motion (such as cerebrospinal fluid pulsation) will cause the problem of phase inconsistency between multishot data. If the phase inconsistency problem is not corrected, artifacts will appear in the image. Currently, the commonly used phase correction methods include the method with navigator echoes and the self-navigated echo method. The method with navigator echoes obtains phase information by additionally acquiring a set of navigator echo data and uses it for phase correction. This method will additionally increase the scanning time. The self-navigated echo uses parallel imaging technology to reconstruct the image of the imaging echo itself and extracts phase information for phase correction. This method does not require additional scanning time. Among the self-navigated echo methods, the MUSE and POCSMUSE technologies successively proposed by the research group of Nan-kueri Chen in 2013 and 2015 have received wide attention. POCSMUSE uses the method of projection onto convex sets (POCS) to achieve better motion correction effect than MUSE. However, the current ms-EPI reconstruction based on self-navigated echo correction usually reconstructs the DKI images of each b value and each direction independently, without using the correlation between DKI images of different b values and different directions for joint reconstruction, resulting in the image and parameters still being greatly affected by noise. Summary of the Invention

[0004] In order to overcome the above problems or at least partially solve the above problems, the present invention provides a multishot diffusion kurtosis imaging method based on projection onto convex sets and joint reconstruction, which uses the correlation between DKI images for joint reconstruction and at the same time adopts total variation denoising to reduce the influence of noise on reconstruction.

[0005] To solve the above technical problems, the technical solution adopted by the present invention is as follows:

[0006] In a first aspect, the present invention provides a multishot diffusion kurtosis imaging method based on projection onto convex sets and joint reconstruction, including the following steps:

[0007] S1. Data acquisition is performed on an imaging target under different diffusion encoding intensities and different diffusion encoding directions to obtain multishot, multi-b value, multi-direction, and multi-coil raw k-space data;

[0008] S2. Merge the multi-excitation raw k-space data with b value of 0 to obtain the fully sampled raw k-space data with b = 0;

[0009] S3. Perform inverse Fourier transform on the fully sampled raw k-space data with b = 0 to obtain the corresponding image, and calculate the corresponding coil sensitivity information;

[0010] S4. According to the coil sensitivity information, perform parallel reconstruction on the multi-coil raw k-space data for each excitation, each b value, and each direction respectively, obtain the DKI images for each excitation, each b value, and each direction, and extract the phase information of the DKI images for each excitation, each b value, and each direction;

[0011] S5. According to the preset initial DKI tensor and DKI signal model, calculate the initial multi-b value, multi-direction DKI images; multiply the initial DKI images for each b value and each direction by the corresponding phase information and coil sensitivity information to obtain the multi-excitation, multi-b value, multi-direction, multi-coil DKI images;

[0012] S6. Fourier transform the multi-excitation, multi-b value, multi-direction, multi-coil DKI images to the k-space to obtain the new k-space data of the multi-excitation, multi-b value, multi-direction, multi-coil DKI;

[0013] S7. Perform data projection operation on the new k-space data to obtain the projected k-space data; inverse Fourier transform the projected k-space data to the image domain to obtain the projected multi-excitation, multi-b value, multi-direction, multi-coil DKI images;

[0014] S8. Merge the projected multi-excitation, multi-b value, multi-direction, multi-coil DKI images to obtain the merged multi-b value, multi-direction DKI images;

[0015] S9. According to the merged multi-b value, multi-direction DKI images and the DKI signal model, perform data fitting to obtain the DKI tensor;

[0016] S10. Perform total variation denoising on the fitted DKI tensor to obtain the denoised DKI tensor;

[0017] S11. According to the preset iteration conditions, return to step S5 for multiple iterations until the iteration termination condition is reached to obtain the final DKI tensor and image.

[0018] The present invention introduces the prior information of the correlation obeying the DKI signal model between different b values and different directions to realize the joint reconstruction of multi-b value, multi-direction, multi-excitation data; introduces the total variation denoising of the DKI tensor to reduce the influence of noise on the reconstruction.

[0019] Based on the first aspect, further, the method for acquiring data of the imaging target under different diffusion encoding strengths and different diffusion encoding directions includes the following steps:

[0020] Use a multi-channel coil and an ms-EPI sequence to acquire data of the imaging target under different diffusion encoding strengths and different diffusion encoding directions.

[0021] Based on the first aspect, further, the method for calculating the corresponding coil sensitivity information includes the following steps:

[0022] Calculate the corresponding coil sensitivity information according to the formula S = m0 / |m0|; where m0 is the image when b = 0, |*| is the absolute value operation, and S is the coil sensitivity.

[0023] Based on the first aspect, further, the DKI signal model expression is: where b n is the b value of the nth diffusion encoding, g n is the direction of the nth diffusion encoding, m0 is the signal value when b = 0, D(g n ) is the diffusion coefficient along the direction of g n , and the expression is: K(g n ) is the kurtosis coefficient along the direction of g n , and the expression is: where D ij is the ijth element value of the diffusion tensor D, W ijkl is the ijklth element value of the kurtosis tensor W, g ni , g nj , g nk , g nl are the ni, nj, nk, and nlth element values of the direction g n respectively, MD is the mean diffusion coefficient, θ is the DKI model parameter, including m0, {D ij} i≤j≤3 , {W ijkl} i≤j≤k≤l≤3 .

[0024] Based on the first aspect, further, the method for performing a data projection operation on the new k-space data to obtain the projected k-space data includes the following steps:

[0025] Replace the data at the sampling positions in the new k-space data with the data at the corresponding positions in the original k-space data, while keeping the data at the non-sampled positions unchanged, to obtain the projected k-space data.

[0026] Based on the first aspect, further, the method for merging the projected multi-excitation, multi-b value, multi-direction, multi-coil DKI images includes the following steps:

[0027] Perform ① multi-coil merging and ② multi-excitation merging on the projected multi-excitation, multi-b value, multi-direction, multi-coil DKI images.

[0028] Based on the first aspect, further, the above ① multi-coil merging formula: where i represents the coil index, N c represents the total number of coils, S i represents the coil sensitivity information of the i-th coil, I i represents the image of the i-th coil, I represents the image after merging N c coil images, and H represents the complex conjugate operation.

[0029] Based on the first aspect, further, the above ② multi-excitation merging formula: where i represents the excitation index, Ns represents the total number of excitations, Ii represents the image of the i-th excitation, H represents the complex conjugate operation, |*| represents the absolute value operation, represents the low-resolution image extracted from the i-th excitation image I i ; the formula for extracting the low-resolution image is: where IDFT represents the inverse Fourier transform, DFT represents the Fourier transform, H LP represents the low-pass filter.

[0030] Based on the first aspect, further, the method for performing data fitting according to the merged multi-b value, multi-direction DKI image and the DKI signal model to obtain the DKI tensor includes the following steps:

[0031] According to the merged multi-b value, multi-direction DKI image and the DKI signal model, use the constrained weighted linear least squares method for data fitting to obtain the DKI tensor.

[0032] The present invention has at least the following advantages or beneficial effects:

[0033] The present invention provides a multi-excitation diffusion kurtosis imaging method based on convex set projection and joint reconstruction, introducing the prior information of the correlation obeying the DKI signal model between different b values and different directions to realize the joint reconstruction of multi-b value, multi-direction, multi-excitation data; introducing the total variation denoising of the DKI tensor to reduce the influence of noise on the reconstruction. Description of the Drawings

[0034] To more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the accompanying drawings required in the embodiments. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as limiting the scope. For those of ordinary skill in the art, without creative efforts, other related drawings can also be obtained based on these drawings.

[0035] Figure 1 It is a flowchart of a multi-excitation diffusion kurtosis imaging method based on projection onto convex sets and joint reconstruction according to an embodiment of the present invention;

[0036] Figure 2 It is a schematic diagram of the projection operation according to an embodiment of the present invention;

[0037] Figure 3 It is a structural block diagram of an electronic device provided by an embodiment of the present invention.

[0038] Explanation of reference numerals: 101, memory; 102, processor; 103, communication interface. Detailed implementation manners

[0039] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. Usually, the components of the embodiments of the present invention described and shown in the accompanying drawings here can be arranged and designed in various different configurations.

[0040] Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed present invention, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0041] It should be noted that: similar reference numerals and letters represent similar items in the following drawings. Therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings.

[0042] It should be noted that in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "including" or any other variant thereof is intended to cover non-exclusive inclusion, such that a process, method, article, or device that includes a series of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or device. Without further limitation, an element defined by the statement "including one..." does not exclude the presence of additional identical elements in the process, method, article, or device that includes the element.

[0043] Embodiment:

[0044] As Figure 1 shown, in a first aspect, an embodiment of the present invention provides a multi-excitation diffusion kurtosis imaging method based on projection onto convex sets and joint reconstruction, including the following steps:

[0045] S1. Collect data of the imaging target under different diffusion encoding intensities and different diffusion encoding directions to obtain multi-excitation, multi-b value, multi-direction, and multi-coil raw k-space data;

[0046] Further, it includes: using a multi-channel coil and an ms-EPI sequence to collect data of the imaging target under different diffusion encoding intensities (b values) and different diffusion encoding directions. The above ms-EPI sequence refers to collecting signals by combining the SE sequence with the EPI technique. The EPI sequence (Echo Planar Imaging) is an ultra-fast imaging technique that can complete single-shot data acquisition at the millisecond level.

[0047] S2. Merge the multi-excitation raw k-space data with a b value of 0 to obtain fully sampled raw k-space data with b = 0;

[0048] S3. Perform an inverse Fourier transform on the fully sampled raw k-space data with b = 0 to obtain the corresponding image, and calculate the corresponding coil sensitivity information;

[0049] Further, it includes: calculating the corresponding coil sensitivity information according to the formula S = m0 / |m0|; where m0 is the image when b = 0, |*| is the absolute value operation, and S is the coil sensitivity.

[0050] S4. According to the coil sensitivity information, perform parallel reconstruction on the multi-coil raw k-space data for each excitation, each b-value, and each direction respectively, obtain DKI images for each excitation, each b-value, and each direction, and extract the phase information of the DKI images for each excitation, each b-value, and each direction;

[0051] S5. According to the preset initial DKI tensor and DKI signal model, calculate the initial multi-b-value, multi-direction DKI images; multiply the initial DKI images for each b-value and each direction by the corresponding phase information and coil sensitivity information to obtain the multi-excitation, multi-b-value, multi-direction, multi-coil DKI images; set the initial DKI tensor θ to 0.

[0052] Further, the expression of the above DKI signal model is: where b n is the b-value of the nth diffusion encoding, g n is the direction of the nth diffusion encoding, m0 is the signal value when b = 0, D(g n ) is the diffusion coefficient along the direction of g n , and the expression is: K(g n ) is the kurtosis coefficient along the direction of g n , and the expression is: where D ij is the value of the ijth element of the diffusion tensor D, W ijkl is the value of the ijklth element of the kurtosis tensor W, g ni , g nj , g nk , g nl are the values of the ni, nj, nk, and nl elements of the direction g n respectively, MD is the mean diffusion coefficient, θ is the DKI model parameter, including m0, {D ij} i≤j≤3 , {W ijkl} i≤j≤k≤l≤3 .

[0053] S6. Fourier transform the multi-excitation, multi-b-value, multi-direction, multi-coil DKI images to the k-space to obtain the new k-space data of the multi-excitation, multi-b-value, multi-direction, multi-coil DKI;

[0054] S7. Perform data projection operation on the new k-space data to obtain the projected k-space data; inverse Fourier transform the projected k-space data to the image domain to obtain the projected multi-excitation, multi-b-value, multi-direction, multi-coil DKI images;

[0055] Further, it includes: replacing the data at the sampling positions in the new k-space data with the data at the corresponding positions in the original k-space data, while keeping the data at the unsampled positions unchanged, to obtain the projected k-space data; the projection operation is as Figure 2 shown.

[0056] S8. Merge the projected multi-excitation, multi-b value, multi-direction, multi-coil DKI images to obtain the merged multi-b value, multi-direction DKI image;

[0057] Further, it includes: performing ① multi-coil merging and ② multi-excitation merging on the projected multi-excitation, multi-b value, multi-direction, multi-coil DKI images. The above ① multi-coil merging formula: where i represents the coil index, N c represents the total number of coils, S i represents the coil sensitivity information of the i-th coil, I i represents the image of the i-th coil, I represents the image after merging the N c coil images, and H represents the complex conjugate operation. The above ② multi-excitation merging formula: where i represents the excitation index, Ns represents the total number of excitations, Ii represents the image of the i-th excitation, H represents the complex conjugate operation, |*| represents the absolute value operation, represents the low-resolution image extracted from the i-th excitation image I i ; the formula for extracting the low-resolution image is: where IDFT represents the inverse Fourier transform, DFT represents the Fourier transform, and H LP represents the low-pass filter.

[0058] S9. According to the merged multi-b value, multi-direction DKI image and the DKI signal model, perform data fitting to obtain the DKI tensor;

[0059] Further, it includes: according to the merged multi-b value, multi-direction DKI image and the DKI signal model, use the constrained weighted linear least squares method to perform data fitting to obtain the DKI tensor.

[0060] S10. Perform total variation denoising on the fitted DKI tensor to obtain the denoised DKI tensor;

[0061] S11. According to the preset iteration conditions, return to step S5 for multiple iterations until the iteration termination condition is reached, to obtain the final DKI tensor and image.

[0062] The present invention introduces the prior information of the correlation obeying the DKI signal model between different b values and different directions to realize the joint reconstruction of multi-b value, multi-direction and multi-excitation data; and introduces the total variation denoising of the DKI tensor to reduce the influence of noise on the reconstruction.

[0063] As Figure 3 shown, in a third aspect, an embodiment of the present application provides an electronic device, which includes a memory 101 for storing one or more programs; and a processor 102. When the one or more programs are executed by the processor 102, the method according to any one of the above first aspects is implemented.

[0064] It further includes a communication interface 103, and the memory 101, the processor 102 and the communication interface 103 are directly or indirectly electrically connected to each other to realize data transmission or interaction. For example, these components can be electrically connected to each other through one or more communication buses or signal lines. The memory 101 can be used to store software programs and modules, and the processor 102 executes various functional applications and data processing by executing the software programs and modules stored in the memory 101. The communication interface 103 can be used for signaling or data communication with other node devices.

[0065] Among them, the memory 101 can be, but is not limited to, a random access memory (Random Access Memory, RAM), a read-only memory (Read Only Memory, ROM), a programmable read-only memory (Programmable Read-Only Memory, PROM), an erasable programmable read-only memory (Erasable Programmable Read-Only Memory, EPROM), an electrically erasable programmable read-only memory (Electric Erasable Programmable Read-Only Memory, EEPROM), etc.

[0066] The processor 102 can be an integrated circuit chip with signal processing capabilities. The processor 102 can be a general-purpose processor, including a central processing unit (Central Processing Unit, CPU), a network processor (Network Processor, NP), etc.; it can also be a digital signal processor (Digital Signal Processing, DSP), an application specific integrated circuit (Application Specific Integrated Circuit, ASIC), a field programmable gate array (Field-Programmable Gate Array, FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components.

[0067] In the embodiments provided in the present application, it should be understood that the disclosed method and system can also be implemented in other ways. The method and system embodiments described above are merely illustrative. For example, the flowcharts and block diagrams in the accompanying drawings show the possible architectures, functions, and operations of the method and system, method, and computer program product according to multiple embodiments of the present application. In this regard, each block in the flowchart or block diagram may represent a module, a program segment, or a part of code, and the module, program segment, or part of code contains one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than marked in the accompanying drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in the reverse order, depending on the functions involved. It should also be noted that each block in the block diagram and / or flowchart, as well as the combination of blocks in the block diagram and / or flowchart, can be implemented by a dedicated hardware-based system for performing the specified functions or actions, or can be implemented by a combination of dedicated hardware and computer instructions.

[0068] In addition, in each embodiment of the present application, the various functional modules can be integrated together to form an independent part, or each module can exist separately, or two or more modules can be integrated to form an independent part.

[0069] Fourthly, an embodiment of the present application provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by the processor 102, the method according to any one of the above first aspects is implemented. If the function is implemented in the form of a software functional module and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of the present application, in essence, or the part that contributes to the prior art, or a part of this technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present application. The foregoing storage medium includes: various media such as USB flash drives, mobile hard disks, read-only memories (ROM, Read-Only Memory), random access memories (RAM, Random Access Memory), magnetic disks, or optical discs that can store program codes.

[0070] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention can have various modifications and changes. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

[0071] For those skilled in the art, it is obvious that this application is not limited to the details of the above-described exemplary embodiments, and that this application can be implemented in other specific forms without departing from the spirit or basic characteristics of this application. Therefore, from any point of view, the embodiments should be regarded as exemplary and non-limiting. The scope of this application is defined by the appended claims rather than the above description. Therefore, it is intended to embrace all changes that fall within the meaning and scope of the equivalent elements of the claims in this application. Any reference signs in the claims should not be construed as limiting the claims involved.

Claims

1. A multi-excitation diffusion kurtosis imaging method based on projection onto convex sets and joint reconstruction, characterized in that It includes the following steps: S1. Collect data on the imaging target under different diffusion encoding intensities and different diffusion encoding directions to obtain multi-excitation, multi-b value, multi-direction, and multi-coil raw k-space data; S2. Merge the multi-excitation raw k-space data with b value of 0 to obtain fully sampled raw k-space data with b = 0; S3. Perform inverse Fourier transform on the fully sampled raw k-space data with b = 0 to obtain the corresponding image, and calculate the corresponding coil sensitivity information; S4. According to the coil sensitivity information, perform parallel reconstruction on the multi-coil raw k-space data for each excitation, each b value, and each direction respectively, obtain the DKI images for each excitation, each b value, and each direction, and extract the phase information of the DKI images for each excitation, each b value, and each direction; S5. Calculate the initial multi-b value and multi-direction DKI images according to the preset initial DKI tensor and DKI signal model; Multiply the initial DKI images for each b value and each direction by the corresponding phase information and coil sensitivity information to obtain multi-excitation, multi-b value, multi-direction, and multi-coil DKI images; S7. Fourier transform the multi-excitation, multi-b value, multi-direction, and multi-coil DKI images to the k-space to obtain new k-space data of multi-excitation, multi-b value, multi-direction, and multi-coil DKI; S8. Perform data projection operation on the new k-space data to obtain projected k-space data; perform inverse Fourier transform on the projected k-space data to the image domain to obtain projected multi-excitation, multi-b value, multi-direction, and multi-coil DKI images; S9. Merge the projected multi-excitation, multi-b value, multi-direction, and multi-coil DKI images to obtain merged multi-b value and multi-direction DKI images; S10. Perform data fitting according to the merged multi-b value and multi-direction DKI images and DKI signal model to obtain the DKI tensor; S11. Perform total variation denoising on the fitted DKI tensor to obtain the denoised DKI tensor; S12. According to the preset iteration conditions, return to step S5 for multiple iterations until the iteration termination condition is reached to obtain the final DKI tensor and image.

2. The multi-excitation diffusion kurtosis imaging method based on projection onto convex sets and joint reconstruction according to claim 1, characterized in that The method for collecting data on the imaging target under different diffusion encoding intensities and different diffusion encoding directions includes the following steps: Use a multi-channel coil and an ms-EPI sequence to collect data on the imaging target under different diffusion encoding intensities and different diffusion encoding directions.

3. A multi-excitation diffusion kurtosis imaging method based on projection onto convex sets and joint reconstruction according to claim 1, characterized in that The method for calculating the corresponding coil sensitivity information includes the following steps: Calculate the corresponding coil sensitivity information according to the formula S = m0 / |m0|; where m0 is the image when b = 0, |*| is the absolute value operation, and S is the coil sensitivity.

4. A multi-excitation diffusion kurtosis imaging method based on projection onto convex sets and joint reconstruction according to claim 1, wherein The DKI signal model expression is as follows: where b n is the b-value of the nth diffusion encoding, g n is the direction of the nth diffusion encoding, m0 is the signal value when b = 0, D(g n ) is the diffusion coefficient along the direction of g n , and the expression is: K(g n ) is the kurtosis coefficient along the direction of g n , and the expression is: where D ij is the value of the ijth element of the diffusion tensor D, W ijkl is the value of the ijklth element of the kurtosis tensor W, g ni , g nj , g nk , g nl are the values of the ni, nj, nk, and nl elements of the direction g n respectively, MD is the mean diffusion coefficient, θ is the DKI model parameter, including m0, {D ij} i≤j≤3 , {W ijkl} i≤j≤k≤l≤3 .

5. A multi-excitation diffusion kurtosis imaging method based on projection onto convex sets and joint reconstruction according to claim 1, wherein The method for performing data projection operation on the new k-space data to obtain projected k-space data includes the following steps: Replace the data at the sampling positions in the new k-space data with the data at the corresponding positions in the raw k-space data, and keep the data at the unsampled positions unchanged to obtain the projected k-space data.

6. A multi-excitation diffusion kurtosis imaging method based on projection onto convex sets and joint reconstruction according to claim 1, characterized in that The method for merging the projected multi-excitation, multi b-value, multi-direction, multi-coil DKI images includes the following steps: Perform ① multi-coil merging and ② multi-excitation merging on the projected multi-excitation, multi b-value, multi-direction, multi-coil DKI images.

7. A multi-excitation diffusion kurtosis imaging method based on projection onto convex sets and joint reconstruction according to claim 6, wherein The multi - coil combination formula: where i represents the coil index, N c represents the total number of coils, S i represents the coil sensitivity information of the i - th coil, I i represents the image of the i - th coil, and I represents the image after combining the images of N c coils, and H represents the complex conjugate operation.

8. A multi-excitation diffusion kurtosis imaging method based on projection onto convex sets and joint reconstruction according to claim 6, characterized in that The multi-excitation merging formula described above: where i represents the excitation index, Ns represents the total number of excitations, Ii represents the image of the i-th excitation, H represents the complex conjugate operation, and |*| represents the absolute value operation. represents the low-resolution image extracted from the i-th excitation image I i ; the formula for extracting the low-resolution image is: where IDFT represents the inverse Fourier transform, DFT represents the Fourier transform, and H LP represents the low-pass filter.

9. A multi-excitation diffusion kurtosis imaging method based on projection onto convex sets and joint reconstruction according to claim 1, wherein The method for performing data fitting based on the merged multi b-value, multi-direction DKI images and the DKI signal model to obtain the DKI tensor includes the following steps: Based on the merged multi b-value, multi-direction DKI images and the DKI signal model, use the constrained weighted linear least squares method to perform data fitting to obtain the DKI tensor.

Images