Limited angle electron paramagnetic resonance imaging method, system and equipment based on high-order direction total variation

Abstract

The invention relates to the technical field of medical image reconstruction, in particular to a finite angle electron paramagnetic resonance imaging method, system and device based on high-order direction total variation, and the method comprises the steps: obtaining sparse and finite angle projection data of a to-be-reconstructed image; according to the sparse and limited angle projection data in the to-be-reconstructed image, constructing an optimization model based on the high-order direction total variation, and reconstructing the to-be-reconstructed image by using the optimization model; and the optimal model is solved by adopting a Chambolle-Pock solving algorithm, so that a reconstructed electron paramagnetic resonance image can be obtained. According to the method, non-constant characteristics can be effectively handled, and textural features and edge information of the image can be maintained.

Description

Technical Field

[0001] The invention relates to the technical field of medical image reconstruction, and in particular to a limited-angle electron paramagnetic resonance imaging method, system and device based on total variation of high-order directions. Background Art

[0002] Electron paramagnetic resonance imaging (EPRI) can achieve targeted radiotherapy and improve tumor cure rates by imaging oxygen in tumors. There has been a significant increase in interest in EPRI data acquisition within a limited angle range (LAR). This is because when data is acquired within the LAR, the scan time can be significantly shortened. In order to significantly improve imaging efficiency and shorten scan time, this paper cleverly introduces sparse reconstruction based on the limited angle of EPRI. 3D EPR sparse reconstruction refers to uniformly reducing the projection angles to ensure a constant stereo angle relationship between the projection angles. The effectiveness of sparse reconstruction has been proven in fields such as CT, MRI, and EPRI.

[0003] Sparse limited-angle reconstruction is a serious undersampled data recovery problem. The total variation (TV) minimization model is widely used due to its powerful sparse reconstruction capability. Since TV is an isotropic term, which is the sum of the gradient amplitudes of all pixels in the image, this undifferentiated processing method leads to a relative weakening of the ability to preserve edges in the non-blurred direction, thus affecting image accuracy. In order to further improve the generalization performance of the TV model, various variants and improvements of the TV model have been proposed. For CT limited-angle reconstruction, the upgraded version of anisotropic total variation (ATV) applies different weights according to the angle value to balance TV minimization and data fidelity constraints. For 3D limited-angle EPRI, since the projection angle is affected by the polar angle ( ) and azimuth ( ) are jointly determined, so it is difficult to use angle information to assist 3D limited-angle EPRI.

[0004] Recently, the Directional TV (DTV) algorithm uses the spatial relationship between image pixels to constrain the horizontal and vertical directions of the digital phantom with a limited angle range, effectively reducing limited angle artifacts. However, when it is applied to the real data of EPRI, serious block artifacts appear inside the image and obvious staircase artifacts appear at the edge of the image. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide an electron paramagnetic resonance imaging method, system and device based on high-order directional total variation in view of the deficiencies in the above-mentioned prior art, so as to solve the technical problems of slow scanning speed and artifacts at the edge of reconstructed image in current electron paramagnetic resonance imaging.

[0006] The objective of the present invention is achieved by the following technical solutions: In a first aspect, the present invention provides a limited angle electron paramagnetic resonance imaging method based on high-order directional total variation, comprising: Acquire sparse data of an image to be reconstructed and limited-angle projection data; According to the sparse data of the image to be reconstructed and the limited angle projection data, an optimization model based on the total variation of the high-order direction is constructed, and the image to be reconstructed is reconstructed using the optimization model; The optimization model is solved using the Chambolle-Pock solution algorithm to obtain a reconstructed electron paramagnetic resonance image. As a further improvement of the present invention, the optimization model based on the total variation in the higher-order direction specifically includes: , ,

[0007] In the formula, u * represents the solution of the optimization model, i.e., the reconstructed electron paramagnetic resonance image; g Represents the actual measured value of the 3D EPR image after 3D Radon transformation; Au Representing model data g ; u represents the image vector to be reconstructed, and its minimum volume is called a voxel; A is the system matrix, and its elements A i,j Represents the model data of the jth voxel of the image Contribution is the high-order TV norm of the image to be reconstructed in the x direction; is the high-order TV norm of the image to be reconstructed in the y direction; is the high-order TV norm of the image to be reconstructed in the z direction; , and They are the TV limits in different directions respectively.

[0008] As a further improvement of the present invention, the high-order TV norms of the image to be reconstructed in the three-dimensional direction are defined as:

[0009]

[0010]

[0011] in,

[0012]

[0013]

[0014] In the formula, represents the number of voxels along the 𝑥-axis, represents the number of voxels along the y-axis, represents the number of voxels along the z-axis, is the gradient of the object along the x direction, is the gradient of the object along the y direction, is the gradient of the object along the z direction.

[0015] As a further improvement of the present invention, the Chambolle-Pock solution algorithm is used to solve the optimization model, which specifically includes: Convert the corresponding expression of the optimization model of the total variation in the higher-order direction into the form of the Chambolle-Pock algorithm; Solve the convex conjugate function of the transformed optimization model; The proximal mapping calculation is performed on the convex conjugate function, and the original variable and the dual variable are continuously and alternately updated until the set convergence condition is reached, thereby obtaining the optimal electron paramagnetic resonance image reconstruction result; the original variable is the image to be reconstructed.

[0016] As a further improvement of the present invention, The corresponding expression of the optimization model of the total variation in the higher-order direction is converted into the Chambolle-Pock algorithm form, specifically: According to the general form of the Chambolle-Pock algorithm framework, the corresponding expression of the optimization model of the total variation in the higher-order direction is converted to: , , , , , , , In the formula, is the image vector to be reconstructed u The transformed variable, is the result of linear transformation of the image vector to be reconstructed, , and are algorithm parameters; is the first dual variable; is the second dual variable; is the third dual variable; is the fourth dual variable; K is the system matrix A and the transformation operator in different directions related to the high-order total variation. The transformed optimization model is defined as:

[0017] in,

[0018]

[0019]

[0020]

[0021]

[0022] In the formula, is the optimal model after conversion; is the first function with respect to the first dual variable p; is about the second dual variable The second function of is about the third dual variable The third function of is about the fourth dual variable The fourth function of is the fifth function in the Chambolle-Pock algorithm, and the fifth function is set to 0; is the indicator function; y is the dual variable vector formed according to each dual variable; is the regularization parameter.

[0023] As a further improvement of the present invention, the convex conjugate function corresponding to each function in the converted optimization model is:

[0024]

[0025]

[0026]

[0027] In the formula, is the convex conjugate function corresponding to the first function; is the convex conjugate function corresponding to the second function; is the convex conjugate function corresponding to the third function; is the convex conjugate function corresponding to the fourth function; , , are the total variation weight parameters in the x, y, and z directions respectively; , and They are the TV limits in different directions respectively.

[0028] As a further improvement of the present invention, the nearest neighbor mapping calculation result is:

[0029]

[0030]

[0031]

[0032]

[0033] In the formula, is the nearest neighbor mapping result of the convex conjugate function corresponding to the first function; is the nearest neighbor mapping result of the convex conjugate function corresponding to the second function; is the nearest neighbor mapping result of the convex conjugate function corresponding to the third function; is the nearest neighbor mapping result of the convex conjugate function corresponding to the fourth function; The fifth function The nearest neighbor mapping result; is the step size parameter. As a further improvement of the present invention, the convergence condition is determined according to nRMSE, NDE and NTVE, which are defined as: ( )

[0034] ( )

[0035] ( )

[0036] In the formula, is the normalized distance between the reconstructed image after n iterations of the algorithm and the image to be reconstructed; Reconstruct the image for the band; For model data With measurement data NTVE is the error between the TV value of the reconstructed image and the TV value of the true image.

[0037] In a second aspect, the present invention provides an electron paramagnetic resonance imaging system based on total variation in high-order directions, which is used to implement the above-mentioned limited-angle electron paramagnetic resonance imaging method based on total variation in high-order directions, comprising: A projection data acquisition module, used to acquire sparse and limited-angle projection data of an image to be reconstructed; An optimization model construction module is used to construct an optimization model based on high-order directional total variation according to sparse and limited-angle projection data of the image to be reconstructed, and reconstruct the image to be reconstructed using the optimization model; The optimization model solving module is used to solve the optimization model by using the Chambolle-Pock solving algorithm to obtain a reconstructed electron paramagnetic resonance image.

[0038] In a third aspect, the present invention provides a computer-readable storage medium storing one or more programs, wherein the one or more programs include instructions, which, when executed by a computing device, enable the computing device to perform the above-mentioned limited-angle electron paramagnetic resonance imaging method based on total variation of higher-order directions.

[0039] In a fourth aspect, the present invention provides a computing device, comprising: One or more processors, a memory and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the one or more programs include steps for executing the above-mentioned limited angle electron paramagnetic resonance imaging method based on high-order directional total variation.

[0040] The beneficial effects of the present invention are as follows: the limited angle electron paramagnetic resonance imaging method based on high-order directional total variation provided by the present invention effectively utilizes sparse data, reduces redundant information, can effectively reconstruct under limited angle data, and improves reconstruction accuracy. Compared with some traditional measurement methods, the high-order directional total variation can more finely characterize the edge, texture and other detail information of the image. In the electron paramagnetic resonance image, these details are often crucial for accurately reflecting the microstructure, physical properties and the like of the sample. Through the optimization model, these key features can be better retained and restored during the reconstruction process, so that the reconstructed image is closer to the original real image in structure and details. The high-order directional total variation effectively controls the image smoothness and retains the image details and edge information. The high efficiency of the Chambolle-Pock algorithm greatly shortens the calculation time. When the ROI is not piecewise constant, the high-order TV minimization method can effectively deal with this non-constant characteristic and provide an accurate solution. The present invention considers a wider range of neighborhood information and the nonlinear characteristics of the interaction between pixels, and helps to maintain the texture features and edge information of the image.

[0041] Furthermore, the high-order directional total variation constraint can effectively retain the edge information of the image, avoid edge blur, and improve the clarity and recognizability of the image. The use of sparse data and limited angle data can shorten the scanning time. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0043] Figure 1 The following are representative slice images and cross-sectional views of the 3D digital model reconstructed through reverse crime research in this example; (a) is the image of the cross-section of the real image, (b) is the image of the cross-section of the reconstructed image, and the display window is [0, 1]; (c) is the horizontal center cross-sectional view of the two cross-sectional images; (d) is the horizontal 1 / 4 cross-sectional view; they are drawn along the yellow and red horizontal lines in the real image, respectively.

[0044] Figure 2 This is an iterative graph of the reconstruction of the 3D digital phantom through the inverse crime study in this example (Case 2). Specifically, it shows the convergence graph of nRMSE (a), NDE (b), and NTVE (c) of the image reconstructed from 828 views.

[0045] Figure 3 These are representative slice images of EPRI reconstructed using different methods in this example.

[0046] Figure 4 These are representative slice images of EPRI reconstructed using different methods in this example.

[0047] FIG5 is a representative slice image of EPRI reconstructed by different methods in this example, (a) is the nRMSE curve, and (b) is the PCC curve.

[0048] Figure 6 These are representative slice images of EPRI reconstructed using different methods in this example.

[0049] FIG7 shows representative slice images of EPRI reconstructed by different methods in this example, (a) is the nRMSE curve, and (b) is the PCC curve.

[0050] Figure 8 Schematic diagram of the structure of the electronic device in this embodiment. DETAILED DESCRIPTION

[0051] In order to make the purpose and technical solution of the present invention clearer and easier to understand, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. The specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0052] The technical solution of the present invention will be clearly and completely described below in conjunction with the accompanying drawings and specific embodiments, wherein the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments.

[0053] Example 1 like Figure 1 As shown in FIG. 7 , this embodiment provides a limited-angle electron paramagnetic resonance imaging method based on total variation in high-order directions.

[0054] Sparse and limited-angle projection data of the image to be reconstructed are obtained. In this embodiment, the image with reconstruction obtained is a 3D discrete image, and its smallest volume is called a voxel.

[0055] According to the sparse and limited-angle projection data of the image to be reconstructed, an optimization model based on high-order directional total variation is constructed, and the image to be reconstructed is reconstructed using the optimization model.

[0056] In this embodiment, a 3D discretized EPR image is given. , based on the optimization model of total variation in higher-order directions, specifically including: , , (1) In the formula, u * represents the solution of the optimization model, i.e., the reconstructed electron paramagnetic resonance image; g Represents the actual measured value of the 3D EPR image after 3D Radon transformation; Au Representing model data g ; u represents the image vector to be reconstructed, and its minimum volume is called a voxel; A is the system matrix, and its elements A i,j Represents the model data of the jth voxel of the image Contribution is the high-order TV norm of the image to be reconstructed in the x direction; is the high-order TV norm of the image to be reconstructed in the y direction; is the high-order TV norm of the image to be reconstructed in the z direction; represent The square of the norm; , and They are the total variation constraint parameters in different directions. Different projection point distributions and different angle domains covered by projection points require adjustment. , and , in order to meet the requirements of 3D sparse limited-angle EPR reconstruction quality.

[0057] The high-order TV norm of the image to be reconstructed in the three-dimensional direction is defined as: (2) (3) (4) in, (5) (6) (7) In the formula, represents the number of voxels along the 𝑥-axis, represents the number of voxels along the y-axis, represents the number of voxels along the z-axis, .

[0058] The optimization model is solved using the Chambolle-Pock solution algorithm to obtain a reconstructed electron paramagnetic resonance image.

[0059] Specifically, the solution method includes: Initialize the parameters, including model parameters and algorithm parameters. Model parameters are used to determine the solution of the optimization model; algorithm parameters are used to set the convergence speed and convergence path of the Chambolle-Pock solution algorithm.

[0060] Specifically, the model parameters include the system matrix A, TV limit ( , and ), projection method, etc. This embodiment uses isotropic cubic voxels as the image basis and calculates the system matrix A in real time. The matrix consists of the intersection area of ​​the plane and the voxel. TV limit ( , and ) represents the upper limit of the HTV constraint. The TV limit is dynamically adjusted according to the angle range covered by the projection point as shown in Table 1. , and The TV limit is adjusted dynamically. The projection method uses the voxel-driven method. The algorithm parameters include , , , , , and . It can optimize the path of the HDTV-CP algorithm leading to the feasible solution set specified by the HDTV optimization model, thereby improving the convergence speed. is the largest singular value of the matrix, , and Represents the maximum singular value of the object along the x, y and z axes respectively.

[0061] Table 1. Concise definition of angular ranges.

[0062] In Table 1, R is the data of the full angle range, and the polar angle for , azimuth for . The data of the full angle range is expressed as In the form of: - This is limited angle data.

[0063] According to the parameters set by initialization, dual variables are introduced, and the corresponding expression of the optimization model of the total variation in the high-order direction is converted into the form of the Chambolle-Pock algorithm; the convex conjugate function of the converted optimization model is solved.

[0064] According to the general form of the CP algorithm framework, equation (1) is converted to: , , , , , , , In the formula, is the image vector to be reconstructed u The transformed variable, is the result of linear transformation of the image vector to be reconstructed, , and are algorithm parameters; is the first dual variable; is the second dual variable; is the third dual variable; is the fourth dual variable; K is the system matrix A and the transformation operator in different directions related to the high-order total variation. The transformed optimization model is defined as:

[0065] in,

[0066]

[0067]

[0068]

[0069]

[0070] In the formula, is the optimal model after conversion; is the first function with respect to the first dual variable p; is about the second dual variable The second function of is about the third dual variable The third function of is about the fourth dual variable The fourth function of It is the fifth function in the CP algorithm, which is set to 0 here; is the indicator function; y is the dual variable vector formed according to each dual variable; is the regularization parameter.

[0071] According to the derivation process of the CP algorithm example, solve , , and The convex conjugate function of :

[0072]

[0073]

[0074]

[0075] In the formula, is the convex conjugate function corresponding to the first function; is the convex conjugate function corresponding to the second function; is the convex conjugate function corresponding to the third function; is the convex conjugate function corresponding to the fourth function; , , are the total variation weight parameters in the x, y, and z directions respectively; , and are the total variation constraint parameters in different directions respectively.

[0076] The proximal mapping calculation is performed on the convex conjugate function, and the original variable and the dual variable are continuously and alternately updated until the set convergence condition is reached, thereby obtaining the optimal electron paramagnetic resonance image reconstruction result; the original variable is the image to be reconstructed.

[0077] Specifically, , , , and The proximal mapping calculation results are as follows:

[0078]

[0079]

[0080]

[0081]

[0082] In the formula, is the nearest neighbor mapping result of the convex conjugate function corresponding to the first function; is the nearest neighbor mapping result of the convex conjugate function corresponding to the second function; is the nearest neighbor mapping result of the convex conjugate function corresponding to the third function; is the nearest neighbor mapping result of the convex conjugate function corresponding to the fourth function; The fifth function The nearest neighbor mapping result; is the step size parameter; Used to compute neighbor maps. In this embodiment, an algorithm pseudo code is designed according to the above-mentioned reconstruction method example, as shown in Table 2.

[0083] Table 2 HDTV-CP algorithm pseudo code

[0084] Image reconstruction is essentially an inverse problem, and inverse crime is an effective way to evaluate whether the inverse problem is correct. Figure 1If the inverse crime is successful, the normalized root-mean-square error (nRMSE), normalized data error (NDE) and normalized TV error (NTVE) are introduced as convergence criteria. Their mathematical expressions are as follows: ( )

[0085] ( )

[0086] ( )

[0087] In the formula, is the normalized distance between the reconstructed image after n iterations of the algorithm and the image to be reconstructed; Reconstruct the image for the band; For model data With measurement data NTVE is the error between the TV value of the reconstructed image and the TV value of the real image. The three dimensions of image pixel error, projection error and gradient error systematically evaluate the convergence performance of the HDTV-CP algorithm proposed in this paper to ensure that it reaches the expected convergence state. The convergence condition is defined as follows: ( )

[0088] ( )

[0089] ( )

[0090] The full angle is generated by the above method ( , ) of the 3D six-ball phantom, the image size is , the central cross-section image is as follows Figure 1 (a) shown. Figure 1 (b) is the reconstructed image, it can be observed that Figure 1 (b) with Figure 1 (a) Visually identical. Figure 1 (c) and Figure 1(d) is the contour selected from the horizontal center position and the horizontal 1 / 4 position of the central cross-slice image, and it can be observed that the two contours completely overlap. Figure 2 It can be seen that the convergence images of nRMSE, NDE and NTVE reach and exceed the set convergence conditions. Therefore, the reverse crime research proves that the HDTV-CP algorithm designed in this embodiment is completely correct.

[0091] When this method is applied to real data research, since there is no ground-truth image, it is necessary to select the reconstructed image as the reference image. Figure 3 , specifically, the slice image of the reconstructed object at y = 28. From left to right, they are respectively 1 -R 5 Finite angle EPRI performed within five finite angle ranges. The display window is [0, 0.0021]. Figure 3 From the R column in , we can see that the edge of TVcDM is too smooth, the edge of DTV has stair-step artifacts, and HDTV is in between the two, eliminating both the smoothness of TV and the stair-step artifacts of DTV, and reconstructing the image edge very well. Therefore, this embodiment selects the image reconstructed from the full-angle data by the HDTV-CP algorithm as the reference image. In qualitative analysis, the cross-sectional images of the reconstructed images are used for visual inspection to compare the reconstruction performance of different algorithms on the EPR limited-angle data. Figure 3 As can be seen in Figure 2, the edges of the image reconstructed by the TVcDM-CP algorithm are severely missing and the contours are too smooth. TVcDM lacks the ability to reconstruct images in limited angle data. 1 -R 4 When the angle is 0.04, the upper right corner of the image edge reconstructed by the DTV-CP algorithm is missing. However, the HDTV-CP algorithm 1 When the angle is 0.04, the image edge is completely reconstructed. This result can be understood as follows: the edge is the area where the EPR signal changes dramatically. The HDTV method takes into account the second-order derivatives of the image, which enables it to more accurately represent the local changes of the image, thereby retaining more edge details during the EPR image reconstruction process. In addition, by considering the high-order derivatives of the image, the HDTV method can more finely control the smoothness of the image, reduce the staircase effect, and make the reconstructed image more natural. Figure 4 Visual assessment of cross-sectional images taken along the physical phantom bottle reconstructed using HDTV, DTV and TVcDM methods. Figure 4 Specifically, the slice image of the object reconstructed at x = 27. From left to right, they are 1 -R 5 Finite angle EPRI performed in five finite angle ranges. The display window is [0, 0.0022].

[0092] from Figure 4 It can be seen that the ERP image reconstructed by the HDTV-CP algorithm has no obvious staircase artifacts inside, and the image edge is more complete. 1 -R 4 The reconstructed EPR image has little visual difference from the EPR image reconstructed at full angle R. Experiments have shown that the HDTV-CP algorithm has better texture feature and edge information preservation capabilities in limited-angle EPRI. In the quantitative analysis, the nRMSE and PCC indicators are used to compare the reconstruction performance of TVcDM, DTV and HDTV in the five projection point distributions of limited-angle EPRI. As can be seen from Figure 5 (a) and Figure 5 (b), compared with the TVcDM and DTV methods, the nRMSE and PCC of all EPR limited-angle images reconstructed by the HDTV minimization method are the best. Figure 5 calculates the nRMSE and PCC of different methods in the limited angle range R. 1 -R 5 nRMSE and PCC metrics.

[0093] In R 1 -R 5 Among these five projection point distributions, select R 1 As the minimum angle on the XOY plane, we study its reconstruction performance in sparse limited angle EPRI. In the real data study, since there is no ground-truth image, it is necessary to select the reconstructed image as the reference image. Figure 6 As shown in the figure, the slice images of the reconstructed object at y = 28 by different methods are shown. From left to right, they are the sparse reconstruction images of the limited angle EPRI at 50 projection points, 100 projection points, 150 projection points, and 200 projection points. Figure 6 As can be seen from the last column of the figure, the edges of the EPR images reconstructed by the TVcDM and DTV methods are incomplete, and the edges of the EPR images reconstructed by the TVcDM method are too smooth. The EPR images reconstructed by the DTV method have serious staircase artifacts inside. Therefore, this embodiment selects the HDTV-CP algorithm from R 1 The reconstructed image in the projection point distribution is used as the reference image. In qualitative analysis, the cross-sectional images of the reconstructed image are used for visual inspection to compare the reconstruction performance of different algorithms on EPR sparse limited angle data. Figure 6As can be seen in the figure, the EPR image reconstructed by the TVcDM-CP algorithm has serious missing edges and too smooth contours. TVcDM lacks the ability to reconstruct images in sparse limited-angle EPR data. At 50-200 views, the upper right corner of the EPR image reconstructed by the DTV-CP algorithm is missing. However, the HDTV-CP algorithm completely reconstructs the image edge at 50 views, achieving the same level as the limited-angle R 1 The same effect is achieved. In the quantitative analysis, the nRMSE and PCC indicators are used to compare the reconstruction performance of TVcDM, DTV and HDTV methods in sparse limited angle EPRI. As shown in Figure 7, the nRMSE and PCC metrics of different methods in the sparse reconstruction of limited angle EPRI are calculated. It can be seen from Figure 7 that compared with the TVcDM and DTV methods, the nRMSE and PCC of all sparse limited angle EPR images reconstructed by the HDTV minimization method are the best. Experiments have shown that the HDTV-CP algorithm has better texture features and edge information preservation capabilities in sparse limited angle EPRI.

[0094] Example 2 This embodiment provides a limited angle electron paramagnetic resonance imaging system based on total variation in high-order directions, which is used to implement the limited angle electron paramagnetic resonance imaging method based on total variation in high-order directions in the above embodiment 1, including: A projection data acquisition module, used to acquire sparse and limited-angle projection data of an image to be reconstructed; An optimization model construction module is used to construct an optimization model based on high-order directional total variation according to sparse and limited-angle projection data of the image to be reconstructed, and reconstruct the image to be reconstructed using the optimization model; The optimization model solving module is used to solve the optimization model by using the Chambolle-Pock solving algorithm to obtain a reconstructed electron paramagnetic resonance image.

[0095] Example 3 In another embodiment of the present invention, the present invention also provides a storage medium, specifically a computer-readable storage medium (Memory), which is a memory device in a terminal device for storing programs and data. It is understandable that the computer-readable storage medium here can include both the built-in storage medium in the terminal device and the extended storage medium supported by the terminal device, and can be any tangible medium containing or storing a program, which can be used by an instruction execution system, device or device or used in combination with it. The computer-readable storage medium provides a storage space, which stores the operating system of the terminal. In addition, one or more instructions suitable for being loaded and executed by the processor are also stored in the storage space, and these instructions can be one or more computer programs (including program codes). It should be noted that more specific examples (non-exhaustive list) of the computer-readable storage medium here include: an electrical connection with one or more wires, a portable disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above.

[0096] Computer readable storage media also include data signals propagated in baseband or as part of a carrier wave, which carry readable program codes. Such propagated data signals can take a variety of forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. The readable storage medium can also be any readable medium other than a readable storage medium, which can send, propagate, or transmit a program for use by or in conjunction with an instruction execution system, device, or device. The program code contained on the readable storage medium can be transmitted using any appropriate medium, including but not limited to wireless, wired, optical cable, RF, etc., or any suitable combination of the above.

[0097] Program code for performing the operations of the present invention may be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java, C++, etc., and conventional procedural programming languages ​​such as "C" or similar programming languages. The program code may be executed entirely on the user computing device, partially on the user device, as a separate software package, partially on the user computing device and partially on a remote computing device, or entirely on a remote computing device or server. In the case of a remote computing device, the remote computing device may be connected to the user computing device through any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computing device (e.g., through the Internet using an Internet service provider).

[0098] One or more instructions stored in a computer-readable storage medium may be loaded and executed by a processor to implement the corresponding steps of the method for limited angle electron paramagnetic resonance imaging based on high-order directional total variation in the above embodiment; one or more instructions in the computer-readable storage medium are loaded and executed by the processor as follows: Acquire sparse and limited-angle projection data of an image to be reconstructed; According to the sparse and limited-angle projection data of the image to be reconstructed, an optimization model based on the total variation of the high-order direction is constructed, and the image to be reconstructed is reconstructed using the optimization model; The optimization model is solved using the Chambolle-Pock solution algorithm to obtain a reconstructed electron paramagnetic resonance image.

[0099] Example 4 See also Figure 8 , the terminal device is a computer device, and the computer device 60 of this embodiment includes: a processor 61, a memory 62, and a computer program 63 stored in the memory 62 and executable on the processor 61. When the computer program 63 is executed by the processor 61, the limited angle electron paramagnetic resonance imaging method based on total variation of high-order directions in the embodiment is implemented. To avoid repetition, it is not described one by one here. Alternatively, when the computer program 63 is executed by the processor 61, the functions of each model / unit constituting the computing system in the limited angle electron paramagnetic resonance imaging method based on total variation of high-order directions in embodiment 1 are implemented. To avoid repetition, it is not described one by one here.

[0100] The computer device 60 may be a computing device such as a desktop computer, a notebook, a PDA, or a cloud server. The computer device 60 may include, but is not limited to, a processor 61 and a memory 62. Those skilled in the art will appreciate that Figure 8 This is only an example of the computer device 60 and does not constitute a limitation of the computer device 60. It may include more or fewer components than shown in the figure, or a combination of certain components, or different components. For example, the computer device may also include input and output devices, network access devices, buses, etc.

[0101] The processor 61 may be a central processing unit (CPU), or other general-purpose processors, central processing units, graphics processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, data processing logic based on quantum computing, discrete hardware components, etc. A general-purpose processor may be a microprocessor or the processor may be any conventional processor, etc.

[0102] The memory 62 may be an internal storage unit of the computer device 60, such as a hard disk or memory of the computer device 60. The memory 62 may also be an external storage device of the computer device 60, such as a plug-in hard disk, a smart memory card (SmartMediaCard, SMC), a secure digital (SecureDigital, SD) card, a flash card (FlashCard), etc. equipped on the computer device 60.

[0103] Furthermore, the memory 62 may include both an internal storage unit of the computer device 60 and an external storage device. The memory 62 is used to store computer programs and other programs and data required by the computer device. The memory 62 may also be used to temporarily store data that has been output or is to be output.

[0104] Any reference to a memory, database or other medium used in the embodiments provided in this application may include at least one of a non-volatile and a volatile memory. Non-volatile memory may include a read-only memory (ROM), a magnetic tape, a floppy disk, a flash memory, an optical memory, a high-density embedded non-volatile memory, a resistive random access memory (ReRAM), a magnetic random access memory (MRAM), a ferroelectric random access memory (FRAM), a phase change memory (PCM), a graphene memory, etc. Volatile memory may include a random access memory (RAM) or an external cache memory, etc. As an illustration and not limitation, RAM may be in various forms, such as a static random access memory (SRAM) or a dynamic random access memory (DRAM), etc.

[0105] The database involved in each embodiment provided in this application may include at least one of a relational database and a non-relational database. The non-relational database may include a distributed database based on blockchain, etc., but is not limited thereto. The processor involved in each embodiment provided in this application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., but is not limited thereto.

Claims

1. A limited angle electron paramagnetic resonance imaging method based on total variation of high-order directions, characterized in that: include: Acquire sparse and limited-angle projection data in an image to be reconstructed; According to the sparse and limited-angle projection data of the image to be reconstructed, an optimization model based on the total variation of the high-order direction is constructed, and the image to be reconstructed is reconstructed using the optimization model; The optimization model is solved using the Chambolle-Pock solution algorithm to obtain a reconstructed electron paramagnetic resonance image.

2. The limited angle electron paramagnetic resonance imaging method based on high-order directional total variation according to claim 1, characterized in that: The optimization model based on the total variation in the higher-order direction specifically includes: , , In the formula, u * represents the solution of the optimization model, i.e., the reconstructed electron paramagnetic resonance image; g Represents the actual measured value of the 3D EPR image after 3DRadon transformation; Au Representing model data g ; u represents the image vector to be reconstructed, and its minimum volume is called a voxel; A is the system matrix, and its elements A i,j Represents the model data of the j-th voxel of the image Contribution is the high-order TV norm of the image to be reconstructed in the x direction; is the high-order TV norm of the image to be reconstructed in the y direction; is the high-order TV norm of the image to be reconstructed in the z direction; , and They are the TV limits in different directions respectively.

3. The limited angle electron paramagnetic resonance imaging method based on high-order directional total variation according to claim 2, characterized in that: The high-order TV norm of the image to be reconstructed in the three-dimensional direction is defined as: in, In the formula, represents the number of voxels along the 𝑥-axis, represents the number of voxels along the y-axis, represents the number of voxels along the z-axis, is the gradient of the object along the x direction, is the gradient of the object along the y direction, is the gradient of the object along the z direction.

4. The limited angle electron paramagnetic resonance imaging method based on high-order directional total variation according to claim 2, characterized in that: The Chambolle-Pock solution algorithm is used to solve the optimization model, specifically including: Convert the corresponding expression of the optimization model of the total variation in the higher-order direction into the form of the Chambolle-Pock algorithm; Solve the convex conjugate function of the transformed optimization model; The proximal mapping calculation is performed on the convex conjugate function, and the original variable and the dual variable are continuously and alternately updated until the set convergence condition is reached, thereby obtaining the optimal electron paramagnetic resonance image reconstruction result; the original variable is the image to be reconstructed.

5. The limited angle electron paramagnetic resonance imaging method based on high-order directional total variation according to claim 4, characterized in that: The corresponding expression of the optimization model of the total variation in the higher-order direction is converted into the Chambolle-Pock algorithm form, specifically: According to the general form of the Chambolle-Pock algorithm framework, the corresponding expression of the optimization model of the total variation in the higher-order direction is converted to: , , , , , , , In the formula, is the image vector to be reconstructed u The transformed variable, is the result of linear transformation of the image vector to be reconstructed, , and are algorithm parameters; is the first dual variable; is the second dual variable; is the third dual variable; is the fourth dual variable; K is the system matrix A and the transformation operator in different directions related to the high-order total variation. The transformed optimization model is defined as: in, In the formula, is the optimal model after conversion; is the first function with respect to the first dual variable p; is about the second dual variable The second function of is about the third dual variable The third function of is about the fourth dual variable The fourth function of is the fifth function in the Chambolle-Pock algorithm, and the fifth function is set to 0; is the indicator function; y is the dual variable vector formed according to each dual variable; is the regularization parameter.

6. The limited angle electron paramagnetic resonance imaging method based on high-order directional total variation according to claim 4, characterized in that: The convex conjugate functions corresponding to each function in the converted optimization model are: In the formula, is the convex conjugate function corresponding to the first function; is the convex conjugate function corresponding to the second function; is the convex conjugate function corresponding to the third function; is the convex conjugate function corresponding to the fourth function; , , are the total variation weight parameters in the x, y, and z directions respectively; , and They are the TV limits in different directions respectively.

7. The limited angle electron paramagnetic resonance imaging method based on high-order directional total variation according to claim 6, characterized in that: The nearest neighbor mapping calculation result is: In the formula, is the nearest neighbor mapping result of the convex conjugate function corresponding to the first function; is the nearest neighbor mapping result of the convex conjugate function corresponding to the second function; is the nearest neighbor mapping result of the convex conjugate function corresponding to the third function; is the nearest neighbor mapping result of the convex conjugate function corresponding to the fourth function; The fifth function The nearest neighbor mapping result; is the step size parameter.

8. The limited angle electron paramagnetic resonance imaging method based on high-order directional total variation according to claim 4, characterized in that: The convergence condition is determined based on nRMSE, NDE and NTVE, which are defined as: ( ) ( ) ( ) In the formula, is the normalized distance between the reconstructed image after n iterations of the algorithm and the image to be reconstructed; Reconstruct the image for the band; For model data With measurement data NTVE is the error between the TV value of the reconstructed image and the TV value of the true image.

9. A limited angle electron paramagnetic resonance imaging system based on high-order directional total variation, used to implement the limited angle electron paramagnetic resonance imaging method based on high-order directional total variation according to any one of claims 1 to 8, characterized in that: include: A projection data acquisition module, used to acquire sparse and limited-angle projection data of an image to be reconstructed; An optimization model construction module is used to construct an optimization model based on high-order directional total variation according to sparse and limited-angle projection data of the image to be reconstructed, and reconstruct the image to be reconstructed using the optimization model; The optimization model solving module is used to solve the optimization model by using the Chambolle-Pock solving algorithm to obtain a reconstructed electron paramagnetic resonance image.

10. A computing device, characterized in that include: One or more processors, a memory and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the one or more programs include steps for executing the limited angle electron paramagnetic resonance imaging method based on high-order directional total variation as claimed in any one of claims 1 to 8.

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