Magnetic particle imaging image reconstruction method based on min-max concave and total variation constraint

Abstract

The present application belongs to the field of magnetic particle imaging, and particularly relates to a magnetic particle imaging image reconstruction method, system and device based on a max-min concave and total variation constraint, aiming to solve the problem of large error, poor precision and low quality of the MPI image reconstructed by the existing magnetic particle imaging image reconstruction method. The method comprises: acquiring a time domain voltage signal as an input signal; performing Fourier transform on the input signal and constructing a system matrix; based on the system matrix, constructing a mapping equation between the concentration of magnetic particle imaging and the input signal after Fourier transform as a first equation; combining isotropic total variation and max-min concave constraint to reconstruct the first equation to obtain a second equation; and iteratively solving the second equation by an alternating direction multiplier method with a mixed penalty function to obtain the concentration of magnetic particle imaging and perform image reconstruction. The present application reduces the error of the reconstructed MPI image, and improves the precision and quality of the reconstructed MPI image.

Description

Technical Field

[0001] This invention belongs to the field of magnetic particle imaging, specifically relating to a magnetic particle imaging image reconstruction method, system, and device based on maxima and minima concave and total variation constraints. Background Technology

[0002] Magnetic particle imaging (MPI) is an emerging tomographic imaging technique that enables in vivo quantitative imaging of magnetic nanoparticles with high spatiotemporal resolution. Furthermore, MPI specifically images only magnetic nanoparticles, eliminating background signal interference. Therefore, the acquired signal intensity is directly proportional to the concentration of magnetic nanoparticles. This combination of high sensitivity and the ability to quantify magnetic particle concentration makes MPI a very promising imaging method for biomedical applications.

[0003] MPI image reconstruction mainly includes two methods: X-space-based reconstruction and system matrix-based reconstruction. The X-space-based method approximates the MPI imaging system as a linear time-invariant system, transforming the measured time-domain signal into the image domain, and then using gridding to obtain the distribution of magnetic particles within the target area, enabling rapid MPI imaging. However, the X-space-based reconstruction theory is derived based on a series of ideal assumptions and cannot be completely equivalent to the actual physical properties of the system and magnetic particles, resulting in slightly inferior image quality. In the system matrix-based reconstruction method, the system matrix is ​​constructed based on actual measurements, incorporating complex system characteristics and the physical properties of magnetic particles, leading to more accurate reconstruction results. Therefore, this invention proposes to use the system matrix-based reconstruction method.

[0004] Since the MPI system matrix is ​​ill-conditioned, appropriate regularization is needed to stabilize the solution. Two commonly used regularization methods are L2 regularization and fused L1 regularization, which combines Total Variation (TV) and L1 regularization. L2 regularization combined with the Kaczmarz row iterative method provides a fast solution but can lead to overly smooth reconstruction results. While fused L1 regularization can reconstruct sharper edges, it underestimates the image amplitude, hindering accurate quantification. Therefore, a suitable regularization term is needed that can reconstruct sharp edges while maintaining the amplitude of the reconstruction result. Based on this, this invention proposes a magnetic particle imaging image reconstruction method based on minimax concavity and total variation constraints. Summary of the Invention

[0005] To address the aforementioned problems in existing technologies, namely, the large errors, poor accuracy, and low quality of MPI images reconstructed by current magnetic particle imaging image reconstruction methods, this invention proposes a magnetic particle imaging image reconstruction method based on maxima and minima concavity and total variation constraints. This method includes:

[0006] S100: Acquire the time-domain voltage signal collected after the phantom model of the object to be reconstructed in the magnetic particle imaging system moves pixel by pixel in the target area and is used as the input signal.

[0007] S200, Perform a Fourier transform on the input signal and construct a system matrix based on the Fourier transformed input signal;

[0008] S300, based on the system matrix, and according to the principle of magnetic particle imaging, a mapping equation between the concentration of magnetic particles and the Fourier transform input signal is constructed as the first equation;

[0009] S400, combining isotropic total variation and maxima-minima concave constraints, the first equation is reconstructed to obtain the second equation;

[0010] S500, the second equation is solved iteratively by adding the alternating direction multiplier method of the mixed penalty function to obtain the concentration of magnetic particles corresponding to the object to be imaged and reconstructed, and then the image is reconstructed.

[0011] In some preferred embodiments, the mapping equation between the concentration of magnetic particles in imaging and the Fourier-transformed input signal is as follows:

[0012] Sc = u

[0013] Where S represents the system matrix, c represents the concentration of magnetic particle imaging, and u represents the input signal after Fourier transform.

[0014] In some preferred embodiments, the second equation is:

[0015] min c≥0 λ TV ||c|| TV +λ MC ||c|| MC

[0016] st‖Sc-u‖2≤ε

[0017] in,‖·‖ TV For isotropic total variational regularization terms, ||·|| MC For the maxima and minima concave regular terms, λ MC With λ TV ε is the weighting coefficient, ||Sc-u||2 is the data fidelity term, ε≥0, and ε is a constraint term related to the noise level.

[0018] In some preferred embodiments, the concentration of magnetic particles corresponding to the object to be reconstructed is obtained by iteratively solving the second equation using the alternating direction multiplier method with an added hybrid penalty function. The method is as follows:

[0019] The second equation is solved using the alternating direction multiplier method with an added mixed penalty function, and an intermediate variable z = [z (0) , z (1) , z (2) ] H G = [S H II] H ;

[0020] The second equation can be transformed into:

[0021] min x f1(c)+f2(z)

[0022] stPc+Qz-s=0

[0023] Where, P = G, Q = -I, s = 0, f1(c) = 0, f2(z) = ι E(ε，I，u) (z (0) )+λ TV ||c|| TV +λ MC ||c|| MC , [·] H For conjugate transpose, ι E(ε，I，u) (z 0 ) represents the indicator function for the data fidelity term, and I represents the identity matrix;

[0024] Based on the transformed second equation, combined with Lagrange multipliers Construct the augmented Lagrangian function:

[0025]

[0026] Where d is the Lagrange multiplier, β is the penalty coefficient, and M is the number of frequency points;

[0027] The iterative steps of the alternating direction multiplier method are then obtained as follows:

[0028] A1:

[0029] A2:

[0030] A3:d k+1 =d k -Gc k+1 +z k+1

[0031] Where k represents the number of iterations, z k d k Let z, d, and c represent the values ​​in the k-th iteration. k+1 z k+1 d k+1 Let c, z, and d represent the (k+1)th iteration;

[0032] The concentration of magnetic particles corresponding to the object to be imaged and reconstructed is obtained by iteratively solving A1, A2, and A3.

[0033] In some preferred embodiments, A1 is solved as follows:

[0034] Expand A1: Where i∈[0,1,2];

[0035] The solution of the expanded A1 is accelerated by using the LU decomposition method.

[0036] In some preferred embodiments, A2 is solved as follows:

[0037] Expand A2:

[0038] B1:

[0039] B2:

[0040] A3:

[0041] For problem B1, using the Moreau proximal operator, it is transformed into The form is solved using the following formula:

[0042]

[0043] For problem B2, the Chambolle projection algorithm is used to transform it into... The form is solved using the following formula:

[0044]

[0045]

[0046] Where p is the dual operator, τ is the gradient operator, div is the divergence operator, τ represents the iteration step size, and t represents the t-th iteration.

[0047] For problem B3, using the Moreau proximal operator, it is transformed into The form is solved using the following formula:

[0048]

[0049] Where Y = cd, X = c, θ is the internal parameter of the minima concave constraint.

[0050] In some preferred embodiments, A3 is solved as follows:

[0051] Expand A3 to solve for the problem. The expanded A3 is:

[0052] In a second aspect, the present invention proposes a magnetic particle imaging image reconstruction system based on maxima and minima concave and total variation constraints. The system includes: a signal acquisition module, a system matrix construction module, a first equation construction module, a second equation construction module, and an image reconstruction module.

[0053] The signal acquisition module is configured to acquire the time-domain voltage signal collected after the phantom model of the object to be reconstructed in the magnetic particle imaging system moves pixel by pixel in the target area and is used as the input signal.

[0054] The system matrix construction module is configured to perform a Fourier transform on the input signal and construct a system matrix based on the Fourier transformed input signal.

[0055] The first equation construction module is configured to construct a mapping equation between the concentration of magnetic particles and the Fourier transform input signal based on the system matrix and the principle of magnetic particle imaging, as the first equation;

[0056] The second equation construction module is configured to reconstruct the first equation by combining isotropic total variation and maxima-minima concave constraints to obtain the second equation;

[0057] The image reconstruction module is configured to iteratively solve the second equation by adding a hybrid penalty function and an alternating direction multiplier method to obtain the concentration of magnetic particles corresponding to the object to be imaged and reconstructed, and then perform image reconstruction.

[0058] A third aspect of the present invention provides an electronic device comprising: at least one processor; and a memory communicatively connected to at least one of the processors; wherein the memory stores instructions executable by the processor for implementing the above-described magnetic particle imaging image reconstruction method based on maxima and minima concave and total variation constraints.

[0059] In a fourth aspect, the present invention provides a computer-readable storage medium, characterized in that the computer-readable storage medium stores computer instructions for execution by a computer to implement the above-described magnetic particle imaging image reconstruction method based on maxima and minima concave and total variation constraints.

[0060] The beneficial effects of this invention are:

[0061] This invention reduces the error of the reconstructed MPI image and improves the accuracy and quality of the reconstructed MPI image.

[0062] This invention establishes a mathematical model for solving the inverse problem of magnetic particle imaging reconstruction, incorporates sparse non-convex constraints of isotropic total variation and unbiased estimation for reconstruction, employs the alternating direction multiplier method for iterative optimization, and accelerates the solution of sub-problems using LU decomposition, Chambolle projection, and hard thresholding to obtain the optimal magnetic particle concentration distribution for image reconstruction. Compared to the currently most commonly used L2 regularization constraint, the hybrid regularization term of isotropic total variation and minima concavity provides more obvious edge information in the reconstructed image. Compared to the TV L1 regularization term proposed by Storath, the MC non-convex regularization term can reduce the bias effect of the L1 regularization term while maintaining high sparsity, reducing the underestimation of the reconstructed amplitude by the L1 regularization term, achieving a smaller error and more accurate reconstruction effect. Attached Figure Description

[0063] Other features, objects, and advantages of this application will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings.

[0064] Figure 1 This is a schematic flowchart of a magnetic particle imaging image reconstruction method based on maxima and minima concave and total variation constraints according to an embodiment of the present invention.

[0065] Figure 2 This is a schematic diagram of the framework of a magnetic particle imaging image reconstruction system based on maxima and minima concave and total variation constraints according to an embodiment of the present invention.

[0066] Figure 3 This is an example diagram of a multi-grayscale elliptical phantom according to an embodiment of the present invention;

[0067] Figure 4 This is a schematic diagram showing the reconstruction results of the method of the present invention, the Kaczmarz method based on L2 regularization, and the fusion cable method under different signal-to-noise ratios;

[0068] Figure 5 This is a schematic diagram comparing the method of this invention with the Kaczmarz method based on L2 regularization and the fusion cable method under the NRMSE index;

[0069] Figure 6 This is a schematic diagram comparing the method of this invention with the Kaczmarz method based on L2 regularization and the fusion cable method under the PSNR index;

[0070] Figure 7 This is a schematic diagram comparing the method of this invention with the Kaczmarz method based on L2 regularization and the fusion cable method under the SSIM metric;

[0071] Figure 8 This is a schematic diagram of the structure of a computer system suitable for implementing an electronic device according to an embodiment of the present invention. Detailed Implementation

[0072] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0073] The present application will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. It should be noted that, unless otherwise specified, the embodiments and features described herein can be combined with each other.

[0074] A magnetic particle imaging image reconstruction method based on maxima and minima concave and total variation constraints according to the first embodiment of the present invention, such as... Figure 1 As shown, the method includes:

[0075] S100: Acquire the time-domain voltage signal collected after the phantom model of the object to be reconstructed in the magnetic particle imaging system moves pixel by pixel in the target area and is used as the input signal.

[0076] S200, Perform a Fourier transform on the input signal and construct a system matrix based on the Fourier transformed input signal;

[0077] S300, based on the system matrix, and according to the principle of magnetic particle imaging, a mapping equation between the concentration of magnetic particles and the Fourier transform input signal is constructed as the first equation;

[0078] S400, combining isotropic total variation and maxima-minima concave constraints, the first equation is reconstructed to obtain the second equation;

[0079] S500, the second equation is solved iteratively by adding the alternating direction multiplier method of the mixed penalty function to obtain the concentration of magnetic particles corresponding to the object to be imaged and reconstructed, and then the image is reconstructed.

[0080] To more clearly illustrate the magnetic particle imaging image reconstruction method based on maxima and minima concave and total variation constraints of the present invention, the steps of one embodiment of the method of the present invention will be described in detail below with reference to the accompanying drawings.

[0081] This invention provides a magnetic particle imaging image reconstruction method based on minimax concave and total variation constraints. It establishes a mathematical model for solving the inverse problem of magnetic particle imaging reconstruction, incorporates isotropic total variation (TV) and unbiased estimation sparse non-convex constraint terms for reconstruction, and uses the Alternating Direction Method of Multipliers (ADMM) for iterative optimization. Furthermore, it accelerates the solution of sub-problems using LU decomposition, Chambolle projection, and hard thresholding, ultimately obtaining the optimal result. Compared to the most commonly used L2 regularization constraint, the hybrid regularization term of TV and minimax concave (MC) provides more obvious edge information in the reconstructed image. Compared to the fusion regularization term combining TV and L1 proposed by Storath, the MC non-convex regularization term can reduce the bias effect of the L1 regularization term while maintaining high sparsity, reducing the underestimation of the reconstructed amplitude by the L1 regularization term and achieving a more accurate reconstruction effect. Specifically:

[0082] S100: Acquire the time-domain voltage signal collected after the phantom model of the object to be reconstructed in the magnetic particle imaging system moves pixel by pixel in the target area and is used as the input signal.

[0083] In this embodiment, a phantom model filled with magnetic nanoparticles of unit concentration (i.e., a phantom model of the object to be imaged and reconstructed) is moved pixel by pixel within the target area of ​​the magnetic particle imaging system for measurement until every pixel within the target area has been measured, and the resulting time-domain voltage signal u is saved. t .

[0084] S200, Perform a Fourier transform on the input signal and construct a system matrix based on the Fourier transformed input signal;

[0085] In this embodiment, the time-domain signal u t Perform a Fourier transform to obtain u, and arrange them in a single order to form the system matrix S∈C of this type of magnetic nanoparticle in the magnetic particle imaging system. M×N Where M is the number of frequency points and N is the number of pixels.

[0086] S300, based on the system matrix, and according to the principle of magnetic particle imaging, a mapping equation between the concentration of magnetic particles and the Fourier transform input signal is constructed as the first equation;

[0087] In this embodiment, based on the principle of magnetic particle imaging, the concentration c∈R of the magnetic particle imaging is constructed. N×1 With the measured signal u∈C M×1 The mapping equation between them:

[0088] Sc=u (1)

[0089] Where u represents the input signal after Fourier transform.

[0090] S400, combining isotropic total variation and maxima-minima concave constraints, the first equation is reconstructed to obtain the second equation;

[0091] In this embodiment, by introducing isotropic total variation and maxima-minima concave constraints into the mapping equation, the magnetic particle imaging reconstruction model (i.e., the second equation) is as follows:

[0092] min c≥0 λ TV ||c|| TV +λ MC ||c|| MC (2)

[0093] st||Sc-u||2≤ε (3)

[0094] Among them, ||·|| TV For isotropic total variational regularization terms, ||·|| MC For the maxima and minima concave regular terms, λ MC With λ TV ε is the weighting coefficient, ||Sc-u||2 is the data fidelity term, ε≥0, and ε is a constraint term related to the noise level.

[0095] S500, the second equation is solved iteratively by adding the alternating direction multiplier method of the mixed penalty function to obtain the concentration of magnetic particles corresponding to the object to be imaged and reconstructed, and then the image is reconstructed.

[0096] In this embodiment, based on the constructed second equation, the complex hybrid loss function optimization problem is decomposed into simpler subproblems using the alternating direction multiplier method. Specifically:

[0097] The second equation is solved using the alternating direction multiplier method with an added mixed penalty function, and an intermediate variable z = [z (0) , z (1) , z (2) ]H G = [S H II] H ;

[0098] The second equation can be transformed into:

[0099] min x f1(c)+f2(z) (4)

[0100] stPc+Qz-s=0 (5)

[0101] Where, P = G, Q = -I, s = 0, f1(c) = 0, f2(z) = ι E(ε，I，u) (z (0) )+λ TV ||c|| TV +λ MC ||c|| MC , [·] H For conjugate transpose, ι E(ε，I，u) (z 0 ) represents the indicator function for the data fidelity term, and I represents the identity matrix;

[0102] Based on the transformed second equation, combined with Lagrange multipliers Construct the augmented Lagrangian function:

[0103]

[0104] Where d is the Lagrange multiplier, β is the penalty coefficient, and M is the number of frequency points;

[0105] The iterative steps of the alternating direction multiplier method are then obtained as follows:

[0106] A1:

[0107] A2:

[0108] A3:d k+1 =d k -Gc k+1 +z k+1 (9)

[0109] Where k represents the number of iterations;

[0110] The method for solving A1 is as follows:

[0111] Expand A1:

[0112]

[0113] To avoid (2I+S) H S) -1The solution is obtained by directly inverting the value and then using the LU decomposition method to accelerate the solution of the expanded A1.

[0114] The method for solving A2 is as follows:

[0115] Expand A2:

[0116] B1:

[0117] B2:

[0118] B3:

[0119] For problem B1, using the Moreau proximal operator, it is transformed into The form is solved using the following formula:

[0120]

[0121] For problem B2, the Chambolle projection algorithm is used to transform it into... The form is solved using the following formula:

[0122]

[0123]

[0124] Where p is the dual operator, Here, is the gradient operator, div is the divergence operator, τ represents the iteration step size (preferably 0.248), and t represents the t-th iteration.

[0125] For problem B3, using the Moreau proximal operator, it is transformed into The form is solved using the following formula:

[0126]

[0127] Where Y = cd, X = c, θ represents the internal parameter of the minimax concave constraint. The value of θ affects the convexity of the subproblem. In order to keep the subproblem convex, we let θ = 2.

[0128] The method for solving A3 is as follows:

[0129] Expand A3 to solve for the problem. The expanded A3 is:

[0130] The concentration of magnetic particles corresponding to the object to be imaged and reconstructed is obtained by iteratively solving A1, A2, and A3.

[0131] The specific iterative loop process is as follows:

[0132] S50], Obtain parameters: Measure voltage signal System Matrix Lagrange multipliers intermediate variables Regularization parameter λ TV , λ M C, ε, β≥0, maximum number of iterations K MAx ;

[0133] S502, Initialization: d = 0, z = 0, k = 0;

[0134] S503, determine whether the set termination condition has been met or k > K. MAX If so, output Otherwise, iterate in a loop:

[0135]

[0136]

[0137]

[0138]

[0139]

[0140]

[0141]

[0142] k = k + 1.

[0143] Furthermore, to verify the method of this invention, reconstruction experiments were conducted with the most widely used L2-regularized Kaczmarz method and the state-of-the-art Fussed Lasso (FL) method proposed by Storath under different signal-to-noise ratios, and the reconstruction results were compared. In the reconstruction experiments, the following methods were selected... Figure 3 The multi-grayscale elliptical phantom shown is 51×51 pixels. The reconstruction result is as follows. Figure 4 As shown, three indicators were selected for quantitative evaluation: structural similarity (SSIM), peak signal-to-noise ratio (PSNR), and normalized root mean square error (NRMSE).

[0144] from Figure 4It can be seen that the method proposed in this invention, compared with the Kaczmarz method based on L2 regularization, ( Figure 4 L2 regularization (abbreviated as L2) can preserve more edge information and suppress noise better; compared with the fusion cable method ( Figure 4 For the purpose of fusing cables (abbreviated as fusion cable), the method of this invention provides more accurate amplitude reconstruction of the phantom with smaller errors. Figure 5 , 6 As can be seen from 7, the method of the present invention can achieve better reconstruction results by quantitatively evaluating the reconstruction results from three aspects: PSNR, SSIM, and NRMSE.

[0145] A magnetic particle imaging system for image reconstruction based on maxima and minima concave and total variation constraints according to a second embodiment of the present invention, such as... Figure 2 As shown, the system includes: a signal acquisition module 100, a system matrix construction module 200, a first equation construction module 300, a second equation construction module 400, and an image reconstruction module 500;

[0146] The signal acquisition module 100 is configured to acquire the time-domain voltage signal collected after the phantom model of the object to be reconstructed in the magnetic particle imaging system moves pixel by pixel in the target area, and use it as the input signal.

[0147] The system matrix construction module 200 is configured to perform a Fourier transform on the input signal and construct a system matrix based on the Fourier transformed input signal.

[0148] The first equation construction module 300 is configured to construct a mapping equation between the concentration of magnetic particles and the Fourier transform input signal based on the system matrix and the principle of magnetic particle imaging, as the first equation;

[0149] The second equation construction module 400 is configured to reconstruct the first equation by combining isotropic total variation and maxima-minima concave constraints to obtain the second equation;

[0150] The image reconstruction module 500 is configured to iteratively solve the second equation by adding a hybrid penalty function to obtain the concentration of magnetic particles corresponding to the object to be imaged and reconstructed, and then perform image reconstruction.

[0151] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working process and related descriptions of the system described above can be found in the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0152] It should be noted that the magnetic particle imaging image reconstruction system based on minimax and total variation constraints and / or the magnetic particle imaging system based on minimax and total variation constraints provided in the above embodiments are only illustrative examples of the above functional module division. In practical applications, the above functions can be assigned to different functional modules as needed, that is, the modules or steps in the embodiments of the present invention can be further decomposed or combined. For example, the modules in the above embodiments can be merged into one module, or further divided into multiple sub-modules to complete all or part of the functions described above. The names of the modules and steps involved in the embodiments of the present invention are only for distinguishing the various modules or steps and are not considered as an improper limitation of the present invention.

[0153] A third embodiment of the present invention provides an electronic device comprising at least one processor and a memory communicatively connected to at least one of the processors; wherein the memory stores instructions executable by the processor to implement the magnetic particle imaging image reconstruction method based on maxima and minima concave and total variation constraints as described above.

[0154] A computer-readable storage medium according to a fourth embodiment of the present invention stores computer instructions for execution by a computer to implement the magnetic particle imaging image reconstruction method based on maxima and minima concave and total variation constraints as described above.

[0155] Those skilled in the art will understand that, for the convenience and simplicity of the undescribed electronic devices and computer-readable storage media, the specific working process and related explanations can be found in the corresponding processes in the foregoing method examples, and will not be repeated here.

[0156] The following is for reference. Figure 8 It shows a schematic diagram of the structure of a computer system suitable for implementing the system, method, and device embodiments of this application. Figure 8 The server shown is merely an example and should not impose any limitations on the functionality and scope of use of the embodiments of this application.

[0157] like Figure 8As shown, the computer system includes a Central Processing Unit (CPU) 801, which can perform various appropriate actions and processes based on programs stored in Read Only Memory (ROM) 802 or programs loaded from storage section 808 into Random Access Memory (RAM) 803. RAM 803 also stores various programs and data required for system operation. The CPU 801, ROM 802, and RAM 803 are interconnected via bus 804. An Input / Output (I / O) interface 805 is also connected to bus 804.

[0158] The following components are connected to I / O interface 805: an input section 806 including a keyboard, mouse, etc.; an output section 807 including a cathode ray tube, liquid crystal display, etc., and speakers, etc.; a storage section 808 including a hard disk, etc.; and a communication section 809 including a network interface card, such as a local area network card, modem, etc. The communication section 809 performs communication processing via a network such as the Internet. A drive 810 is also connected to I / O interface 805 as needed. A removable medium 811, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., is installed on drive 810 as needed so that computer programs read from it can be installed into storage section 808 as needed.

[0159] Specifically, according to embodiments of this disclosure, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments of this disclosure include a computer program product comprising a computer program carried on a computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via communication section 809, and / or installed from removable medium 811. When the computer program is executed by CPU 801, it performs the functions defined in the methods of this application. It should be noted that the computer-readable medium described above in this application can be a computer-readable signal medium or a computer-readable storage medium, or any combination of the two. A computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of computer-readable storage media may include, but are not limited to: electrical connections having one or more wires, portable computer disks, hard disks, RAM, ROM, erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this application, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in connection with an instruction execution system, apparatus, or device. In this application, a computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A computer-readable signal medium can also be any computer-readable medium other than a computer-readable storage medium, which can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on a computer-readable medium can be transmitted using any suitable medium, including but not limited to: wireless, wire, optical fiber, etc., or any suitable combination thereof.

[0160] Computer program code for performing the operations of this application can be written in one or more programming languages ​​or a combination thereof. These programming languages ​​include object-oriented programming languages ​​such as Java, Smalltalk, and C++, as well as conventional procedural programming languages ​​such as C or similar languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0161] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0162] The terms “first”, “second”, etc., are used to distinguish similar objects, not to describe or indicate a specific order or sequence.

[0163] The term "comprising" or any other similar term is intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus / device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent in such process, method, article, or apparatus / device.

[0164] The technical solution of the present invention has been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after such changes or substitutions will all fall within the scope of protection of the present invention.

Claims

1. A magnetic particle imaging image reconstruction method based on max-min concave and total variation constraints, characterized by, The method comprises: S100, acquiring a time-domain voltage signal collected after pixel-by-pixel movement measurement of a phantom model of a to-be-reconstructed object in a target area of a magnetic particle imaging system as an input signal; S200, performing Fourier transform on the input signal, and constructing a system matrix based on the input signal after Fourier transform; S300, constructing a mapping equation between a concentration of magnetic particle imaging and the input signal after Fourier transform based on the system matrix according to a principle of magnetic particle imaging as a first equation; S400, reconstructing the first equation in combination with isotropic total variation and maximum-minimum concave constraint to obtain a second equation; S500, iteratively solving the second equation by an alternating direction multiplier method with a mixed penalty function to obtain the concentration of magnetic particle imaging corresponding to the to-be-reconstructed object, and then performing image reconstruction; The mapping equation between the concentration of magnetic particle imaging and the input signal after Fourier transform is: ； wherein, denotes a system matrix, denotes a concentration of magnetic particle imaging, denotes a Fourier transformed input signal; The second equation is: ； ； wherein, is an isotropic total variation regularizer, is a min-max concave regularizer, and is a weight coefficient, is a data fidelity term, , is a constraint term related to the noise size.

2. The magnetic particle imaging image reconstruction method based on max-min concave and total variation constraints of claim 1, wherein, The concentration of magnetic particle imaging corresponding to the to-be-reconstructed object is obtained by iteratively solving the second equation by the alternating direction multiplier method with the mixed penalty function, and the method is: solving the second equation using an alternating direction method of multipliers with an increased mixing penalty function and introducing intermediate auxiliary variables , ; The second equation is converted into: ； ； wherein , , , , , is the conjugate transpose, denotes an indicator function of a data fidelity term, denotes the identity matrix; Based on the transformed second equation, an augmented Lagrangian function is constructed by combining the Lagrange multiplier , ； wherein, is a Lagrange multiplier, is a penalty coefficient, is the number of frequency points; And then the steps of the alternating direction multiplier method iteration are as follows: ； ； ； wherein denotes the iteration number, , denotes the iteration number of the , , , , , denotes the iteration number of the , , , ; To , , iteratively solve, to obtain the concentration of the magnetic particle imaging corresponding to the object to be imaged.

3. The magnetic particle imaging image reconstruction method based on max-min concave and total variation constraints of claim 2, wherein, The method for solving is: Will Unfolding: ; wherein, ; The LU decomposition method is used to solve the expanded accelerated solution.

4. The magnetic particle imaging image reconstruction method based on max-min concave and total variation constraints of claim 2, wherein, The method for solving is: To be continued Unfolding: ； ； ； For the problem, using Moreau's proximal operator, the problem is transformed into the form, which is solved by the following equation: ； right The problem, using the Chambolle projection algorithm, is transformed into... The form is solved using the following formula: ； ； wherein, is a dual operator, is a gradient operator, is a divergence operator, denotes an iteration step size, denotes the th iteration; right The problem, using the Moreau proximal operator, is transformed into... The form is solved using the following formula: ； wherein , , , are interior parameters of the min-max concave constraint.

5. The magnetic particle imaging image reconstruction method based on max-min concave and total variation constraints of claim 2, wherein, The method for solving is: Will be solved by expansion, the expansion of is: ; ; .

6. A magnetic particle imaging image reconstruction system based on max-min concave and total variation constraints, characterized by, The system comprises a signal acquisition module, a system matrix construction module, a first equation construction module, a second equation construction module, and an image reconstruction module; The signal acquisition module is configured to acquire a time-domain voltage signal collected after pixel-by-pixel movement measurement of a phantom model of a to-be-reconstructed object in a target area of a magnetic particle imaging system as an input signal; The system matrix construction module is configured to perform Fourier transform on the input signal, and construct a system matrix based on the input signal after Fourier transform; The first equation construction module is configured to construct a mapping equation between a concentration of magnetic particle imaging and the input signal after Fourier transform based on the system matrix according to a principle of magnetic particle imaging as a first equation; The second equation construction module is configured to reconstruct the first equation in combination with isotropic total variation and maximum-minimum concave constraint to obtain a second equation; The image reconstruction module is configured to iteratively solve the second equation by an alternating direction multiplier method with a mixed penalty function to obtain the concentration of magnetic particle imaging corresponding to the to-be-reconstructed object, and then perform image reconstruction; The mapping equation between the concentration of magnetic particle imaging and the input signal after Fourier transform is: wherein denotes the system matrix, denotes the concentration of the magnetic particle imaging, denotes the Fourier transformed input signal; The second equation is: ； ； wherein, is an isotropic total variation regularizer, is a min-max concave regularizer, and is a weight coefficient, is a data fidelity term, , is a constraint term related to the noise size.

7. An electronic device, comprising: The system comprises: at least one processor; and a memory connected in communication with the at least one processor; The memory stores instructions executable by the processor, and the instructions are used to be executed by the processor to implement the magnetic particle imaging image reconstruction method based on maximum-minimum concave and total variation constraint according to any one of claims 1-5.

8. A computer-readable storage medium, characterized in that, The computer readable storage medium stores computer instructions, and the computer instructions are used to be executed by a computer to implement the magnetic particle imaging image reconstruction method based on maximum-minimum concave and total variation constraint according to any one of claims 1-5.

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