Image Reconstruction Method, Device, Computer Equipment and Readable Storage Medium

Abstract

An embodiment of the present application provides an image reconstruction method, apparatus, computer device, and readable storage medium. The method includes: obtaining a measurement matrix and an observation vector of an image to be reconstructed; dividing the measurement matrix into a cascaded orthogonal matrix composed of multiple sub-matrices, and dividing the observation vector according to the multiple sub-matrices to obtain corresponding multiple sub-allocation vectors; fusing based on each sub-matrix and multiple sub-initial solutions corresponding to each sub-allocation vector to obtain a first initial solution corresponding to the image to be reconstructed; obtaining a first image sparsity estimation value of the first initial solution, and determining a first non-significant index set in the first initial solution based on the first image sparsity estimation value; constructing a first constraint model based on the first non-significant index set, the measurement matrix, and the observation vector, and solving for minimizing the difference of the first constraint model to obtain a reconstruction result of the image to be reconstructed. In this way, the efficiency and accuracy of image reconstruction can be improved.

Description

Technical Field

[0001] The present application relates to the technical field of image processing, and in particular, to an image reconstruction method, apparatus, computer device, and readable storage medium. Background Art

[0002] Image reconstruction is one of the common techniques for solving many scientific and engineering problems. Through image reconstruction, many practical problems can be effectively solved. Image reconstruction technology has a wide range of applications in multiple fields, including system identification, medical imaging, computer vision, signal processing, geophysics, process control, remote sensing, wireless communication, nondestructive testing, and artificial intelligence, etc. Image reconstruction technology provides strong support for technological innovation in all walks of life.

[0003] In related technologies, generally, convex optimization algorithms (such as least absolute shrinkage and selection operator and L1-minimization method, etc.) are used to reconstruct images. Convex optimization algorithms can use sparse regularization terms to restore images. However, as the scale of the image reconstruction problem continues to increase, the number of variables included in many actual image reconstruction problems often reaches the scale of hundreds of millions, resulting in the convex optimization algorithm falling into an insurmountable computational bottleneck, and then there are problems of reduced reconstruction efficiency and reconstruction accuracy when dealing with large-scale image reconstruction. Summary of the Invention

[0004] The main purpose of the embodiments of the present application is to propose an image reconstruction method, apparatus, computer device, and readable storage medium, which can improve the efficiency and accuracy of image reconstruction.

[0005] To achieve the above object, a first aspect of the embodiments of the present application proposes an image reconstruction method, and the method includes:

[0006] Obtain a measurement matrix of the image to be reconstructed, and perform linear measurement on the image to be reconstructed through the measurement matrix to obtain an observation vector of the image to be reconstructed;

[0007] Divide the measurement matrix into a cascaded orthogonal matrix composed of multiple sub-matrices, and divide the observation vector according to the multiple sub-matrices to obtain multiple sub-allocation vectors corresponding to the multiple sub-matrices;

[0008] Determine corresponding sub-initial solutions based on each sub-matrix and each sub-allocation vector, and fuse the multiple sub-initial solutions corresponding to the multiple sub-matrices and the multiple sub-allocation vectors to obtain a first initial solution corresponding to the image to be reconstructed;

[0009] Obtain a first image sparsity estimation value of the first initial solution, and determine a first non-significant index set in the first initial solution based on the first image sparsity estimation value;

[0010] Construct a first constraint model based on the first non-significant index set, the measurement matrix, and the observation vector, and solve for the minimum difference of the first constraint model to obtain the reconstruction result of the image to be reconstructed.

[0011] To achieve the above object, a second aspect of the embodiments of the present application proposes an image reconstruction apparatus, the apparatus includes:

[0012] An acquisition module, configured to acquire a measurement matrix of an image to be reconstructed, and perform linear measurement on the image to be reconstructed through the measurement matrix to obtain an observation vector of the image to be reconstructed;

[0013] A partitioning module, configured to partition the measurement matrix into a cascaded orthogonal matrix composed of multiple sub-matrices, and partition the observation vector according to the multiple sub-matrices to obtain multiple sub-allocation vectors corresponding to the multiple sub-matrices;

[0014] A fusion module, configured to determine corresponding sub-initial solutions based on each sub-matrix and each sub-allocation vector, and fuse the multiple sub-initial solutions corresponding to the multiple sub-matrices and the multiple sub-allocation vectors to obtain a first initial solution corresponding to the image to be reconstructed;

[0015] A determination module, configured to obtain a first image sparsity estimation value of the first initial solution, and determine a first non-significant index set in the first initial solution based on the first image sparsity estimation value;

[0016] A solving module, configured to construct a first constraint model based on the first non-significant index set, the measurement matrix, and the observation vector, and solve for the minimum difference of the first constraint model to obtain the reconstruction result of the image to be reconstructed.

[0017] In some embodiments, the determination module is further configured to:

[0018] Determine a first extraction threshold for the first initial solution based on the first image sparsity estimation value;

[0019] In the first initial solution, determine a plurality of first solution components equal in number to the first extraction threshold according to the absolute values of the sub-initial solutions;

[0020] Obtain a plurality of position indexes of the plurality of first solution components in the first initial solution, and determine a first significant index set of the first initial solution based on the position indexes;

[0021] Determine a first non-significant index set of the first initial solution based on the significant index set.

[0022] In some embodiments, the solving module is further configured to:

[0023] Solve for the minimization difference of the first constraint model to obtain a first intermediate solution;

[0024] Obtain a second image sparsity estimation value of the first intermediate solution;

[0025] Determine a second non-significant index set in the first intermediate solution based on the second image sparsity estimation value; wherein, the second image sparsity estimation value is less than the first extraction threshold;

[0026] Construct a second constraint model based on the second non-significant index set, the measurement matrix, and the observation vector, and solve for the minimization difference of the second constraint model to obtain a reconstruction result of the image to be reconstructed.

[0027] In some embodiments, the image reconstruction device further includes an update module for:

[0028] Divide the observation vector according to the reconstruction result and the multiple sub-matrices to obtain multiple updated sub-allocation vectors corresponding to the multiple sub-matrices;

[0029] Determine corresponding updated sub-initial solutions based on each sub-matrix and each updated sub-allocation vector, and fuse the multiple updated sub-initial solutions to obtain a second initial solution corresponding to the image to be reconstructed;

[0030] Obtain a third image sparsity estimation value of the second initial solution, and determine a third non-significant index set in the second initial solution based on the third image sparsity estimation value;

[0031] Construct a third constraint model based on the third non-significant index set, the measurement matrix, and the observation vector, and solve for the minimization difference of the third constraint model to obtain an updated reconstruction result of the image to be reconstructed;

[0032] Repeatedly partition the observation vector according to the updated reconstruction result and the multiple sub - matrices to obtain multiple updated sub - allocation vectors corresponding to the multiple sub - matrices; determine corresponding updated sub - initial solutions based on each sub - matrix and each updated sub - allocation vector, and fuse the multiple updated sub - initial solutions to obtain an updated second initial solution corresponding to the image to be reconstructed; obtain an updated third image sparsity estimation value of the updated second initial solution, and determine an updated third non - significant index set in the updated second initial solution based on the updated third image sparsity estimation value; construct an updated third constraint model based on the updated third non - significant index set, the measurement matrix, and the observation vector, and perform a minimization - of - difference solution on the updated third constraint model to obtain an updated reconstruction result of the image to be reconstructed, until the difference between the updated reconstruction result and the previous reconstruction result is less than a preset threshold, and use the updated reconstruction result as the reconstruction result of the image to be reconstructed.

[0033] In some embodiments, the image reconstruction apparatus further includes a re - partitioning module, configured to:

[0034] Determine the clustering coefficient of the first initial solution according to the distribution of multiple invalid components in the first initial solution;

[0035] When the clustering coefficient is greater than the clustering threshold, re - partition the measurement matrix based on the distribution of the multiple invalid components to obtain multiple updated sub - matrices;

[0036] Partition the observation vector according to the multiple updated sub - matrices to obtain multiple updated sub - allocation vectors corresponding to the multiple updated sub - matrices;

[0037] Determine corresponding updated sub - initial solutions based on each updated sub - matrix and each updated sub - allocation vector, and fuse the multiple updated sub - initial solutions corresponding to the multiple updated sub - matrices and the multiple updated sub - allocation vectors to obtain an updated first initial solution corresponding to the image to be reconstructed.

[0038] In some embodiments, the partitioning module is further configured to:

[0039] Obtain a preset reference solution for the image to be reconstructed, and determine an initial sub - allocation vector corresponding to each sub - matrix based on the reference solution;

[0040] Determine the first sub - allocation vector based on the observation vector and multiple initial sub - allocation vectors;

[0041] Add the first sub - allocation vector to the allocated set, and determine subsequent sub - allocation vectors of the first sub - allocation vector based on the observation vector, the allocated set, and the multiple initial sub - allocation vectors;

[0042] Repeat adding the first sub-allocation vector and the subsequent sub-allocation vectors to the allocated set, and determine subsequent updated sub-allocation vectors based on the observation vector, the allocated set, and the multiple initial sub-allocation vectors until the number of sub-allocation vectors is the same as the number of the multiple sub-matrices.

[0043] In some embodiments, the solving module is further configured to:

[0044] Obtain a vector to be solved, and obtain a first product according to the product of the vector to be solved and the measurement matrix;

[0045] Obtain a first difference based on the difference between the observation vector and the first product;

[0046] Construct a first constraint model for the first difference based on the first non-significant index set as a constraint condition.

[0047] To achieve the above object, a third aspect of the embodiments of the present application provides a computer device, which includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, the image reconstruction method according to any one of the embodiments of the first aspect of the present application is implemented.

[0048] To achieve the above object, a fourth aspect of the embodiments of the present application provides a computer-readable storage medium, which stores a computer program, and when the computer program is executed by a processor, the image reconstruction method according to any one of the embodiments of the first aspect of the present application is implemented.

[0049] In the embodiment of the present application, a measurement matrix of an image to be reconstructed is obtained, and the image to be reconstructed is linearly measured by the measurement matrix to obtain an observation vector of the image to be reconstructed; the measurement matrix is divided into a cascaded orthogonal matrix composed of multiple sub-matrices, and the observation vector is divided according to the multiple sub-matrices to obtain multiple sub-allocation vectors corresponding to the multiple sub-matrices; a corresponding sub-initial solution is determined based on each sub-matrix and each sub-allocation vector, and the multiple sub-initial solutions corresponding to the multiple sub-matrices and the multiple sub-allocation vectors are fused to obtain a first initial solution corresponding to the image to be reconstructed; a first image sparsity estimation value of the first initial solution is obtained, and a first non-significant index set in the first initial solution is determined based on the first image sparsity estimation value; a first constraint model is constructed based on the first non-significant index set, the measurement matrix, and the observation vector, and the first constraint model is solved by minimizing the difference to obtain a reconstruction result of the image to be reconstructed. In this way, a large-scale measurement matrix can be transformed into a cascaded orthogonal matrix to simplify the solution process, accelerate the solution efficiency of each sub-matrix, and further accelerate the overall solution efficiency. Moreover, after the first initial solution is obtained by fusing multiple sub-initial solutions obtained locally, the parts that have little or no influence on the image in the first initial solution can be extracted to obtain the first non-significant index set, and constraint projection is performed according to the non-significant index set, so as to ensure that the difference between the reconstruction result and the original image is minimized under the constraint of the non-significant index set, and the accuracy of image reconstruction is improved. In summary, the present application can improve the efficiency and accuracy of image reconstruction. Description of the Drawings

[0050] Figure 1 is a schematic structural diagram of an image reconstruction system provided by an embodiment of the present application;

[0051] Figure 2 is a flowchart of an image reconstruction method provided by an embodiment of the present application;

[0052] Figure 3 is an overall flowchart of an image reconstruction method provided by an embodiment of the present application;

[0053] Figure 4 is a schematic diagram of functional modules of an image reconstruction device provided by an embodiment of the present application;

[0054] Figure 5 is a schematic hardware structure diagram of a computer device provided by an embodiment of the present application. Detailed Embodiments

[0055] In order to make the objectives, technical solutions, and advantages of the present application clearer, the present application will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0056] It should be noted that although functional modules are divided in the schematic diagram of the device and the logical sequence is shown in the flowchart, in some cases, the steps shown or described can be executed in a different module division from that in the device or a different order from that in the flowchart. Terms such as "first" and "second" in the specification, claims, and the above-mentioned drawings are used to distinguish similar objects and do not necessarily need to describe a specific order or sequence.

[0057] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which this application belongs. The terms used herein are only for the purpose of describing the embodiments of this application and are not intended to limit this application.

[0058] Image reconstruction is one of the commonly used techniques for solving many scientific and engineering problems. Through image reconstruction, many practical problems can be effectively solved. Image reconstruction technology has a wide range of applications in multiple fields, including system identification, medical imaging, computer vision, signal processing, geophysics, process control, remote sensing, wireless communication, non-destructive testing, and artificial intelligence, etc. Image reconstruction technology provides strong support for technological innovation in all walks of life.

[0059] In the related art, generally, convex optimization algorithms (such as least absolute shrinkage, selection operator, and L1-minimization method, etc.) are used to reconstruct images. Convex optimization algorithms can use sparse regularization terms to restore images. However, as the scale of the image reconstruction problem continues to increase, the number of variables included in many actual image reconstruction problems often reaches the scale of hundreds of millions, which leads to convex optimization algorithms falling into an insurmountable computational bottleneck, and then there are problems of reduced reconstruction efficiency and reconstruction accuracy when dealing with large-scale image reconstruction.

[0060] Based on this, the embodiments of this application provide an image reconstruction method, device, computer device, and readable storage medium, which can improve the efficiency and accuracy of image reconstruction.

[0061] The image reconstruction method, device, computer device, and readable storage medium provided by the embodiments of this application are specifically described through the following embodiments. First, the image reconstruction system in the embodiments of this application is described.

[0062] The embodiments of this application provide an image reconstruction system. Please refer to Figure 1 , in some embodiments, the image reconstruction system includes a terminal 11 and a server side 12.

[0063] Exemplarily, the terminal 11 can be a mobile device, a computer, an embedded device, a camera system, etc. The terminal 11 can provide a user interface that enables a user to upload images, set parameters, start a reconstruction process, etc., to achieve user interaction. The terminal 11 can also perform preliminary data processing tasks, such as preprocessing and uploading of images, and display the images returned after being reconstructed by the server side 12.

[0064] The server side 12 can be a cloud server, a local server, a high-performance computing cluster, a graphics processing server, etc. The server side 12 can execute the core algorithm for image reconstruction to process the image data from the terminal 11, and perform preprocessing, reconstruction algorithm, postprocessing, etc. on the image data, and finally generate the reconstruction result of the image data and return the reconstruction result to the terminal 11.

[0065] The image reconstruction method in the embodiments of the present application can be illustrated by the following embodiments.

[0066] It should be noted that in each specific implementation manner of the present application, when it comes to relevant processing that needs to be performed based on data related to the user identity or characteristics, such as user information, user behavior data, user historical data, and user location information, the user's permission or consent will be obtained first. Moreover, the collection, use, and processing of these data will comply with relevant laws, regulations, and standards. In addition, when the embodiments of the present application need to obtain the user's sensitive personal information, the user's separate permission or separate consent will be obtained by means of a pop-up window or jumping to a confirmation page, etc. After clearly obtaining the user's separate permission or separate consent, the necessary user-related data for enabling the embodiments of the present application to operate normally will be obtained.

[0067] In the embodiments of the present application, a description will be made from the dimension of an image reconstruction device, and the image reconstruction device can be specifically integrated in a computer device. Refer to Figure 2 , Figure 2 which is the flowchart of the steps of the image reconstruction method provided by the embodiments of the present application. In the embodiments of the present application, taking the image reconstruction device being specifically integrated in a terminal or a server as an example, when the processor on the terminal or the server executes the program instructions corresponding to the image reconstruction method, the specific process is as follows:

[0068] Step 101, obtain the measurement matrix of the image to be reconstructed, and perform linear measurement on the image to be reconstructed through the measurement matrix to obtain the observation vector of the image to be reconstructed.

[0069] In some implementation manners, in order to effectively perform image reconstruction, the image to be reconstructed can be linearly measured through the measurement matrix to obtain the observation vector of the image to be reconstructed, so as to simplify the calculation process and improve the efficiency and accuracy of the reconstruction algorithm.

[0070] Among them, the image to be reconstructed can be the original image to be restored. The image to be reconstructed can be represented by an n-dimensional vector w, and the vector w contains all the pixel values of the image to be reconstructed.

[0071] Among them, the measurement matrix can be an m×n matrix, where m is the dimension of the observed data, that is, the number of measurement times, n is the total number of pixels of the image to be reconstructed, and m is much smaller than n. The measurement matrix can be used to perform linear measurement on the image w to be reconstructed, so as to transform the high-dimensional image data into a low-dimensional space.

[0072] Among them, the observation vector can be an m-dimensional vector, which can be represented by b. The observation vector is an accurate low-dimensional representation of the image w to be reconstructed. Specifically, the observation vector can be obtained by adding the product of the measurement matrix and the image to be reconstructed and possible measurement errors, that is, b = Aw + e, where e represents measurement interference or error, and e = 0 means that the observation vector b is accurate, that is, there is no measurement error.

[0073] Exemplarily, the image to be reconstructed is an 8×8 grayscale image, and each pixel value is between 0 and 255. The image to be reconstructed is represented as a 64-dimensional vector w. Assuming that the measurement matrix is a 32×64 Gaussian random matrix, linear measurement is performed on the image w to be reconstructed through the measurement matrix A, and the observation vector b = Aw can be obtained.

[0074] Through the above method, the amount of data that needs to be stored and transmitted can be significantly reduced, so as to significantly improve the efficiency and robustness of data processing while maintaining the reconstruction quality.

[0075] Step 102: Divide the measurement matrix into a cascaded orthogonal matrix composed of multiple sub-matrices, and divide the observation vector according to the multiple sub-matrices to obtain multiple sub-allocation vectors corresponding to the multiple sub-matrices.

[0076] In some embodiments, for scenarios with high requirements for reconstruction speed, in order to minimize the computational complexity as much as possible, the policy matrix can be divided into a cascaded orthogonal matrix composed of multiple sub-matrices, and the observation vector can be adaptively divided to greatly reduce the computational time and memory requirements, so as to achieve fast image reconstruction.

[0077] Among them, the sub-matrix can be a small-scale matrix obtained by column-orthogonal splitting of the original measurement matrix A. Each sub-matrix A j is a column-orthogonal matrix, that is where I is the identity matrix.

[0078] Among them, the cascaded orthogonal matrix can be a matrix composed of multiple column-orthogonal sub-matrices, and can be formally expressed as A = [A1, A2,..., A J , where J > 1, and each A jIt is a sub - matrix.

[0079] Among them, the sub - allocation vector can be obtained by partitioning the observation vector b to get the partial observation vectors corresponding to each sub - matrix A j For example, b is partitioned into J sub - allocation vectors b1, b2,..., b J , such that b = b1 + b2 +... + b J .

[0080] It can be understood that the total number of sub - matrices should be equal to the total number of sub - allocation vectors.

[0081] In some embodiments, when the image to be reconstructed is a sparse image, the measurement matrix corresponding to the image to be reconstructed can be directly partitioned into a cascaded orthogonal matrix composed of multiple sub - matrices, and the observation vector can be partitioned according to the multiple sub - matrices to obtain multiple sub - allocation vectors corresponding to the multiple sub - matrices. When the image to be reconstructed is a non - sparse image, the image to be reconstructed can be dimension - expanded and sparsified, that is, by adding 0 elements to increase the dimension sum of the image to be reconstructed w, so as to convert the image to be reconstructed into a sparse image, and convert the complex image reconstruction problem into a simpler sparse optimization problem, thereby improving the quality and efficiency of image reconstruction.

[0082] It can be understood that in the field of image reconstruction, especially when facing large - scale or high - dimensional data, directly solving using the complete measurement matrix may lead to too high computational costs. To reduce the computational complexity and improve the algorithm efficiency, the present application partitions the measurement matrix into a series of smaller sub - matrices, and these sub - matrices are column - orthogonal (that is, the column vectors within each sub - matrix are orthogonal), and the entire matrix is called a cascaded orthogonal matrix. By partitioning the measurement matrix into multiple sub - matrices, the multiple sub - matrices can be processed in parallel to significantly reduce the computational time and memory requirements.

[0083] Furthermore, after partitioning the measurement matrix into a series of sub - matrices, these sub - matrices can be effectively utilized to process the observation vector, and according to the splitting method of the measurement matrix, the measurement matrix can be reasonably allocated to each sub - module, which is convenient for subsequent solving of the image to be reconstructed.

[0084] Exemplarily, the following uses an embodiment to introduce the process of partitioning the measurement matrix into a cascaded orthogonal matrix composed of multiple sub - matrices, and partitioning the observation vector according to the multiple sub - matrices to obtain multiple sub - allocation vectors corresponding to the multiple sub - matrices.

[0085] Exemplarily, if there is a measurement matrix A of 32×64, when the measurement matrix needs to be divided into two sub-blocks, the measurement matrix can be divided into two column-orthogonal sub-matrices A1 and A2 of 32×32, and both A1 and A2 are orthogonal matrices. To ensure that A1 and A2 are orthogonal matrices, QR decomposition or other methods can be used to generate orthogonal matrices. Further, the present application does not limit the number of sub-matrices into which the measurement matrix is divided, as long as each divided sub-matrix is an orthogonal matrix. On the premise of not violating the concept of the present application, the number of divided sub-matrices can be determined according to the actual situation.

[0086] Further, after obtaining multiple sub-matrices corresponding to the measurement matrix, the observation vector can be divided to obtain multiple sub-allocation vectors. For example, assuming that the image to be reconstructed has not been solved before, an initial reference solution x = x1, x2,..., x J can be preset to preliminarily allocate the observation vector. For example, b′1 = A1x1, b′2 = A2x2. At this time, the initial sub-allocation vectors obtained for the observation vector b can be obtained.

[0087] Further, to ensure that the sum of the multiple sub-allocation vectors finally obtained is equal to the observation vector, the observation vector can be re-divided based on the initial sub-allocation vectors. For example, b1 = b - b′2, then b2 = b - b1.

[0088] That is to say, when updating the (j + 1)-th allocation b j+1 , the latest completed j updates (respectively represented as b1, b2,..., b j , and the remaining allocations generated by the previous round of iteration that have not been updated in the current observation vector b are used to generate the update allocation amount of the (j + 1)-th sub-module:

[0089] b j+1 = b - (b1 + b2 + b j +... + b j ′ +2 + b j ′ +3 +,,, + b J ′)

[0090] By effectively splitting the measurement matrix and adopting a dynamic observation vector allocation strategy, it is convenient to independently process each sub-problem subsequently, thereby improving the calculation efficiency.

[0091] In some embodiments, in order to achieve efficient and accurate large-scale image reconstruction, the observation vector can be dynamically partitioned into multiple sub-allocation vectors corresponding to multiple sub-matrices, so as to decompose the large-scale optimization problem into multiple small-scale sub-problems, thereby significantly reducing the total computation time. For example, "partitioning the observation vector according to multiple sub-matrices to obtain multiple sub-allocation vectors corresponding to the multiple sub-matrices" in step 102 may include:

[0092] (102.1) Obtain a preset reference solution for the image to be reconstructed, and determine an initial sub-allocation vector corresponding to each sub-matrix based on the reference solution;

[0093] (102.2) Determine the first sub-allocation vector based on the observation vector and the multiple initial sub-allocation vectors;

[0094] (102.3) Add the first sub-allocation vector to the allocated set, and determine the subsequent sub-allocation vectors of the first sub-allocation vector based on the observation vector, the allocated set, and the multiple initial sub-allocation vectors;

[0095] (102.4) Repeat adding the first sub-allocation vector and the subsequent sub-allocation vectors to the allocated set, and determine the subsequent updated sub-allocation vectors based on the observation vector, the allocated set, and the multiple initial sub-allocation vectors until the number of sub-allocation vectors is the same as the number of the multiple sub-matrices.

[0096] Among them, the reference solution can be a preset initial solution for initial allocation of the observation vector. The reference solution can be a preset evaluation value or an approximate solution obtained based on prior knowledge. For example, the reference solution x1, x2,..., x J can all be 0.

[0097] Among them, the initial sub-allocation vector can be a preliminary allocation of the observation vector for subsequent generation of sub-allocation vectors.

[0098] Among them, the allocated set can be a set composed of the determined sub-allocation vectors, and the sub-allocation vectors generated in each iteration will be added to the allocated set.

[0099] Exemplarily, assuming that the image to be reconstructed has not been solved before, an initial reference solution x = x1, x2,..., x J can be preset at this time. For example, x1 = x2 =... = x J = 0 can be set to quickly perform a preliminary allocation of the observation vector.

[0100] Further, based on each sub-matrix and the reference solution, the initial sub-allocation vector corresponding to each sub-matrix can be determined. For example, A = [A1, A2, A3, A4], that is to say, the measurement matrix A is divided into 4 sub-matrices. At this time, b′1 = A1x1, b′2 = A2x2, b′3 = A3x3, b′4 = A4x4.

[0101] Specifically, after obtaining the initial sub-allocation vectors corresponding to all sub-matrices, the sub-allocation vector can be determined. For example, the first sub-allocation vector = the observation vector - the allocated vectors before the first sub-allocation vector - all the unallocated vectors after the first sub-allocation vector, that is, b1 = b - b′2 - b′3 - b′4. At this time, b1 is added to the allocated set.

[0102] When the corresponding sub-allocation vectors have not been allocated to all sub-matrices, continue to determine the subsequent sub-allocation vectors. And each subsequent sub-allocation vector = the observation vector - the sub-allocation vectors in the allocated vector set - all the unallocated vectors after the current sub-allocation vector. For example, b2 = b - b1 - b′3 - b′4, b3 = b - b1 - b2 - b44, b4 = b - b1 - b2 - b3. In this way, the global state change can be considered in each update, and the allocation of the sub-allocation vectors corresponding to all sub-matrices can be accurately completed, and the sum of all sub-allocation vectors is equal to the observation vector.

[0103] Through the above method, on the premise of complete information of the observation vector, the observation vector can be dynamically allocated to different sub-matrices, so that the algorithm can more flexibly adapt to the changes of the local structure and more efficiently solve the problems of non-linear or complex constraints.

[0104] Step 103, determine the corresponding sub-initial solution based on each sub-matrix and each sub-allocation vector, and fuse the multiple sub-initial solutions corresponding to the multiple sub-matrices and multiple sub-allocation vectors to obtain the first initial solution corresponding to the image to be reconstructed.

[0105] In some embodiments, in order to gradually approximate and finally obtain a high-quality reconstruction of the entire image to be reconstructed, the solution can be obtained according to each sub-matrix and the corresponding sub-allocation vector to obtain multiple sub-initial solutions, and then the large problem is decomposed into multiple small problems to improve the overall calculation efficiency.

[0106] Among them, the sub-initial solution can be the preliminary estimated solution of the local image block obtained based on each sub-matrix and the corresponding sub-allocation vector.

[0107] Among them, the first initial solution can be the preliminary estimated solution of the local image block obtained based on each sub-matrix and the corresponding sub-allocation vector.

[0108] Specifically, when the measurement matrix is partitioned into a cascaded orthogonal matrix composed of multiple sub-matrices, and the sub-allocation vectors of the sub-matrices in the observation vector are updated sequentially, the sub-initial solution can be obtained by multiplying the transpose matrix of the sub-matrix and the corresponding sub-allocation vector. For example, for the sub-matrix (orthogonal matrix) A i , the corresponding sub-initial solution x i is x i = (A i ) T b i .

[0109] Furthermore, the position of the sub-initial solution in the image to be reconstructed can be determined according to the position of each sub-matrix in the image to be reconstructed, that is, each sub-initial solution is spliced according to its position in the image to be reconstructed to obtain the first initial solution. Exemplarily, assume that the image is divided into 4 orthogonal sub-matrices of 4×4, so each corresponding sub-initial solution is 16-dimensional. If the sub-initial solutions are x1, x2, x3, x4 respectively, then x1, x2, x3, x4 can be spliced to form a 64-dimensional vector.

[0110] By decomposing a large-scale problem into small-scale sub-problems, each sub-problem can be independently solved to obtain a sub-initial solution, and then all sub-initial solutions are fused, which can improve the calculation efficiency and ensure the accuracy of the reconstruction result.

[0111] In some embodiments, when a higher-precision reconstruction result is desired for the image to be reconstructed, after obtaining the first initial solution, the distribution of the first initial solution can be observed. When the invalid components in the first initial solution gather, or the valid components are dense, the measurement matrix and the observation vector can be re-partitioned, so that more computing resources are used for the region containing important components, and a high-quality image reconstruction result can be obtained faster and more accurately. For example, after step 103 is executed to obtain the first initial solution, it may further include:

[0112] (A.1) Determine the clustering coefficient of the first initial solution according to the distribution of multiple invalid components in the first initial solution;

[0113] (A.2) When the clustering coefficient is greater than the clustering threshold, re-partition the measurement matrix based on the distribution of multiple invalid components to obtain multiple updated sub-matrices;

[0114] (A.3) Partition the observation vector according to the multiple updated sub-matrices to obtain multiple updated sub-allocation vectors corresponding to the multiple updated sub-matrices;

[0115] (A.4) Determine the corresponding updated sub-initial solution based on each updated sub-matrix and each updated sub-assignment vector, and fuse the multiple updated sub-initial solutions corresponding to the multiple updated sub-matrices and the multiple updated sub-assignment vectors to obtain the updated first initial solution corresponding to the image to be reconstructed.

[0116] Among them, the invalid component can be an element with a value of 0 (or close to 0) in the first initial solution. The invalid component indicates that the corresponding pixel contributes little or no contribution to the finally reconstructed image, and can be ignored to improve the reconstruction efficiency and avoid interfering with the final reconstruction result. Similarly, the valid component can be a non-zero value in the first initial solution.

[0117] Among them, the clustering coefficient can be used to measure the concentration degree of the distribution of invalid components in the first initial solution. The smaller the clustering coefficient, the more dispersed the invalid components are, and the larger the clustering coefficient, the more concentrated the invalid components are.

[0118] Among them, the clustering threshold can be a threshold used to evaluate whether it is necessary to re-partition the measurement matrix adaptively.

[0119] Exemplarily, when the invalid component is 0, the positions of the 0 values in the first initial solution can be regarded as the nodes of the image to be reconstructed. If two 0 values are adjacent, an edge is established between these two nodes to construct an invalid component distribution map representing the distribution of 0 values, and the clustering coefficient of the invalid component distribution map is calculated.

[0120] For example, for each node i, the actual number of connections E between its neighbor nodes can be calculated i and the possible maximum number of connections k i (k i -1) / 2 of the first ratio, where k i is the degree of node i, that is, the number of nodes adjacent to node i. Then, the average value of the first ratios of all nodes can be taken as the clustering coefficient C of the entire invalid component distribution map. Specifically, the calculation formula of the clustering coefficient C can be as follows:

[0121]

[0122] Among them, n is the total number of nodes, and E i is the number of edges existing between the neighbor nodes of node i.

[0123] In some embodiments, the clustering threshold can be flexibly set according to the actual situation. When the clustering coefficient is greater than the clustering threshold, it indicates that in the first initial solution, the distribution of invalid components is relatively concentrated, indicating that the previously divided sub-problems may contain a large amount of unnecessary information. At this time, the measurement matrix can be re-divided according to the distribution of the first initial solution, so that the connected regions containing a large number of invalid components in the first initial solution are divided into the same region (merged into a large sub-problem), while the connected regions with valid components can be further refined into multiple regions (further refined into more sub-problems), so that the computing resources can be more concentrated in the regions containing important information, ensuring that each sub-problem contains enough information to obtain an accurate solution, improving the computing efficiency and accuracy, converging to the optimal solution faster, and improving the quality of the reconstructed image.

[0124] In some embodiments, the distribution of invalid vectors and valid vectors in the first initial solution can also be actively identified according to the model, and the regions for dividing the measurement matrix can be automatically determined. In some embodiments, it can also be manually divided by technicians.

[0125] In some embodiments, the clustering coefficient of the first initial solution can be determined according to the distribution of multiple invalid components in the first initial solution. When the clustering coefficient is greater than the clustering threshold, the measurement matrix is re-divided based on the distribution of the multiple invalid components to obtain multiple updated sub-matrices. The observation vector is divided according to the multiple updated sub-matrices to obtain multiple updated sub-allocation vectors corresponding to the multiple updated sub-matrices. Then, based on the multiple sub-matrices and the corresponding multiple sub-allocation vectors, an updated first initial solution is calculated. At this time, continue to calculate the clustering sparsity of the first initial solution. When the clustering coefficient is greater than the clustering threshold, continue to adaptively divide the measurement matrix to obtain an updated first initial solution, and loop in turn until the clustering coefficient is less than the clustering threshold. The division of the measurement matrix can be stopped, and the last updated first initial solution is used as the final first initial solution, and the subsequent steps of obtaining the reconstruction result of the reconstructed image through the first initial solution and other data are performed according to the final first initial solution.

[0126] Exemplarily, the clustering threshold T can be set according to the actual situation. For example, it can be set to 0.5. When the calculated clustering coefficient is 0.8, it indicates that the clustering coefficient is greater than the clustering threshold, and re-division is required according to the first initial solution.

[0127] Exemplarily, it is assumed that the measurement matrix is first randomly divided or divided by a cascaded orthogonal matrix to obtain multiple sub-matrices and calculate the corresponding observation vectors, and the first initial solution is calculated. Further, the clustering threshold T can be set according to the actual situation. For example, it can be set to 0.5. When the clustering coefficient of the first initial solution is calculated to be 0.8, the measurement matrix needs to be re-divided based on the distribution of invalid components.

[0128] Measurement matrix A:

[0129]

[0130] It should be noted that the process of obtaining sub - matrices (either randomly or by partitioning a cascaded orthogonal matrix) from the measurement matrix and obtaining sub - allocation vectors has been elaborated above, so it will not be repeated here. Further, after obtaining the final first initial solution based on the sub - matrix and the sub - allocation vector, assuming the first initial solution is x:

[0131]

[0132] From the first initial solution, it can be seen that the components of the 5th and 6th columns are non - zero, and the rest of the components are 0 (invalid components). If the calculated clustering coefficient is greater than the clustering threshold of 0.5 at this time, then the measurement matrix needs to be re - partitioned according to the first initial solution. For example, the measurement matrix can be partitioned into the following sub - matrices:

[0133] Sub - matrix A5 obtained by partitioning according to valid components:

[0134]

[0135] Sub - matrix A6 obtained by partitioning according to valid components:

[0136]

[0137] Sub - matrix A0 obtained by partitioning according to invalid components:

[0138]

[0139] In some embodiments, the way of partitioning the measurement matrix pair is determined according to the actual situation. As long as the matrices containing 0 are combined and the matrices of valid components are further refined. After partitioning the measurement matrix, the first initial solution can be used as a reference solution to determine the updated initial sub - allocation vector corresponding to each sub - matrix from the multiple updated sub - matrices obtained by partitioning. Then, based on the observation vector and the initial sub - allocation vector, the updated sub - allocation vector is re - partitioned. Finally, the updated sub - initial solution is calculated according to the multiple updated sub - matrices and the corresponding multiple updated sub - allocation vectors, and the multiple sub - initial solutions are fused to obtain the updated first initial solution. Further, the way of obtaining the sub - allocation vector has been elaborated above, please refer to the above text and will not be repeated here.

[0140] In some embodiments, it is possible to determine whether it is necessary to re-partition the measurement matrix according to the connected area of the connected regions of the invalid components in the first initial solution. For example, the connected area of the connected regions of the invalid vectors in the first initial solution can be calculated. When the number of connected regions with a connected area greater than a preset area threshold is greater than a preset number, the measurement matrix is re-partitioned, and then the observation vector is partitioned, and the updated first initial solution is obtained by re-solving until the number of connected regions with a connected area greater than the preset area threshold is less than the preset number. For example, if the number of connected regions with a connected area greater than the preset area s is 1, which is less than the preset number 5, then the partitioning of the measurement matrix can be stopped, and the last updated first initial solution is used as the final first initial solution, and the subsequent steps of obtaining the reconstruction result of the reconstructed image through the first initial solution and other data are performed according to the final first initial solution.

[0141] In some embodiments, there is a case where the measurement matrix cannot be partitioned into a cascaded orthogonal matrix. At this time, the measurement matrix can be first partitioned in a random partitioning manner. After obtaining the first initial solution, the partitioning method of the measurement matrix is continuously adjusted according to the first initial solution until the obtained first initial solution satisfies the condition that the clustering coefficient is less than the clustering threshold.

[0142] Through the above method, the invalid components that are useless for the result can be merged to save computing resources, concentrate the computing resources on the effective component part in the first initial solution, and flexibly re-partition the matrix through the result of each iteration, approaching the highest-precision solution more quickly, thereby effectively reducing the computing scale and improving the reconstruction accuracy of the important regions.

[0143] Step 104, obtain the first image sparsity estimate value of the first initial solution, and determine the first non-significant index set in the first initial solution based on the first image sparsity estimate value.

[0144] In some embodiments, in order to focus on the important regions more quickly, the components that have less influence on image reconstruction can be identified by determining the first non-significant index set in the first initial solution, so as to reduce the influence of noise interference and reduce the computational complexity, and thus improve the efficiency and accuracy of reconstruction.

[0145] Among them, the first image sparsity estimate value can be an estimate of the number of non-zero elements (i.e., significant elements) in the finally determined first initial solution, and is used to determine the important components in the image to be reconstructed.

[0146] Among them, the first non-significant index set can be a set of pixel positions that contribute less or can be ignored to the image to be reconstructed. Each pixel value included in the first non-significant index set can be considered not to carry key information during the reconstruction process and is set to 0.

[0147] Exemplarily, the first image sparsity estimation value of the first initial solution can be obtained by analyzing the first initial solution \(x = x_1, x_2, \cdots, x\). J For example, a pre - estimated sparsity \(K\) can be selected, which represents the number of expected important (non - zero) components in the image to be reconstructed. The specific value of \(K\) can be set according to the characteristics of the problem and experience, or can be dynamically adjusted based on prior knowledge or the running situation of the algorithm.

[0148] Furthermore, the first non - significant index set can be determined based on the first image sparsity estimation value. For example, according to the selected first image sparsity estimation value \(K\), the \(3K\) components with the largest absolute values can be selected, and the indices of these components form a first significant index set.

[0149] Exemplarily, when the selected first extraction threshold is 3 times the first image sparsity estimation value, it means that a set of potentially important components larger than the actual sparsity is selected, that is, wide - threshold shrinkage is performed to increase the stability and fault tolerance of the algorithm. Then, the first non - significant index set is the index set of all components except the first significant index set, that is, the positions of those components that are considered not important.

[0150] Furthermore, the first extraction threshold can be 3 times the first image sparsity estimation value, or other multiples, such as 2 times, 4 times, etc., which is set according to the actual situation, and this application does not limit it too much.

[0151] Through the above method, wide - threshold shrinkage can be performed on the first initial solution to facilitate obtaining the reconstruction result of the image to be reconstructed subsequently.

[0152] In some embodiments, in order to enhance the stability of the algorithm and accelerate the image reconstruction process, "determining the first non - significant index set in the first initial solution based on the first image sparsity estimation value" in step 104 may include:

[0153] (104.1) Based on the first image sparsity estimation value, determine the first extraction threshold for the first initial solution;

[0154] (104.2) In the first initial solution, determine a plurality of first solution components equal in number to the first extraction threshold according to the absolute values of the sub - initial solutions;

[0155] (104.3) Obtain the plurality of position indices of the plurality of first solution components in the first initial solution, and based on the position indices, determine the first significant index set of the first initial solution;

[0156] (104.4) Based on the significant index set, determine the first non - significant index set of the first initial solution.

[0157] Among them, the first extraction threshold can be a threshold set according to the estimated value K of the first image sparsity, and is used to screen out the component with the largest absolute value in the first initial solution. The first extraction threshold is greater than the actual estimated value of the first image sparsity to ensure that more potentially important components are taken into account, thereby improving the stability and accuracy of the algorithm.

[0158] Among them, the first solution component can be the elements with the largest absolute values and the same number as the first extraction threshold selected from the first initial solution. The first solution component can be the most important or significant part for the final image reconstruction.

[0159] Among them, the position index can be the specific position identifier of the first solution component in the first initial solution. Each selected first solution component has a corresponding position index in the first initial solution, indicating the arrangement order of the corresponding component in the first initial solution.

[0160] Among them, the first significant index set can be a set formed based on the position indices of the first solution components. The first significant index set contains the position indices of all components considered crucial for image reconstruction. By separately marking multiple position indices, it can provide clear target positioning for subsequent processing.

[0161] Exemplarily, the first initial solution x = [0.1, -0.5, 0.2, 0.8, -0.3, 0.6, 0.4, -0.7, 0.9, 0.0], and the known or estimated value K of the first image sparsity is 3. Then the first extraction threshold can be set to 3K, that is, 9. Next, arrange in descending order of absolute value and take the first 9 components with the largest absolute values as the first solution components, obtaining 0.9, -0.7, 0.8, 0.6, -0.5, 0.4, -0.3, 0.2, 0.1 as the first solution components, a total of 9. Further, the position indices of each first solution component in the first initial solution can be determined, and a first significant index set can be generated based on the position indices. For example, the first significant index set Λ can be {0, 1, 2, 3, 4, 5, 6, 7, 8} (the order of the position indices in the first significant index set can be adjusted).

[0162] Based on the first significant index set, the first significant index set can be excluded from the first initial solution, and then the first non - significant index set can be obtained, that is, Λ c ={9}.

[0163] Through the above method, it is convenient to focus on important components in subsequent processing, effectively reducing the computational burden while maintaining or improving the quality of reconstruction.

[0164] Step 105, construct a first constraint model based on the first non - significant index set, the measurement matrix, and the observation vector, and solve for the minimum difference of the first constraint model to obtain the reconstruction result of the image to be reconstructed.

[0165] In some embodiments, to improve the accuracy and efficiency of image reconstruction, a first constraint model can be constructed based on a first non-significant index set, a measurement matrix, and an observation vector, and the minimization of differences can be solved for the first constraint model to ensure that the finally obtained reconstruction result satisfies specific constraint conditions while minimizing the difference from the observation vector.

[0166] Among them, the first constraint model can be an optimization problem established according to the first non-significant index set, the measurement matrix, and the observation vector. The first constraint model restricts that the part of the reconstruction result (i.e., the solution vector) belonging to the first non-significant index set must be 0, and at the same time requires the difference between the reconstruction result and the observation vector to be minimized.

[0167] Among them, the reconstruction result can be an image vector obtained by solving the first constraint model. The reconstruction result is the best estimate of the image to be reconstructed.

[0168] In some embodiments, by constructing the first non-significant index set, the unimportant components in the first initial solution can be determined, that is, the elements at these positions should be 0. Therefore, the reconstruction result can be obtained by constructing the first constraint model and solving the minimization of differences, so that under the constraint of considering the first non-significant index set, the product of the measurement matrix and the reconstruction result is as close as possible to the observation vector.

[0169] Exemplarily, the constructed first constraint model can be as follows:

[0170] min{‖b - Az‖2: z i = 0, i ∈ Λ c}

[0171] Among them, b represents the observation vector, A represents the measurement matrix, z represents the reconstruction result to be solved, and Λ c represents the first non-significant index set.

[0172] In some embodiments, to solve the problem of the first constraint model, that is, to solve the orthogonal projection problem, the above first constraint model can be solved by the orthogonal projection method. Specifically, the least squares method can be used to solve the reconstruction result of the image to be reconstructed.

[0173] By constructing the first constraint model and solving the minimization of differences, the computational complexity can be reduced, and while ensuring sparsity, the quality and stability of the reconstruction result can be improved.

[0174] In some embodiments, in order to minimize the error between the observed data and the product of the measurement matrix and the unknown vector under given constraints, a first constraint model can be constructed to simplify the solution process and improve the quality of the reconstructed image. For example, "constructing a first constraint model based on the first non-significant index set, the measurement matrix, and the observed vector" in step 105 can include:

[0175] (105.a1) Obtain the vector to be solved, and obtain a first product according to the product of the vector to be solved and the measurement matrix;

[0176] (105.a2) Obtain a first difference based on the difference between the observed vector and the first product;

[0177] (105.a3) Construct a first constraint model for the first difference based on the first non-significant index set as a constraint condition.

[0178] Wherein, the vector to be solved can be a preliminary estimated value, and the vector to be solved can be a vector based on prior information or a randomly initialized vector. By continuously optimizing and solving the first constraint model, the solution of the vector to be solved can be obtained, that is, the reconstruction result of the image to be reconstructed.

[0179] Exemplarily, the form of the constructed first constraint model can be as follows:

[0180] min{‖b - Az‖2: z i = 0, i ∈ Λ c}

[0181] Wherein, b represents the observed vector, A represents the measurement matrix, z represents the reconstruction result to be solved, and Λ c represents the first non-significant index set, Az represents the first product, and b - Az represents the first difference.

[0182] By restricting the first constraint model through the first non-significant index set, while satisfying the sparsity constraint, a solution z can be found to minimize the L2 norm of b - Az, thereby ensuring the consistency between the reconstruction result and the observed vector while maintaining the sparsity of the solution.

[0183] In some embodiments, in order to further improve the quality of the solution, after the wide threshold shrinkage (shrinkage based on the first extraction threshold) has identified a set of the most significant components, the narrow threshold shrinkage (shrinkage based on the second image sparsity estimate) can be used to further reduce the number of non-zero components to better capture the main features of the image and improve the overall quality of the solution. "Performing a minimization difference solution on the first constraint model to obtain the reconstruction result of the image to be reconstructed" in step 105 can include:

[0184] (105.b1) Minimize the difference of the first constraint model to obtain a first intermediate solution;

[0185] (105.b2) Obtain the second image sparsity estimation value of the first intermediate solution;

[0186] (105.b3) Determine the second non-significant index set in the first intermediate solution based on the second image sparsity estimation value; wherein, the second image sparsity estimation value is less than the first extraction threshold;

[0187] (105.b4) Construct a second constraint model based on the second non-significant index set, the measurement matrix, and the observation vector, and minimize the difference of the second constraint model to obtain the reconstruction result of the image to be reconstructed.

[0188] Wherein, the first intermediate solution can be a solution vector obtained by minimizing the difference of the first constraint model.

[0189] Wherein, the second image sparsity estimation value can be an estimation of the number of non-zero elements (i.e., significant elements) in the first intermediate solution, which is used to further determine the important components in the image to be reconstructed. In some embodiments, the second image sparsity estimation value can be estimated from the first initial solution or obtained from the first intermediate solution.

[0190] Wherein, the second non-significant index set can be a set of pixel positions that contribute less or can be ignored to the image to be reconstructed. Each pixel value included in the second non-significant index set can be considered not to carry key information during the reconstruction process and is set to 0.

[0191] Wherein, the second constraint model can be an optimization problem established according to the first non-significant index set, the measurement matrix, and the observation vector. The first constraint model restricts that the part of the reconstruction result (i.e., the solution vector) belonging to the first non-significant index set must be 0, and at the same time requires the difference between the reconstruction result and the observation vector to be minimized.

[0192] In some embodiments, in order to quickly obtain the reconstruction result of the image to be reconstructed, only wide threshold shrinkage can be performed, that is, a first constraint model can be directly constructed based on the first non-significant index set, the measurement matrix, and the observation vector, and the difference of the first constraint model can be minimized to obtain the reconstruction result of the image to be reconstructed. In another embodiment, in order to further improve sparsity and accuracy, after constructing a first constraint model based on the first non-significant index set, the measurement matrix, and the observation vector and minimizing the difference of the first constraint model to obtain a first intermediate solution, a second constraint model can be further constructed according to the first intermediate solution, and the difference of the second constraint model can be minimized to obtain the reconstruction result of the image to be reconstructed.

[0193] In some embodiments, in order to gradually improve the sparsity and accuracy of the solution, for example, in the process of determining the first non-significant index set by wide threshold shrinkage, the corresponding number of first solution components may be determined based on three times the estimated value of the first image sparsity, so as to determine the first significant index set according to the first solution components, and then determine the first non-significant index set. In this application, the corresponding number of second solution components is determined from the first intermediate solution based on one times the estimated value of the second image sparsity, so as to determine the second significant index set according to the second solution components, and then determine the second non-significant index set.

[0194] It can be understood that for the process of constructing the second constraint model based on the second non-significant index set, the measurement matrix, and the observation vector, it is the same as the process of constructing the first constraint model based on the first non-significant index set, the measurement matrix, and the observation vector, except for the difference in the solution constraints, specifically, taking the second non-significant index set as the solution constraint. The embodiments of this application do not elaborate on the process of constructing the second constraint model, and specifically, reference may be made to the aforementioned process of constructing the first constraint model.

[0195] Next, an example of minimizing the difference of the second constraint model to obtain the reconstruction result of the image to be reconstructed is given. Similarly, the process of solving the first constraint model can also refer to the following example.

[0196] Exemplarily, the observation vector b can be:

[0197] b = [1, 2, 3] T

[0198] The observation matrix A can be:

[0199]

[0200] The second non-significant index set Λ c = {1, 3}.

[0201] When solving the second constraint model, a solution vector z needs to be found such that z 1＝0 and z 3＝0 , and ‖b - Az‖2 is minimized.

[0202] At this time, only the second column is retained because Λ = {2}, and the matrix

[0203] Furthermore, the least squares problem can be solved:

[0204] Calculate Calculate Solve Thus, a complete solution vector z is constructed as the reconstruction result of the image to be reconstructed:

[0205] z = [0, 0.387, 0] T

[0206] By first performing a wide-threshold shrinkage on the first initial solution to obtain the first intermediate solution corresponding to the first constraint model, and then performing a narrow-threshold shrinkage on the first intermediate solution to obtain the reconstruction result of the image to be reconstructed corresponding to the second constraint model, it is possible to effectively combine the advantages of rapid screening and precise optimization. By means of wide-threshold shrinkage (such as 3 times the first image sparsity estimate value), the most important components in the signal are initially retained to ensure that key information is not missed, while enhancing the robustness and stability of the algorithm. Subsequently, the narrow threshold (such as 1 time the second image sparsity estimate value) is used to further eliminate relatively unimportant or noise components, thereby gradually refining the solution and improving the sparsity and accuracy of the final reconstruction result. In this way, not only is the convergence speed accelerated, but also the understanding and adaptability of the signal structure are enhanced, enabling efficient image reconstruction while ensuring the quality of the solution.

[0207] In some embodiments, in order to gradually approach the real image data and avoid falling into local minima during the solution process, when the reconstruction result of the image to be reconstructed currently being solved is not satisfactory, multiple iterations can be performed to gradually reduce the reconstruction error, thereby finding a better global solution. For example, after "performing a minimization difference solution on the first constraint model to obtain the reconstruction result of the image to be reconstructed" in step 105, the following may further be included:

[0208] (B.1) Divide the observation vector according to the reconstruction result and multiple submatrices to obtain multiple updated sub-allocation vectors corresponding to the multiple submatrices;

[0209] (B.2) Determine the corresponding updated sub-initial solutions based on each submatrix and each updated sub-allocation vector, and fuse the multiple updated sub-initial solutions to obtain the second initial solution corresponding to the image to be reconstructed;

[0210] (B.3) Obtain the third image sparsity estimate value of the second initial solution, and determine the third non-significant index set in the second initial solution based on the third image sparsity estimate value;

[0211] (B.4) Construct a third constraint model based on the third non-significant index set, the measurement matrix, and the observation vector, and perform a minimization difference solution on the third constraint model to obtain the updated reconstruction result of the image to be reconstructed;

[0212] (B.5) Repeatedly partition the observation vector according to the updated reconstruction result and multiple sub - matrices to obtain multiple updated sub - allocation vectors corresponding to the multiple sub - matrices; determine the corresponding updated sub - initial solutions based on each sub - matrix and each updated sub - allocation vector, and fuse the multiple updated sub - initial solutions to obtain the updated second initial solution corresponding to the image to be reconstructed; obtain the updated third image sparsity estimate value of the updated second initial solution, and determine the updated third non - significant index set in the updated second initial solution based on the updated third image sparsity estimate value; construct an updated third constraint model based on the updated third non - significant index set, the measurement matrix, and the observation vector, and solve the updated third constraint model for minimizing the difference to obtain the updated reconstruction result of the image to be reconstructed, until the difference between the updated reconstruction result and the previous reconstruction result is less than a preset threshold, and take the updated reconstruction result as the reconstruction result of the image to be reconstructed.

[0213] Among them, the second initial solution can be a new iterative solution of the image to be reconstructed obtained by partitioning the observation vector into multiple updated sub - allocation vectors according to the reconstruction result of the previous iteration and multiple sub - matrices, then determining the updated sub - initial solutions based on each sub - matrix and the corresponding updated sub - allocation vector, and fusing the multiple sub - initial solutions.

[0214] Among them, the third image sparsity estimate value can be an estimate of the number of non - zero elements (significant elements) in the second initial solution, which is used to further determine the important components in the image to be reconstructed.

[0215] Among them, the third non - significant index set can be a set of pixel position collections determined from the second initial solution based on the third image sparsity estimate value. These positions are considered to contribute less or can be ignored to the image to be reconstructed, so they can be set to 0 during the reconstruction process.

[0216] Among them, the third constraint model can be an optimization problem constructed based on the third non - significant index set, the measurement matrix, and the observation vector. The third constraint model requires that the part of the updated reconstruction result (the updated solution vector z) belonging to the third non - significant index set must be 0, and minimizes the difference between the reconstruction result and the observation vector.

[0217] In some embodiments, when the reconstruction result does not meet the preset requirements, the iteration can be continued based on the reconstruction result to obtain an updated reconstruction result until the reconstruction result meets the preset requirements, and then the iteration can be stopped to obtain the reconstructed image. For example, the preset requirement can be that the difference between the current updated reconstruction result and the reconstruction result obtained in the previous iteration process is less than a preset threshold. For example, the preset threshold can be 10 -5, the iteration can be stopped and the reconstruction result of the image to be reconstructed can be output. Alternatively, a clarity threshold can be set. When the clarity of the image corresponding to the currently updated reconstruction result is less than the clarity threshold, the iteration can be stopped and the reconstruction result of the image to be reconstructed can be output. Alternatively, an iteration number threshold can be set. When the current reconstruction number reaches the iteration number threshold, the iteration can be stopped and the reconstruction result of the image to be reconstructed can be output. The iteration number threshold can be set to 6 times, 10 times, etc.

[0218] Please refer to Figure 3 In some embodiments, since the submatrix corresponding to the measurement matrix is usually predetermined and remains unchanged during the entire reconstruction process, it describes the linear transformation relationship from the original signal space to the observation vector. Therefore, it is not necessary to re-divide the measurement matrix into multiple submatrices in each iteration. However, since the sub-allocation vector corresponding to the observation vector is determined based on the solution of the image to be reconstructed, it is necessary to re-divide the observation vector to improve the accuracy of image reconstruction.

[0219] In some implementations, the process of dividing the observation vector according to the reconstruction result and the multiple sub-matrices to obtain multiple updated sub-allocation vectors is the same as the aforementioned process of dividing the sub-allocation vectors. The present application embodiment does not elaborate on the process of dividing to obtain multiple updated sub-allocation vectors, and specific reference may be made to the aforementioned process of dividing the sub-allocation vectors.

[0220] Based on each sub-matrix and each updated sub-allocation vector, the corresponding updated sub-initial solution is determined, and multiple updated sub-initial solutions are fused to obtain a second initial solution corresponding to the image to be reconstructed, and a third image sparsity estimate of the second initial solution is obtained. Based on the third image sparsity estimate, a third non-significant indicator set in the second initial solution is determined, and a third constraint model is constructed based on the third non-significant indicator set, the measurement matrix and the observation vector, and the third constraint model is solved by minimizing the difference. The process of obtaining an updated reconstruction result of the image to be reconstructed is the same as the aforementioned process of constructing the first constraint model, constructing the second constraint model, and solving the first constraint model and the second constraint model. The embodiment of the present application does not elaborate on the process of solving the third constraint model. For details, please refer to the aforementioned processing process of solving the first constraint model and solving the second constraint model.

[0221] In an embodiment of the present application, a measurement matrix of an image to be reconstructed is obtained, and the image to be reconstructed is linearly measured by the measurement matrix to obtain an observation vector of the image to be reconstructed; the measurement matrix is divided into a cascaded orthogonal matrix composed of multiple sub-matrices, and the observation vector is divided according to the multiple sub-matrices to obtain multiple sub-allocation vectors corresponding to the multiple sub-matrices; a corresponding sub-initial solution is determined based on each sub-matrix and each sub-allocation vector, and the multiple sub-initial solutions corresponding to the multiple sub-matrices and the multiple sub-allocation vectors are fused to obtain a first initial solution corresponding to the image to be reconstructed; a first image sparsity estimation value of the first initial solution is obtained, and a first non-significant index set in the first initial solution is determined based on the first image sparsity estimation value; a first constraint model is constructed based on the first non-significant index set, the measurement matrix, and the observation vector, and the first constraint model is solved by minimizing the difference to obtain a reconstruction result of the image to be reconstructed. In this way, a large-scale measurement matrix can be transformed into a cascaded orthogonal matrix to simplify the solution process, accelerate the solution efficiency of each sub-matrix, and further accelerate the overall solution efficiency. Moreover, after the first initial solution is obtained by fusing multiple sub-initial solutions obtained locally, parts that have little or no influence on the image in the first initial solution can be extracted to obtain a first non-significant index set, and constraint projection is performed according to the non-significant index set, so as to ensure that the difference between the reconstruction result and the original image is minimized under the constraint of the non-significant index set, and improve the accuracy of image reconstruction. In summary, the present application can improve the efficiency and accuracy of image reconstruction.

[0222] Please refer to Figure 4 , an embodiment of the present application further provides an image reconstruction device that can implement the above image reconstruction method. The image reconstruction device includes:

[0223] An acquisition module 41, configured to acquire a measurement matrix of an image to be reconstructed, and linearly measure the image to be reconstructed by the measurement matrix to obtain an observation vector of the image to be reconstructed;

[0224] A division module 42, configured to divide the measurement matrix into a cascaded orthogonal matrix composed of multiple sub-matrices, and divide the observation vector according to the multiple sub-matrices to obtain multiple sub-allocation vectors corresponding to the multiple sub-matrices;

[0225] A fusion module 43, configured to determine a corresponding sub-initial solution based on each sub-matrix and each sub-allocation vector, and fuse the multiple sub-initial solutions corresponding to the multiple sub-matrices and the multiple sub-allocation vectors to obtain a first initial solution corresponding to the image to be reconstructed;

[0226] A determination module 44, configured to obtain a first image sparsity estimation value of the first initial solution, and determine a first non-significant index set in the first initial solution based on the first image sparsity estimation value;

[0227] A solution module 45, configured to construct a first constraint model based on a first non-significant index set, a measurement matrix, and an observation vector, and perform a minimization difference solution on the first constraint model to obtain a reconstruction result of the image to be reconstructed.

[0228] The specific implementation manner of this image reconstruction apparatus is basically the same as the specific embodiments of the above image reconstruction method, and will not be elaborated here. On the premise of meeting the requirements of the embodiments of this application, other functional modules may be set in the image reconstruction apparatus to implement the image reconstruction method in the above embodiments.

[0229] Embodiments of this application further provide a computer device, which includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, the above image reconstruction method is implemented. This computer device may be any intelligent terminal including a tablet computer, an in-vehicle computer, etc.

[0230] Please refer to Figure 5 , Figure 5 , which schematically shows the hardware structure of a computer device in another embodiment. The computer device includes:

[0231] A processor 51, which may be implemented by using a general-purpose CPU (Central Processing Unit), a microprocessor, an application-specific integrated circuit (ASIC), or one or more integrated circuits, etc., and is configured to execute relevant programs to implement the technical solutions provided by the embodiments of this application;

[0232] A memory 52, which may be implemented in the form of a read-only memory (ROM), a static storage device, a dynamic storage device, or a random access memory (RAM). The memory 52 may store an operating system and other application programs. When implementing the technical solutions provided by the embodiments of this specification through software or firmware, the relevant program codes are stored in the memory 52, and the processor 51 is called to execute the image reconstruction method of the embodiments of this application;

[0233] An input / output interface 53, configured to implement information input and output;

[0234] A communication interface 54, configured to implement communication interaction between this device and other devices, and may implement communication through a wired manner (such as USB, network cable, etc.) or through a wireless manner (such as a mobile network, WI FI, Bluetooth, etc.);

[0235] The bus 55 transmits information among various components of the device (such as the processor 51, the memory 52, the input / output interface 53, and the communication interface 54).

[0236] Among them, the processor 51, the memory 52, the input / output interface 53, and the communication interface 54 achieve communication connections with each other inside the device through the bus 55.

[0237] The embodiment of the present application also provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the above image reconstruction method is implemented.

[0238] As a non-transitory computer-readable storage medium, the memory can be used to store non-transitory software programs and non-transitory computer-executable programs. In addition, the memory can include high-speed random access memory, and can also include non-transitory memory, such as at least one magnetic disk storage device, a flash memory device, or other non-transitory solid-state storage devices. In some embodiments, the memory can optionally include a memory remotely set relative to the processor, and these remote memories can be connected to the processor through a network. Examples of the above networks include, but are not limited to, the Internet, an enterprise intranet, a local area network, a mobile communication network, and combinations thereof.

[0239] The embodiments described in the embodiments of the present application are for more clearly illustrating the technical solutions of the embodiments of the present application, and do not constitute a limitation on the technical solutions provided by the embodiments of the present application. Those skilled in the art can know that with the evolution of technology and the emergence of new application scenarios, the technical solutions provided by the embodiments of the present application are equally applicable to similar technical problems.

[0240] Those skilled in the art can understand that the technical solutions shown in the figures do not constitute a limitation on the embodiments of the present application, and may include more or fewer steps than shown in the figures, or combine certain steps, or different steps.

[0241] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separated, that is, they may be located in one place, or may be distributed to multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0242] Those of ordinary skill in the art can understand that all or some of the steps in the methods disclosed above, and the functional modules / units in the systems and devices can be implemented as software, firmware, hardware, and appropriate combinations thereof.

[0243] In the description of the present application and the above-mentioned drawings, the terms "first", "second", "third", "fourth", etc. (if any) are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged under appropriate circumstances so that the embodiments of the present application described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "comprising" and "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device comprising a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0244] It should be understood that in the present application, "at least one (item)" and "several" mean one or more, and "a plurality" means two or more. "And / or" is used to describe the association relationship of associated objects and indicates that there can be three relationships. For example, "A and / or B" can mean: only A exists, only B exists, and both A and B exist at the same time. Among them, A and B can be singular or plural. The character " / " generally means that the associated objects before and after are in an "or" relationship. "At least one (one) of the following" or a similar expression means any combination of these items, including any combination of single items (ones) or plural items (ones). For example, at least one (one) of a, b or c can mean: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, c can be single or multiple.

[0245] In several embodiments provided by the present application, it should be understood that the disclosed systems and methods can be implemented in other ways. For example, the system embodiments described above are only illustrative. For example, the above-mentioned division of units is only a logical function division. In actual implementation, there can be other division methods. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the displayed or discussed coupling or direct coupling or communication connection between each other can be through some interfaces, and the indirect coupling or communication connection of devices or units can be in an electrical, mechanical or other form.

[0246] The units described above as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they can be located in one place or distributed to multiple network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0247] In addition, in each embodiment of the present application, each functional unit can be integrated into one processing unit, or each unit can exist physically alone, or two or more units can be integrated into one unit. The above-mentioned integrated unit can be implemented in the form of hardware or in the form of a software functional unit.

[0248] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of the present application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes multiple instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods in each embodiment of the present application. The aforementioned storage medium includes: various media that can store programs, such as USB flash drives, mobile hard disks, read-only memories (ROM), random access memories (RAM), magnetic disks, or optical discs.

[0249] The preferred embodiments of the embodiments of the present application have been described above with reference to the accompanying drawings, but this does not limit the scope of the rights of the embodiments of the present application. Any modifications, equivalent replacements, and improvements made by those skilled in the art without departing from the scope and essence of the embodiments of the present application shall be within the scope of the rights of the embodiments of the present application.

Claims

1. An image reconstruction method, characterized in that, The method includes: Obtaining a measurement matrix of the image to be reconstructed, and linearly measuring the image to be reconstructed through the measurement matrix to obtain an observation vector of the image to be reconstructed; Dividing the measurement matrix into a cascaded orthogonal matrix composed of multiple sub-matrices, and dividing the observation vector according to the multiple sub-matrices to obtain multiple sub-allocation vectors corresponding to the multiple sub-matrices; Determining corresponding sub-initial solutions based on each sub-matrix and each sub-allocation vector, and fusing the multiple sub-initial solutions corresponding to the multiple sub-matrices and the multiple sub-allocation vectors to obtain a first initial solution corresponding to the image to be reconstructed; Obtaining a first image sparsity estimation value of the first initial solution, and determining a first non-significant index set in the first initial solution based on the first image sparsity estimation value; Wherein, determining the first non-significant index set in the first initial solution based on the first image sparsity estimation value includes: determining a first extraction threshold for the first initial solution based on the first image sparsity estimation value; in the first initial solution, determining a plurality of first solution components equal in number to the first extraction threshold according to the absolute values of the sub-initial solutions; obtaining a plurality of position indexes of the plurality of first solution components in the first initial solution, and determining a first significant index set of the first initial solution based on the position indexes; determining a first non-significant index set of the first initial solution based on the significant index set; Constructing a first constraint model based on the first non-significant index set, the measurement matrix and the observation vector, and solving the first constraint model for minimizing the difference to obtain a reconstruction result of the image to be reconstructed.

2. The image reconstruction method according to claim 1, wherein The solving the first constraint model for minimizing the difference to obtain a reconstruction result of the image to be reconstructed includes: Solving the first constraint model for minimizing the difference to obtain a first intermediate solution; Obtaining a second image sparsity estimation value of the first intermediate solution; wherein, the second image sparsity estimation value is less than the first extraction threshold; Determining a second non-significant index set in the first intermediate solution based on the second image sparsity estimation value; Constructing a second constraint model based on the second non-significant index set, the measurement matrix and the observation vector, and solving the second constraint model for minimizing the difference to obtain a reconstruction result of the image to be reconstructed.

3. The image reconstruction method according to claim 1, characterized in that After the solving the first constraint model for minimizing the difference to obtain a reconstruction result of the image to be reconstructed, it further includes: Dividing the observation vector according to the reconstruction result and the multiple sub-matrices to obtain multiple updated sub-allocation vectors corresponding to the multiple sub-matrices; Determining corresponding updated sub-initial solutions based on each sub-matrix and each updated sub-allocation vector, and fusing the multiple updated sub-initial solutions to obtain a second initial solution corresponding to the image to be reconstructed; Obtaining a third image sparsity estimation value of the second initial solution, and determining a third non-significant index set in the second initial solution based on the third image sparsity estimation value; Construct a third constraint model based on the third non-significant index set, the measurement matrix, and the observation vector, and solve for the minimization of differences of the third constraint model to obtain an updated reconstruction result of the image to be reconstructed; Repeat the steps of partitioning the observation vector according to the updated reconstruction result and the multiple sub-matrices to obtain multiple updated sub-allocation vectors corresponding to the multiple sub-matrices; determine corresponding updated sub-initial solutions based on each sub-matrix and each updated sub-allocation vector, and fuse the multiple updated sub-initial solutions to obtain an updated second initial solution corresponding to the image to be reconstructed; obtain an updated third image sparsity estimation value of the updated second initial solution, and determine an updated third non-significant index set in the updated second initial solution based on the updated third image sparsity estimation value; construct an updated third constraint model based on the updated third non-significant index set, the measurement matrix, and the observation vector, and solve for the minimization of differences of the updated third constraint model to obtain an updated reconstruction result of the image to be reconstructed, until the difference between the updated reconstruction result and the previous reconstruction result is less than a preset threshold, and use the updated reconstruction result as the reconstruction result of the image to be reconstructed.

4. The image reconstruction method according to claim 1, wherein After fusing the multiple sub-initial solutions corresponding to the multiple sub-matrices and the multiple sub-allocation vectors to obtain a first initial solution corresponding to the image to be reconstructed, it further includes: Determine the clustering coefficient of the first initial solution according to the distribution of multiple invalid components in the first initial solution; When the clustering coefficient is greater than the clustering threshold, re-partition the measurement matrix based on the distribution of the multiple invalid components to obtain multiple updated sub-matrices; Partition the observation vector according to the multiple updated sub-matrices to obtain multiple updated sub-allocation vectors corresponding to the multiple updated sub-matrices; Determine corresponding updated sub-initial solutions based on each updated sub-matrix and each updated sub-allocation vector, and fuse the multiple updated sub-initial solutions corresponding to the multiple updated sub-matrices and the multiple updated sub-allocation vectors to obtain an updated first initial solution corresponding to the image to be reconstructed.

5. The image reconstruction method according to claim 1, characterized in that The step of partitioning the observation vector according to the multiple sub-matrices to obtain multiple sub-allocation vectors corresponding to the multiple sub-matrices includes: Obtain a preset reference solution for the image to be reconstructed, and determine an initial sub-allocation vector corresponding to each sub-matrix based on the reference solution; Determine the first sub-allocation vector based on the observation vector and the multiple initial sub-allocation vectors; Add the first sub-allocation vector to the allocated set, and determine the subsequent sub-allocation vectors of the first sub-allocation vector based on the observation vector, the allocated set, and the multiple initial sub-allocation vectors; Repeat adding the first sub-allocation vector and the subsequent sub-allocation vectors to the allocated set, and determine the subsequent updated sub-allocation vectors based on the observation vector, the allocated set, and the multiple initial sub-allocation vectors until the number of sub-allocation vectors is the same as the number of the multiple sub-matrices.

6. The image reconstruction method according to claim 1, wherein Constructing a first constraint model based on the first non-significant index set, the measurement matrix, and the observation vector includes: Obtaining a vector to be solved, and obtaining a first product according to the product of the vector to be solved and the measurement matrix; Obtaining a first difference based on the difference between the observation vector and the first product; Constructing a first constraint model for the first difference based on the first non-significant index set as a constraint condition.

7. An image reconstruction device, characterized in that, The device includes: An acquisition module, configured to acquire a measurement matrix of an image to be reconstructed, and perform linear measurement on the image to be reconstructed through the measurement matrix to obtain an observation vector of the image to be reconstructed; A partitioning module, configured to partition the measurement matrix into a cascaded orthogonal matrix composed of multiple sub-matrices, and partition the observation vector according to the multiple sub-matrices to obtain multiple sub-allocation vectors corresponding to the multiple sub-matrices; A fusion module, configured to determine corresponding sub-initial solutions based on each sub-matrix and each sub-allocation vector, and fuse the multiple sub-initial solutions corresponding to the multiple sub-matrices and the multiple sub-allocation vectors to obtain a first initial solution corresponding to the image to be reconstructed; A determination module, configured to obtain a first image sparsity estimation value of the first initial solution, and determine a first non-significant index set in the first initial solution based on the first image sparsity estimation value; Wherein, determining the first non-significant index set in the first initial solution based on the first image sparsity estimation value includes: determining a first extraction threshold for the first initial solution based on the first image sparsity estimation value; in the first initial solution, determining multiple first solution components equal in number to the first extraction threshold according to the absolute values of the sub-initial solutions; obtaining multiple position indexes of the multiple first solution components in the first initial solution, and determining a first significant index set of the first initial solution based on the position indexes; determining the first non-significant index set of the first initial solution based on the significant index set; A solution module, configured to construct a first constraint model based on the first non-significant index set, the measurement matrix, and the observation vector, and perform a minimization difference solution on the first constraint model to obtain a reconstruction result of the image to be reconstructed.

8. A computer device, characterized in that, The computer device includes a memory and a processor, the memory stores a computer program, and when the processor executes the computer program, the image reconstruction method according to any one of claims 1 to 6 is implemented.

9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, the image reconstruction method according to any one of claims 1 to 6 is implemented.

Images