Image reconstruction method and device, computer equipment and readable storage medium

Abstract

The embodiment of the invention provides an image reconstruction method and device, computer equipment and a readable storage medium. The method comprises the following steps: acquiring a measurement matrix and an observation vector of a to-be-reconstructed image; dividing the measurement matrix into a cascade orthogonal matrix composed of a plurality of sub-matrixes, and dividing the observation vector according to the plurality of sub-matrixes to obtain a plurality of corresponding sub-distribution vectors; based on each sub-matrix and a plurality of sub-initial solutions corresponding to each sub-distribution vector, performing fusion to obtain a first initial solution corresponding to the to-be-reconstructed image; obtaining a first image sparseness estimated value of the first initial solution, and determining a first non-significant index set in the first initial solution based on the first image sparseness estimated value; and constructing a first constraint model based on the first non-significant index set, the measurement matrix and the observation vector, and performing minimum difference solution on the first constraint model to obtain a reconstruction result of the to-be-reconstructed image. Therefore, the efficiency and the accuracy of image reconstruction can be improved.

Description

Technical Field

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

[0002] Image reconstruction is one of the commonly used technologies to solve 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 many fields, including system identification, medical imaging, computer vision, signal processing, geophysics, process control, remote sensing, wireless communication, non-destructive testing and artificial intelligence. Image reconstruction technology provides strong support for technological innovation in all walks of life.

[0003] In the related art, convex optimization algorithms (such as minimum absolute shrinkage, selection operator and L1-minimization method, etc.) are generally used to reconstruct images. Convex optimization algorithms can use sparsity regularization terms to restore images. However, as the scale of image reconstruction problems continues to increase, the number of variables contained in many actual image reconstruction problems often reaches the scale of hundreds of millions, which causes convex optimization algorithms to fall into an insurmountable computational bottleneck, and then the reconstruction efficiency and reconstruction accuracy are reduced when processing 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 equipment and readable storage medium, which can improve the efficiency and accuracy of image reconstruction.

[0005] To achieve the above object, a first aspect of an embodiment of the present application provides an image reconstruction method, the method comprising:

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

[0007] Dividing the measurement matrix into a cascaded orthogonal matrix consisting of a plurality of sub-matrices, and dividing the observation vector according to the plurality of sub-matrices to obtain a plurality of sub-allocation vectors corresponding to the plurality of sub-matrices;

[0008] Determine a corresponding sub-initial solution based on each sub-matrix and each sub-allocation vector, and fuse 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] Acquire a first image sparsity estimation value of the first initial solution, and determine a first non-significant indicator set in the first initial solution based on the first image sparsity estimation value;

[0010] A first constraint model is constructed based on the first non-significant indicator set, the measurement matrix and the observation vector, and a minimization difference solution is performed on the first constraint model to obtain a reconstruction result of the image to be reconstructed.

[0011] To achieve the above-mentioned purpose, a second aspect of an embodiment of the present application provides an image reconstruction device, the device comprising:

[0012] An acquisition module, used for acquiring a measurement matrix of the image to be reconstructed, and performing 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, used for partitioning the measurement matrix into a cascaded orthogonal matrix consisting of a plurality of sub-matrices, and partitioning the observation vector according to the plurality of sub-matrices to obtain a plurality of sub-allocation vectors corresponding to the plurality of sub-matrices;

[0014] A fusion module, configured to determine a corresponding sub-initial solution based on each sub-matrix and each sub-allocation vector, and fuse a plurality of sub-initial solutions corresponding to the plurality of sub-matrices and the plurality of 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 indicator set in the first initial solution based on the first image sparsity estimation value;

[0016] A solution module is used to construct a first constraint model based on the first non-significant indicator set, the measurement matrix and the observation vector, and perform a minimum difference solution on the first constraint model to obtain a reconstruction result of the image to be reconstructed.

[0017] In some implementations, the determining module is further configured to:

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

[0019] In the first initial solution, a plurality of first solution components equal to the first extraction threshold are determined according to the absolute value of each sub-initial solution;

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

[0021] Based on the salient indicator set, a first non-salient indicator set of the first initial solution is determined.

[0022] In some embodiments, the solution module is further used to:

[0023] Minimizing the difference between the first constraint model and obtaining a first intermediate solution;

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

[0025] Determining a second non-significant indicator 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] A second constraint model is constructed based on the second non-significant indicator set, the measurement matrix and the observation vector, and the second constraint model is solved by minimizing the difference to obtain a reconstruction result of the image to be reconstructed.

[0027] In some embodiments, the image reconstruction apparatus further includes an updating module, configured to:

[0028] 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;

[0029] Determining a corresponding updated sub-initial solution 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;

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

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

[0032] Repeatedly divide 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 the corresponding updated sub-initial solution based on each sub-matrix and each updated sub-allocation vector, and merge 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 estimate of the updated second initial solution, and determine an updated third non-significant indicator set in the updated second initial solution based on the updated third image sparsity estimate; construct an updated third constraint model based on the updated third non-significant indicator set, the measurement matrix and the observation vector, and minimize the difference solution for 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 the updated reconstruction result is used as the reconstruction result of the image to be reconstructed.

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

[0034] Determining a 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 a clustering threshold, re-dividing the measurement matrix based on the distribution of the multiple invalid components to obtain multiple updated sub-matrices;

[0036] Dividing 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] Based on each updated sub-matrix and each updated sub-allocation vector, a corresponding updated sub-initial solution is determined, and multiple updated sub-initial solutions corresponding to the multiple updated sub-matrices and the multiple updated sub-allocation vectors are merged to obtain an updated first initial solution corresponding to the image to be reconstructed.

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

[0039] Acquire 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 a first sub-allocation vector based on the observation vector and a plurality of initial sub-allocation vectors;

[0041] adding the first sub-allocation vector to the allocated set, and determining a subsequent sub-allocation vector of the first sub-allocation vector based on the observation vector, the allocated set and the plurality of initial sub-allocation vectors;

[0042] Repeatingly adding the first sub-allocation vector and the subsequent sub-allocation vectors to the allocated set, and determining subsequent updated sub-allocation vectors based on the observation vector, the allocated set and the multiple initial sub-allocation vectors, until the number of the sub-allocation vectors is consistent with the number of the multiple sub-matrices.

[0043] In some embodiments, the solution module is further used to:

[0044] Acquire 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] Obtaining a first difference based on a difference between the observation vector and the first product;

[0046] A first constraint model for the first difference is constructed based on the first non-significant indicator set as a constraint condition.

[0047] To achieve the above-mentioned purpose, the third aspect of the embodiments of the present application proposes a computer device, which includes a memory and a processor, the memory stores a computer program, and the processor implements the image reconstruction method described in any one of the embodiments of the first aspect of the present application when executing the computer program.

[0048] To achieve the above-mentioned purpose, the fourth aspect of the embodiments of the present application proposes a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it implements the image reconstruction method described in any one of the embodiments of the first aspect of the present application.

[0049] The embodiment of the present application obtains the measurement matrix of the image to be reconstructed, and linearly measures the image to be reconstructed through the measurement matrix to obtain the observation vector of the image to be reconstructed; divides the measurement matrix into a cascaded orthogonal matrix composed of multiple sub-matrices, and divides the observation vector according to the multiple sub-matrices to obtain multiple sub-allocation vectors corresponding to the multiple sub-matrices; determines the corresponding sub-initial solution based on each sub-matrix and each sub-allocation vector, and fuses the multiple sub-initial solutions corresponding to the multiple sub-matrices and the multiple sub-allocation vectors to obtain the first initial solution corresponding to the image to be reconstructed; obtains the first image sparsity estimation value of the first initial solution, and determines the first non-significant indicator set in the first initial solution based on the first image sparsity estimation value; constructs a first constraint model based on the first non-significant indicator set, the measurement matrix and the observation vector, and solves the first constraint model by minimizing the difference to obtain the reconstruction result of the image to be reconstructed. In this way, a large-scale measurement matrix can be converted into a cascaded orthogonal matrix to simplify the solution process, speed up the efficiency of solving each sub-matrix, and thus speed up the efficiency of the overall solution. Furthermore, after the first initial solution is obtained by fusing multiple sub-initial solutions obtained locally, the part of the first initial solution that has little or no effect on the image can be extracted to obtain a first non-significant indicator set, and constrained projection is performed based on the non-significant indicator set, thereby ensuring that under the constraints of the non-significant indicator set, the difference between the reconstruction result and the original image is minimized, thereby improving the accuracy of image reconstruction. In summary, the present application can improve the efficiency and accuracy of image reconstruction. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0051] Figure 2 is a flow chart of an image reconstruction method provided in an embodiment of the present application;

[0052] Figure 3 is an overall flow chart of the image reconstruction method provided in the embodiment of the present application;

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

[0054] Figure 5 It is a schematic diagram of the hardware structure of the computer device provided in the embodiment of the present application. DETAILED DESCRIPTION

[0055] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with 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 the functional modules are divided in the device schematic diagram and the logical order is shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than the module division in the device or the order in the flowchart. The terms "first", "second", etc. in the specification, claims and the above drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence.

[0057] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art 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 technologies to solve 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 many fields, including system identification, medical imaging, computer vision, signal processing, geophysics, process control, remote sensing, wireless communication, non-destructive testing and artificial intelligence. Image reconstruction technology provides strong support for technological innovation in all walks of life.

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

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

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

[0062] The present application embodiment provides an image reconstruction system, please refer to Figure 1 In some implementations, the image reconstruction system includes a terminal 11 and a server 12 .

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

[0064] The server end 12 may be a cloud server, a local server, a high-performance computing cluster, a graphics processing server, etc. The server end 12 may execute a core algorithm for image reconstruction to process image data from the terminal 11, and perform preprocessing, reconstruction algorithm, post-processing, etc. on the image data, and finally generate a 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 of the present application, when it comes to the need to perform relevant processing based on data related to 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 embodiment of the present application needs to obtain the user's sensitive personal information, the user's separate permission or separate consent will be obtained through a pop-up window or by jumping to a confirmation page. After clearly obtaining the user's separate permission or separate consent, the necessary user-related data for enabling the normal operation of the embodiment of the present application will be obtained.

[0067] In the embodiments of the present application, the image reconstruction device will be described from the perspective of the image reconstruction device, which can be integrated into a computer device. Figure 2 , Figure 2 This is a flowchart of the steps of the image reconstruction method provided in the embodiment of the present application. In the embodiment of the present application, the image reconstruction device is specifically integrated on 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 : obtaining a measurement matrix of the image to be reconstructed, and performing linear measurement on the image to be reconstructed using the measurement matrix to obtain an observation vector of the image to be reconstructed.

[0069] In some embodiments, in order to effectively reconstruct an image, a linear measurement may be performed on the image to be reconstructed using a measurement matrix to obtain an 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] The image to be reconstructed may be an original image to be restored, and the image to be reconstructed may be represented by an n-dimensional vector w, where the vector w includes all pixel values ​​of the image to be reconstructed.

[0071] The measurement matrix can be an m×n matrix, where m is the dimension of the observed data, that is, the number of measurements, and 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 measurements on the image to be reconstructed w to convert high-dimensional image data into a low-dimensional space.

[0072] The observation vector may be an m-dimensional vector, which may be represented by b. The observation vector is an accurate low-dimensional representation of the image to be reconstructed w. The observation vector may be obtained by multiplying the measurement matrix and the image to be reconstructed plus the possible measurement error, i.e., b=Aw+e, where e represents the measurement interference or error, and e=0 indicates that the observation vector b is accurate, i.e., there is no measurement error.

[0073] For example, the image to be reconstructed is an 8×8 grayscale image, each pixel value is between 0 and 255, and 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, the measurement matrix A is used to perform linear measurement on the image to be reconstructed w, and the observation vector b=Aw can be obtained.

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

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

[0076] In some embodiments, for scenarios with high requirements for reconstruction speed, in order to minimize the complexity of calculation, the strategy matrix can be divided into a cascaded orthogonal matrix composed of multiple sub-matrices, and the observation vector can be adaptively divided to significantly reduce the calculation time and memory requirements, thereby achieving rapid reconstruction of the image.

[0077] The submatrix can be a small-scale matrix obtained by performing column orthogonal splitting on the original measurement matrix A. Each submatrix A j is a column orthogonal matrix, that is Where I is the identity matrix.

[0078] The cascaded orthogonal matrix can be a matrix composed of multiple column orthogonal sub-matrices, which can be formally expressed as A = [A1, A2, ..., A J ], where J>1, each A jis a sub-matrix.

[0079] Among them, the sub-allocation vector can be obtained by dividing the observation vector b and obtaining the sub-matrix A j For example, b is divided into J sub-allocation vectors b1, b2, ..., b J , so 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 divided into a cascaded orthogonal matrix composed of multiple sub-matrices, and the observation vector can be divided 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 expanded and sparse, that is, the sum of the dimensions of the image to be reconstructed w can be increased by adding 0 elements to convert the image to be reconstructed into a sparse image, and the complex image reconstruction problem can be converted into a simpler sparse optimization problem, thereby improving the quality and efficiency of image reconstruction.

[0082] It is understandable that in the field of image reconstruction, especially when faced with large-scale or high-dimensional data, using the complete measurement matrix to directly solve may result in excessive computational costs. In order to reduce computational complexity and improve algorithm efficiency, this application divides the measurement matrix into a series of smaller sub-matrices, which are column-orthogonal (i.e., the column vectors within each sub-matrix are orthogonal). The entire matrix is ​​called a cascaded orthogonal matrix. By dividing the measurement matrix into multiple sub-matrices, multiple sub-matrices can be processed in parallel to significantly reduce computing time and memory requirements.

[0083] Furthermore, after dividing the measurement matrix into a series of sub-matrices, these sub-matrices can be effectively used to process the observation vectors, so as to reasonably allocate the measurement matrix to each sub-module according to the splitting method of the measurement matrix, so as to facilitate the subsequent solution of the reconstructed image.

[0084] Exemplarily, an embodiment is used below to introduce the process of 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.

[0085] For example, if there is a 32×64 measurement matrix A, when the measurement matrix needs to be divided into two sub-blocks, the measurement matrix can be divided into two 32×32 column orthogonal sub-matrices A1 and A2, and A1 and A2 are both orthogonal matrices. In order to ensure that A1 and A2 are orthogonal matrices, QR decomposition or other methods can be used to generate orthogonal matrices. Furthermore, the present application does not limit the number of sub-matrices divided by the measurement matrix, but only needs to ensure that each sub-matrix divided is an orthogonal matrix. Without violating the concept of the present application, the number of sub-matrices divided can be determined according to the actual situation.

[0086] Furthermore, after obtaining multiple sub-matrices corresponding to the measurement matrix, the observation vector can be divided to obtain multiple sub-distribution vectors. For example, assuming that the image to be reconstructed has not been solved before, an initial reference solution x = x1, x2, ..., x J , to make a preliminary allocation of the observation vector. For example, b'1 = A1x1, b'2 = A2x2, at this time, the initial sub-allocation vector for the observation vector b can be obtained.

[0087] Furthermore, in order to ensure that the sum of the multiple sub-allocation vectors finally obtained by division is equal to the observation vector, the observation vector may be re-divided based on the initial sub-allocation vector, for example, b1=bb′2, then b2=b-b1.

[0088] That is, when updating the j+1th allocation b j+1 When the latest j updates (represented as b1, b2, ..., b j , and the remaining allocations generated by the previous iteration that have not been updated in the current observation vector b, generate the updated allocation amount of the j+1th submodule:

[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 easy to handle each sub-problem independently, thereby improving the efficiency of the calculation.

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

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

[0093] (102.2) determining a first sub-allocation vector based on the observation vector and a plurality of initial sub-allocation vectors;

[0094] (102.3) adding the first sub-allocation vector to the allocated set, and determining a subsequent sub-allocation vector of the first sub-allocation vector based on the observation vector, the allocated set and the plurality of initial sub-allocation vectors;

[0095] (102.4) Repeat adding the first sub-allocation vector and 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 consistent with the number of sub-matrices.

[0096] The reference solution may be a pre-set initial solution for initial allocation of observation vectors. The reference solution may be a pre-set evaluation value or an approximate solution based on prior knowledge. For example, the reference solution x1, x2, ..., x J Both are 0.

[0097] The initial sub-allocation vector may be a preliminary allocation of the observation vector, which is used for subsequent generation of the sub-allocation vector.

[0098] The allocated set may be a set consisting of determined sub-allocation vectors, and the sub-allocation vector generated in each iteration will be added to the allocated set.

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

[0100] Furthermore, the initial sub-allocation vector corresponding to each sub-matrix can be determined based on each sub-matrix and the reference solution. For example, A = [A1, A2, A3, A4], that is, 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 vectors can be determined. For example, the first sub-allocation vector = observation vector - the allocated vectors before the first sub-allocation vector - all unallocated vectors after the first sub-allocation vector, that is, b1 = bb′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, the subsequent sub-allocation vectors are determined. Each subsequent sub-allocation vector = observation vector - sub-allocation vectors in the allocated vector set - all 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, so that the global state changes can be considered in each update, and the allocation of 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] In the above way, the observation vector can be dynamically allocated to different sub-matrices under the premise that the information of the observation vector is complete, so that the algorithm can adapt to the changes of the local structure more flexibly and solve the problems of nonlinear or complex constraints more efficiently.

[0104] Step 103 : determining a corresponding sub-initial solution based on each sub-matrix and each sub-allocation vector, and fusing a plurality of sub-initial solutions corresponding to a plurality of sub-matrices and a plurality of sub-allocation vectors to obtain a first initial solution corresponding to the image to be reconstructed.

[0105] In some embodiments, in order to gradually approach and ultimately obtain a high-quality reconstruction of the entire image to be reconstructed, a solution can be performed based on each sub-matrix and the corresponding sub-allocation vector to obtain multiple sub-initial solutions, thereby decomposing the large problem into multiple small problems to improve the overall computational efficiency.

[0106] The sub-initial solution may be a preliminary estimated solution of the local image block obtained based on each sub-matrix and the corresponding sub-allocation vector.

[0107] The first initial solution may be a 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 ​​divided into a cascaded orthogonal matrix composed of multiple sub-matrices, and the sub-distribution vectors of the sub-matrices in the observation vector are updated in sequence, the sub-initial solution can be obtained by multiplying the transposed matrix of the sub-matrix and the corresponding sub-distribution vector. For example, for the sub-matrix (orthogonal matrix) A i , the corresponding sub-initial solution x i For 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, assuming that the image is divided into 4 4×4 orthogonal sub-matrices, so each corresponding sub-initial solution is 16-dimensional, if the sub-initial solutions are x1, x2, x3, x4, 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 solved independently to obtain a sub-initial solution, and then all sub-initial solutions are fused to improve computational efficiency and ensure the accuracy of the reconstruction results.

[0111] In some embodiments, when it is desired to generate a higher-precision reconstruction result 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 are aggregated 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 area containing important components, and high-quality image reconstruction results are obtained faster and more accurately. For example, after step 103 is executed and the first initial solution is obtained, it can also include:

[0112] (A.1) determining a 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, the measurement matrix is ​​repartitioned based on the distribution of multiple invalid components to obtain multiple updated sub-matrices;

[0114] (A.3) dividing 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 a corresponding updated sub-initial solution based on each updated sub-matrix and each updated sub-allocation vector, and fuse multiple updated sub-initial solutions corresponding to multiple updated sub-matrices and multiple updated sub-allocation vectors to obtain an 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 means that the corresponding pixel has no contribution or very little contribution to the final reconstructed image, and can be ignored to improve the efficiency of reconstruction and avoid interference with the final reconstruction result. Similarly, the valid component can be a value that is not 0 in the first initial solution.

[0117] The clustering coefficient may be used to measure the concentration of the 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] The clustering threshold may be a threshold used to evaluate whether the measurement matrix needs to be adaptively re-partitioned.

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

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

[0121]

[0122] Where n is the total number of nodes, E i is the number of edges between neighbor nodes of node i.

[0123] In some embodiments, the clustering threshold can be flexibly set according to actual conditions. 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 areas containing a large number of invalid components in the first initial solution are divided into the same area (merged into a large sub-problem), and the connected areas with valid components can be further refined into multiple areas (further refined into more sub-problems), so that computing resources can be more concentrated on areas containing important information, ensuring that each sub-problem contains enough information to obtain an accurate solution, so as to improve the efficiency and accuracy of the calculation, converge to the optimal solution faster, and improve 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 region for dividing the measurement matrix can be automatically determined. In some embodiments, the division can also be performed manually by a technician.

[0125] In some embodiments, the clustering coefficient of the first initial solution can be determined based on 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 multiple invalid components to obtain multiple updated sub-matrices, and 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, the updated first initial solution is calculated. At this time, the clustering sparsity calculation of the first initial solution continues. When the clustering coefficient is greater than the clustering threshold, the measurement matrix continues to be adaptively divided to obtain an updated first initial solution. The cycle is repeated 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. 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 actual conditions, 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 into cascaded orthogonal matrices to obtain multiple sub-matrices and the corresponding observation vectors are calculated to obtain the first initial solution. 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 the submatrix (random division or cascade orthogonal matrix division) according to the measurement matrix partition and obtaining the sub-allocation vector has been developed above and will not be repeated here. Further, after the final first initial solution is obtained according to the submatrix and the sub-allocation vector, it is assumed that the first initial solution is x:

[0131]

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

[0133] According to the effective component division, we get the submatrix A5:

[0134]

[0135] According to the effective component division, the submatrix A6 is obtained:

[0136]

[0137] The submatrix A0 is obtained by partitioning according to the invalid components:

[0138]

[0139] In some implementations, the method of dividing the measurement matrix pair is determined according to the actual situation, as long as the matrices containing 0 are merged and the matrices of the effective components are further refined. After the measurement matrix is ​​divided, the updated initial sub-allocation vector corresponding to each sub-matrix can be determined based on the first initial solution as a reference solution and the multiple updated sub-matrices obtained by the division, and then the updated sub-allocation vector is re-divided based on the observation vector and the initial sub-allocation vector. Finally, the updated sub-initial solution is calculated based on the multiple updated sub-matrices and the corresponding multiple updated sub-allocation vectors, and the multiple sub-initial solutions are merged to obtain the updated first initial solution. Furthermore, the method of dividing to obtain the sub-allocation vector has been expanded above, please refer to the above, and will not be repeated here.

[0140] In some embodiments, it can be determined whether the measurement matrix needs to be re-divided based on the connected area of ​​the connected area of ​​the invalid components in the first initial solution. For example, the connected area of ​​the connected area of ​​the invalid vector in the first initial solution can be calculated. When the number of connected areas with a connected area greater than a preset area threshold is greater than a preset number, the measurement matrix is ​​re-divided, and then the observation vector is divided, and the updated first initial solution is re-solved until the number of connected areas with a connected area greater than the preset area threshold is less than a preset number. For example, if the number of connected areas with a connected area greater than the preset area s is 1, which is less than the preset number 5, then the division of the measurement matrix can be stopped, and the last updated first initial solution can be 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 situation where the measurement matrix cannot be divided into a cascaded orthogonal matrix. In this case, the measurement matrix can be first divided by random division. After obtaining the first initial solution, the division method of the measurement matrix is ​​continued to be adjusted according to the first initial solution until the first initial solution satisfies the situation that the clustering coefficient is less than the clustering threshold.

[0142] Through the above method, invalid components that are useless for the result can be merged to save computing resources, and computing resources can be concentrated on the effective components in the first initial solution. Through the results of each iteration, the matrix can be flexibly redivided to more quickly approach the highest accuracy solution, thereby effectively reducing the scale of calculation and improving the reconstruction accuracy of important areas.

[0143] Step 104: Obtain a first image sparsity estimation value of the first initial solution, and determine a first non-salient indicator set in the first initial solution based on the first image sparsity estimation value.

[0144] In some embodiments, in order to focus on important areas more quickly, a first set of non-significant indicators in a first initial solution can be determined to identify components that have less impact on image reconstruction, thereby reducing the impact of noise interference and reducing computational complexity, thereby improving reconstruction efficiency and accuracy.

[0145] The first image sparsity estimation value may be an estimation of the number of non-zero elements (ie, significant elements) in the finally determined first initial solution, and is used to determine important components in the image to be reconstructed.

[0146] The first non-significant indicator set may be a set of pixel positions that contribute little or can be ignored to the reconstructed image. Each pixel value included in the first non-significant indicator set may be considered to carry no key information and be set to 0 during the reconstruction process.

[0147] For example, the first initial solution x=x1,x2,...,x J To obtain the first image sparsity estimate of the first initial solution. For example, an 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, and can also be dynamically adjusted based on previous knowledge or the operation of the algorithm.

[0148] Furthermore, the first non-salient indicator set may be determined based on the first image sparsity estimation value. For example, 3K components with the largest absolute values ​​may be selected based on the selected first image sparsity estimation value K, and the indexes of these components may be combined into a first salient indicator set.

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

[0150] Furthermore, the first extraction threshold may be 3 times the first image sparsity estimation value, or other multiples, such as 2 times, 4 times, etc., and is set according to actual conditions, and this application does not impose too many restrictions on this.

[0151] By means of the above method, the first initial solution can be shrunk by a wide threshold value, so as to obtain a reconstruction result of the image to be reconstructed subsequently.

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

[0153] (104.1) determining a first extraction threshold for a first initial solution based on a first image sparsity estimate;

[0154] (104.2) In the first initial solution, a plurality of first solution components equal to the first extraction threshold are determined according to the absolute value of each sub-initial solution;

[0155] (104.3) obtaining a plurality of position indexes of the plurality of first solution components in the first initial solution, and determining a first saliency indicator set of the first initial solution based on the position indexes;

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

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

[0158] The first solution component may be the elements with the largest absolute value selected from the first initial solution and equal to the first extraction threshold. The first solution component may be the most important or significant part for the final image reconstruction.

[0159] The position index may be a 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 salient indicator set can be a set formed based on the position index of the first solution component. The first salient indicator set contains the position indexes of all components that are considered to be crucial for image reconstruction. By marking multiple position indexes separately, clear target positioning can be provided 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 first image sparsity estimate K is 3, then the first extraction threshold can be set to 3K, that is, 9. Next, the first solution components with the first 9 largest absolute values ​​are arranged in descending order of absolute value, and 0.9, -0.7, 0.8, 0.6, -0.5, 0.4, -0.3, 0.2, 0.1 are obtained as the first solution components, a total of 9. Further, the position index of each first solution component in the first initial solution can be determined, and the first salient indicator set is generated based on the position index, for example, the first salient indicator set Λ can be {0, 1, 2, 3, 4, 5, 6, 7, 8} (the order of the position index in the first salient indicator set is adjustable).

[0162] Based on the first significant indicator set, the first significant indicator set can be excluded from the first initial solution to obtain the first non-significant indicator set, that is, Λ c ={9}.

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

[0164] Step 105: construct a first constraint model based on the first non-significant indicator 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.

[0165] In some embodiments, in order to improve the accuracy and efficiency of image reconstruction, a first constraint model can be constructed based on the first non-significant indicator set, the measurement matrix and the observation vector, and the first constraint model is solved by minimizing the difference to ensure that the final reconstruction result satisfies specific constraints while minimizing the difference with the observation vector.

[0166] The first constraint model can be an optimization problem established based on the first non-significant indicator set, the measurement matrix and the observation vector. The first constraint model restricts the part of the reconstruction result (i.e., the solution vector) belonging to the first non-significant indicator set to be 0, and requires that the difference between the reconstruction result and the observation vector be minimized.

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

[0168] In some implementations, by constructing the first non-significant indicator set, 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 performing a minimum difference solution, so that under the constraint of the first non-significant indicator set, the product of the measurement matrix and the reconstruction result is as close as possible to the observation vector.

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

[0170] min{‖b-Az‖2:z i =0,i∈Λ c}

[0171] Where 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 indicator set.

[0172] In some implementations, the problem of solving the first constraint model, that is, solving the orthogonal projection problem, can be solved by using an orthogonal projection method. Specifically, the least squares method can be used to obtain the reconstruction result of the image to be reconstructed.

[0173] By constructing the first constraint model and performing the minimization difference solution, the computational complexity can be reduced, and the quality and stability of the reconstruction results can be improved while ensuring sparsity.

[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 may be constructed to simplify the solution process and improve the quality of the reconstructed image. For example, the "constructing a first constraint model based on the first non-significant indicator set, the measurement matrix and the observed vector" in step 105 may include:

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

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

[0177] (105.a3) Based on the first non-significant indicator set as a constraint condition, construct a first constraint model for the first difference.

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

[0179] Exemplarily, the constructed first constraint model may be in the following form:

[0180] min{‖b-Az‖2:z i =0,i∈Λ c}

[0181] Where 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 indicator 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 indicator set, a solution z can be found to minimize the L2 norm of b-Az while satisfying the sparsity constraint, thereby ensuring the consistency of the reconstruction result with the observation vector while maintaining the sparsity of the solution.

[0183] In some embodiments, in order to further improve the quality of the solution, after a group of the most significant components have been identified by wide threshold shrinkage (based on the first extraction threshold shrinkage), the number of non-zero components can be further reduced by narrow threshold shrinkage (based on the second image sparsity estimation value shrinkage) to better capture the main features of the image and improve the overall quality of the solution. The "minimizing the difference solution for the first constraint model to obtain the reconstruction result of the image to be reconstructed" in step 105 may include:

[0184] (105.b1) Minimize the difference between the first constraint model and obtain the first intermediate solution;

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

[0186] (105.b3) determining a second non-significant indicator 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) A second constraint model is constructed based on the second non-significant indicator set, the measurement matrix and the observation vector, and the second constraint model is solved by minimizing the difference to obtain a reconstruction result of the image to be reconstructed.

[0188] The first intermediate solution may be a solution vector obtained by minimizing the difference between the first constraint model and the first constraint model.

[0189] The second image sparsity estimate may be an estimate of the number of non-zero elements (i.e., significant elements) in the first intermediate solution, and is used to further determine important components in the image to be reconstructed. In some embodiments, the second image sparsity estimate may be obtained by estimating the first initial solution or the first intermediate solution.

[0190] The second non-significant indicator set may be a set of pixel positions that contribute little or can be ignored to the reconstructed image. Each pixel value included in the second non-significant indicator set may be considered to carry no key information and be set to 0 during the reconstruction process.

[0191] The second constraint model can be an optimization problem established based on the first non-significant indicator set, the measurement matrix and the observation vector. The first constraint model restricts the part of the reconstruction result (i.e., the solution vector) belonging to the first non-significant indicator set to be 0, and requires that the difference between the reconstruction result and the observation vector 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, the first constraint model can be directly constructed based on the first non-significant indicator set, the measurement matrix and the observation vector, and the first constraint model is solved by minimizing the difference to obtain the reconstruction result of the image to be reconstructed. In another embodiment, in order to further improve sparsity and accuracy, the first constraint model can be constructed based on the first non-significant indicator set, the measurement matrix and the observation vector, and the first constraint model is solved by minimizing the difference, and then the first intermediate solution is first obtained, and then the second constraint model is further constructed according to the first intermediate solution, and the second constraint model is solved by minimizing the difference 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 indicator set by wide threshold shrinkage, a corresponding number of first solution components can be determined based on 3 times the sparsity estimation value of the first image, thereby determining the first significant indicator set based on the first solution components, and then determining the first non-significant indicator set. In the present application, a corresponding number of second solution components are determined from the first intermediate solution based on 1 times the sparsity estimation value of the second image, thereby determining the second significant indicator set based on the second classification, and then determining the second non-significant indicator set.

[0194] It can be understood that the process of constructing the second constraint model based on the second non-significant indicator set, the measurement matrix and the observation vector is the same as the process of constructing the first constraint model based on the first non-significant indicator set, the measurement matrix and the observation vector, and the only difference is in solving the constraint, specifically, the second non-significant indicator set is used as the constraint to be solved. The embodiment of the present application does not elaborate on the process of constructing the second constraint model, and the specific process can refer to the aforementioned process of constructing the first constraint model.

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

[0196] Exemplarily, the observation vector b may 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, we need to find a solution vector z such that z 1＝0 and z 3＝0 , and ‖b-Az‖2 is the smallest.

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

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

[0204] calculate calculate Solution Thus, the 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, the advantages of fast screening and precise optimization can be effectively combined. The most important components in the signal are initially retained by shrinking the wide threshold (such as 3 times the sparsity estimate of the first image), ensuring that key information is not missed, while improving the robustness and stability of the algorithm. Subsequently, a narrow threshold (such as 1 times the sparsity estimate of the second image) is used to further eliminate relatively minor or noise components, thereby gradually refining the solution and improving the sparsity and accuracy of the final reconstruction result. In this way, not only the convergence speed is accelerated, but also the understanding and adaptability of the signal structure are enhanced, and efficient image reconstruction can be achieved while ensuring the quality of the solution.

[0207] In some implementations, in order to gradually approach the real image data and avoid falling into a local minimum when solving, when the reconstruction result of the image to be reconstructed is not satisfactory, multiple iterations can be performed to gradually reduce the reconstruction error, thereby finding a better global solution. For example, after "minimizing the difference solution of the first constraint model to obtain the reconstruction result of the image to be reconstructed" in step 105, it can also include:

[0208] (B.1) 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;

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

[0210] (B.3) obtaining a third image sparsity estimation value of the second initial solution, and determining a third non-significant indicator set in the second initial solution based on the third image sparsity estimation value;

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

[0212] (B.5) Repeatedly divide 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 solution 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 estimate of the updated second initial solution, and determine an updated third non-significant indicator set in the updated second initial solution based on the updated third image sparsity estimate; construct an updated third constraint model based on the updated third non-significant indicator set, the measurement matrix and the observation vector, and minimize the difference 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 the updated reconstruction result is used as the reconstruction result of the image to be reconstructed.

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

[0214] The third image sparsity estimation value may be an estimation of the number of non-zero elements (significant elements) in the second initial solution, and is used to further determine important components in the image to be reconstructed.

[0215] The third non-significant indicator set may be a set of pixel positions determined from the second initial solution based on the third image sparsity estimation value. These positions are considered to have a small contribution to the image to be reconstructed or can be ignored, and thus may be set to 0 during the reconstruction process.

[0216] The third constraint model can be an optimization problem, which is constructed based on the third non-significant indicator set, the measurement matrix and the observation vector. The third constraint model requires that the part of the updated reconstruction result (updated solution vector z) belonging to the third non-significant indicator 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 requirement, the iteration can be continued according to the reconstruction result to obtain an updated reconstruction result until the reconstruction result meets the preset requirement, and then the iteration can be stopped to obtain a reconstructed image. For example, the preset requirement can be that the difference between the currently 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] The embodiment of the present application obtains the measurement matrix of the image to be reconstructed, and linearly measures the image to be reconstructed through the measurement matrix to obtain the observation vector of the image to be reconstructed; divides the measurement matrix into a cascaded orthogonal matrix composed of multiple sub-matrices, and divides the observation vector according to the multiple sub-matrices to obtain multiple sub-allocation vectors corresponding to the multiple sub-matrices; determines the corresponding sub-initial solution based on each sub-matrix and each sub-allocation vector, and fuses the multiple sub-initial solutions corresponding to the multiple sub-matrices and the multiple sub-allocation vectors to obtain the first initial solution corresponding to the image to be reconstructed; obtains the first image sparsity estimation value of the first initial solution, and determines the first non-significant indicator set in the first initial solution based on the first image sparsity estimation value; constructs a first constraint model based on the first non-significant indicator set, the measurement matrix and the observation vector, and solves the first constraint model by minimizing the difference to obtain the reconstruction result of the image to be reconstructed. In this way, a large-scale measurement matrix can be converted into a cascaded orthogonal matrix to simplify the solution process, speed up the efficiency of solving each sub-matrix, and thus speed up the efficiency of the overall solution. Furthermore, after the first initial solution is obtained by fusing multiple sub-initial solutions obtained locally, the part of the first initial solution that has little or no effect on the image can be extracted to obtain a first non-significant indicator set, and constrained projection is performed based on the non-significant indicator set, thereby ensuring that under the constraints of the non-significant indicator set, the difference between the reconstruction result and the original image is minimized, thereby improving the accuracy of image reconstruction. In summary, the present application can improve the efficiency and accuracy of image reconstruction.

[0222] See also Figure 4 The embodiment of the present application further provides an image reconstruction device, which can implement the above-mentioned image reconstruction method, and the image reconstruction device includes:

[0223] An acquisition module 41 is used to acquire 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;

[0224] A partitioning module 42, configured to partition the measurement matrix into a cascaded orthogonal matrix consisting of a plurality of sub-matrices, and partition the observation vector according to the plurality of sub-matrices to obtain a plurality of sub-allocation vectors corresponding to the plurality of sub-matrices;

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

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

[0227] The solving module 45 is used to construct a first constraint model based on the first non-significant indicator set, the measurement matrix and the observation vector, and perform a minimum difference solution on the first constraint model to obtain a reconstruction result of the image to be reconstructed.

[0228] The specific implementation of the image reconstruction device is basically the same as the specific implementation of the above-mentioned image reconstruction method, and will not be repeated here. On the premise of meeting the requirements of the embodiment of the present application, the image reconstruction device can also be provided with other functional modules to implement the image reconstruction method in the above-mentioned embodiment.

[0229] The embodiment of the present application also provides a computer device, the computer device includes a memory and a processor, the memory stores a computer program, and the processor implements the above-mentioned image reconstruction method when executing the computer program. The computer device can be any intelligent terminal including a tablet computer, a car computer, etc.

[0230] See also Figure 5 , Figure 5 The hardware structure of a computer device according to another embodiment is shown, and the computer device includes:

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

[0232] The memory 52 can 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 can store an operating system and other application programs. When the technical solution provided in the embodiment of this specification is implemented by software or firmware, the relevant program code is stored in the memory 52, and the processor 51 calls and executes the image reconstruction method of the embodiment of this application;

[0233] Input / output interface 53, used to implement information input and output;

[0234] The communication interface 54 is used to realize the communication interaction between the device and other devices. The communication can be realized through a wired manner (such as USB, network cable, etc.) or a wireless manner (such as mobile network, WI FI, Bluetooth, etc.);

[0235] A bus 55 that transmits information between the various components of the device (e.g., the processor 51, the memory 52, the input / output interface 53, and the communication interface 54);

[0236] The processor 51 , the memory 52 , the input / output interface 53 and the communication interface 54 are connected to each other in communication within the device via a bus 55 .

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

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

[0239] The embodiments described in the embodiments of the present application are intended to more clearly illustrate the technical solutions of the embodiments of the present application and do not constitute a limitation on the technical solutions provided in the embodiments of the present application. Those skilled in the art will appreciate that with the evolution of technology and the emergence of new application scenarios, the technical solutions provided in the embodiments of the present application are also applicable to similar technical problems.

[0240] Those skilled in the art will appreciate 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 a combination of certain steps, or different steps.

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

[0242] Those skilled in the art will appreciate that all or some of the steps in the methods disclosed above, and the functional modules / units in the systems and devices may be implemented as software, firmware, hardware, or a suitable combination thereof.

[0243] The terms "first", "second", "third", "fourth", etc. (if any) in the specification of the present application and the above-mentioned drawings 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 interchangeable where appropriate, 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 "including" and "having" and any of their variations are intended to cover non-exclusive inclusions, 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 that are 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" refer to one or more, and "plurality" refers to two or more. "And / or" is used to describe the association relationship of associated objects, indicating that three relationships may exist. For example, "A and / or B" can mean: only A exists, only B exists, and A and B exist at the same time, where A and B can be singular or plural. The character " / " generally indicates that the previous and subsequent associated objects are in an "or" relationship. "At least one of the following" or similar expressions refers to any combination of these items, including any combination of single or plural items. For example, at least 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 the several embodiments provided in 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 merely schematic. For example, the division of the above units is only a logical function division. There may be other division methods in actual implementation, such as 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 mutual coupling or direct coupling or communication connection shown or discussed can be an indirect coupling or communication connection through some interfaces, devices or units, which can be electrical, mechanical or other forms.

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

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

[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 this understanding, the technical solution of the present application is essentially 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, and the computer software product is stored in a storage medium, including multiple instructions to enable a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of various embodiments of the present application. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (Read-Only Memory, referred to as ROM), random access memory (Random Access Memory, referred to as RAM), disk or optical disk and other media that can store programs.

[0249] The preferred embodiments of the present invention are described above with reference to the accompanying drawings, but the scope of the rights of the present invention is not limited thereto. Any modification, equivalent substitution and improvement made by a person skilled in the art without departing from the scope and essence of the present invention should be within the scope of the rights of the present invention.

Claims

1. An image reconstruction method, characterized in that: The method comprises: Acquire a measurement matrix of the image to be reconstructed, and perform linear measurement on the image to be reconstructed using the measurement matrix to obtain an observation vector of the image to be reconstructed; Dividing the measurement matrix into a cascaded orthogonal matrix consisting of a plurality of sub-matrices, and dividing the observation vector according to the plurality of sub-matrices to obtain a plurality of sub-allocation vectors corresponding to the plurality of sub-matrices; Determine a corresponding sub-initial solution based on each sub-matrix and each sub-allocation vector, and fuse 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; Acquire a first image sparsity estimation value of the first initial solution, and determine a first non-significant indicator set in the first initial solution based on the first image sparsity estimation value; A first constraint model is constructed based on the first non-significant indicator set, the measurement matrix and the observation vector, and a minimization difference solution is performed on the first constraint model to obtain a reconstruction result of the image to be reconstructed.

2. The image reconstruction method according to claim 1, characterized in that: The determining of a first non-significant indicator set in the first initial solution based on the first image sparsity estimation value comprises: Determining a first extraction threshold for the first initial solution based on the first image sparsity estimation value; In the first initial solution, a plurality of first solution components equal to the first extraction threshold are determined according to the absolute value of each sub-initial solution; Acquire a plurality of position indexes of the plurality of first solution components in the first initial solution, and determine a first significant indicator set of the first initial solution based on the position indexes; Based on the salient indicator set, a first non-salient indicator set of the first initial solution is determined.

3. The image reconstruction method according to claim 2, characterized in that: The step of performing a minimization difference solution on the first constraint model to obtain a reconstruction result of the image to be reconstructed includes: Minimizing the difference between the first constraint model and obtaining 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-salient indicator set in the first intermediate solution based on the second image sparsity estimation value; A second constraint model is constructed based on the second non-significant indicator set, the measurement matrix and the observation vector, and the second constraint model is solved by minimizing the difference to obtain a reconstruction result of the image to be reconstructed.

4. The image reconstruction method according to claim 1, characterized in that: After performing the minimization difference solution on the first constraint model to obtain the reconstruction result of the image to be reconstructed, the method 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 a corresponding updated sub-initial solution 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; Acquire a third image sparsity estimation value of the second initial solution, and determine a third non-salient indicator set in the second initial solution based on the third image sparsity estimation value; constructing a third constraint model based on the third non-significant indicator set, the measurement matrix and the observation vector, and performing a minimization difference solution on the third constraint model to obtain an updated reconstruction result of the image to be reconstructed; Repeatedly divide 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 the corresponding updated sub-initial solution based on each sub-matrix and each updated sub-allocation vector, and merge 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 estimate of the updated second initial solution, and determine an updated third non-significant indicator set in the updated second initial solution based on the updated third image sparsity estimate; construct an updated third constraint model based on the updated third non-significant indicator set, the measurement matrix and the observation vector, and minimize the difference solution for 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 the updated reconstruction result is used as the reconstruction result of the image to be reconstructed.

5. The image reconstruction method according to claim 1, characterized in that: After fusing the plurality of sub-initial solutions corresponding to the plurality of sub-matrices and the plurality of sub-allocation vectors to obtain a first initial solution corresponding to the image to be reconstructed, the method further includes: Determining a 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 a clustering threshold, re-dividing the measurement matrix based on the distribution of the multiple invalid components to obtain multiple updated sub-matrices; Dividing the observation vector according to the multiple updated sub-matrices to obtain multiple updated sub-allocation vectors corresponding to the multiple updated sub-matrices; Based on each updated sub-matrix and each updated sub-allocation vector, a corresponding updated sub-initial solution is determined, and multiple updated sub-initial solutions corresponding to the multiple updated sub-matrices and the multiple updated sub-allocation vectors are merged to obtain an updated first initial solution corresponding to the image to be reconstructed.

6. The image reconstruction method according to claim 1, characterized in that: The step of dividing the observation vector according to the multiple sub-matrices to obtain multiple sub-allocation vectors corresponding to the multiple sub-matrices includes: Acquire 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 a first sub-allocation vector based on the observation vector and a plurality of initial sub-allocation vectors; adding the first sub-allocation vector to the allocated set, and determining a subsequent sub-allocation vector of the first sub-allocation vector based on the observation vector, the allocated set and the plurality of initial sub-allocation vectors; Repeatingly adding the first sub-allocation vector and the subsequent sub-allocation vectors to the allocated set, and determining subsequent updated sub-allocation vectors based on the observation vector, the allocated set and the multiple initial sub-allocation vectors, until the number of the sub-allocation vectors is consistent with the number of the multiple sub-matrices.

7. The image reconstruction method according to claim 1, characterized in that: The constructing a first constraint model based on the first non-significant indicator set, the measurement matrix and the observation vector comprises: Acquire a vector to be solved, and obtain a first product according to the product of the vector to be solved and the measurement matrix; Obtaining a first difference based on a difference between the observation vector and the first product; A first constraint model for the first difference is constructed based on the first non-significant indicator set as a constraint condition.

8. An image reconstruction device, characterized in that: The device comprises: An acquisition module, used for acquiring a measurement matrix of the image to be reconstructed, and performing 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, used for partitioning the measurement matrix into a cascaded orthogonal matrix consisting of a plurality of sub-matrices, and partitioning the observation vector according to the plurality of sub-matrices to obtain a plurality of sub-allocation vectors corresponding to the plurality of sub-matrices; A fusion module, configured to determine a corresponding sub-initial solution based on each sub-matrix and each sub-allocation vector, and fuse a plurality of sub-initial solutions corresponding to the plurality of sub-matrices and the plurality of 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 indicator set in the first initial solution based on the first image sparsity estimation value; A solution module is used to construct a first constraint model based on the first non-significant indicator set, the measurement matrix and the observation vector, and perform a minimum difference solution on the first constraint model to obtain a reconstruction result of the image to be reconstructed.

9. A computer device, characterized in that: The computer device comprises a memory and a processor, the memory stores a computer program, and the processor implements the image reconstruction method according to any one of claims 1 to 7 when executing the computer program.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the image reconstruction method according to any one of claims 1 to 7 is implemented.

Images