Image reconstruction method, apparatus, equipment, and medium based on cooperative block term tensor decomposition.

Abstract

This invention discloses an image reconstruction method, apparatus, device, and medium based on cooperative block term tensor decomposition, relating to the field of signal processing technology. The method includes: decomposing the original tensor into a sum of multiple low-rank terms; decomposing each low-rank term based on a cooperative block term tensor to obtain a low-rank decomposition model of the original tensor, wherein the N mode factor matrices of each low-rank term are represented by shared factor matrices and independent factor matrices; constructing a reconstruction task model based on the low-rank decomposition model, and solving the reconstruction task model using an optimization algorithm to obtain solutions for each factor matrix; substituting the solutions of each factor matrix into the low-rank decomposition model to obtain the reconstructed image. This invention improves the reconstruction effect by enabling different low-dimensional terms to interact through a shared factor mechanism, while significantly reducing computational resources.

Description

Technical Field

[0001] This invention relates to the field of signal processing technology, and in particular to image reconstruction methods, apparatus, devices and media based on cooperative block term tensor decomposition. Background Technology

[0002] Tensor decomposition is one of the core tools in high-dimensional signal processing. Block term tensor decomposition (BTD), as an important tensor model, decomposes a tensor into the sum of multiple low-rank block terms, which can effectively characterize different physical components or structural features in data and shows stronger representational power than CP or Tucker decomposition in tasks such as image reconstruction.

[0003] However, existing block term tensor decomposition techniques have significant drawbacks: Traditional BTD treats each block term as an independent component, and its factor matrices are unrelated between different terms. This approach ignores the potential intrinsic connections and synergistic effects between different components, resulting in insufficient ability of the model to capture potential shared structures in complex signals, thus limiting further improvement in its reconstruction accuracy. Secondly, BTD requires simultaneous optimization of the factor matrices and core tensors of multiple low-rank terms. Its accompanying algorithms (such as alternating least squares) have high computational complexity and consume huge resources, making it difficult to apply to large-scale, high-dimensional real-world scene data, such as high-resolution videos and medical images, which seriously hinders the practical application and promotion of this technology. Summary of the Invention

[0004] This invention provides an image reconstruction method, apparatus, device, and medium based on cooperative block tensor decomposition, which solves the problems that existing block tensor decomposition techniques cannot enable different terms to interact with each other, and have huge computational resource requirements, making it difficult to handle large-scale high-dimensional signal reconstruction.

[0005] This invention is achieved through the following technical solution:

[0006] A first aspect of the present invention provides an image reconstruction method based on cooperative block term tensor decomposition, comprising:

[0007] Obtain the original tensor, which is the image data to be reconstructed;

[0008] The original tensor is decomposed into a sum of multiple low-rank terms, and each low-rank term is decomposed based on a cooperating block term tensor to obtain a low-rank decomposition model of the original tensor.

[0009] The decomposition method based on the cooperating block term tensor is as follows: each low-rank term is represented as the product of N factor matrices and the core tensor along the N patterns of the original tensor, where the nth factor matrix is ​​represented as the product of the nth shared factor matrix and the nth independent factor matrix, n∈[1,N]; the nth shared factor matrix uses the same parameters in all low-rank terms;

[0010] A reconstruction task model is constructed based on the low-rank decomposition model, and the reconstruction task model is solved by an optimization algorithm to obtain the solutions of each factor matrix.

[0011] Substituting the solutions of each factor matrix into the low-rank decomposition model yields the reconstructed image.

[0012] Furthermore, N≥2.

[0013] Furthermore, the low-rank decomposition model of the original tensor is expressed as:

[0014]

[0015] in, For the original tensor, Let r be the core tensor of the r-th low-rank term. , , These represent the shared factor matrices for the three modes, , , Let R represent the independent factor matrices of the three modes of the r-th low-rank term, where R is the number of terms. , , Represent the first and second edges along the tensor, respectively. Each pattern is multiplied by a matrix.

[0016] Furthermore, constructing a reconstruction task model based on the low-rank decomposition model includes: constructing a corresponding reconstruction task model according to the type of reconstruction task;

[0017] The reconstruction task model includes a fidelity term and a regularization term; the fidelity term is configured according to the task type and is used to measure the consistency between the reconstructed image and the original tensor; the regularization term is constructed based on the low-rank decomposition model of the original tensor.

[0018] Furthermore, the types of reconstruction tasks include denoising, interpolation, source separation, and blind deconvolution.

[0019] Furthermore, the optimization algorithms include the proximal alternating minimization algorithm, the alternating direction multiplier method, the alternating least squares method, and the Adam algorithm.

[0020] Furthermore, the shared factor matrix is ​​a single-layer matrix.

[0021] A second aspect of the present invention provides an image reconstruction apparatus based on cooperative block term tensor decomposition, comprising:

[0022] The data acquisition module is used to acquire the original tensor, which is the image data to be reconstructed;

[0023] The block term tensor decomposition module is used to decompose the original tensor into a sum of multiple low-rank terms, and to decompose each low-rank term based on the collaborative block term tensor to obtain the low-rank decomposition model of the original tensor.

[0024] The decomposition method based on the cooperating block term tensor is as follows: each low-rank term is represented as the product of N factor matrices and the core tensor along the N patterns of the original tensor, where the nth factor matrix is ​​represented as the product of the nth shared factor matrix and the nth independent factor matrix, n∈[1,N]; the nth shared factor matrix uses the same parameters in all low-rank terms;

[0025] The model solving module is used to construct a reconstruction task model based on the low-rank decomposition model, and solve the reconstruction task model through an optimization algorithm to obtain the solutions of each factor matrix;

[0026] The reconstruction output module is used to substitute the solutions of each factor matrix into the low-rank decomposition model to obtain the reconstructed image.

[0027] A third aspect of the present invention provides an electronic device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the image reconstruction method based on cooperative block term tensor decomposition as described in any one of the first aspects of the present invention.

[0028] A fourth aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the image reconstruction method based on cooperative block term tensor decomposition as described in any one of the first aspects of the present invention.

[0029] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0030] This invention improves upon traditional block term tensor decomposition by introducing a learnable shared factor matrix. As a common term of all low-rank terms, the shared factor matrix can automatically learn and establish the interactions and dependencies between different components, thereby more accurately mining the intrinsic structure of high-dimensional signals and significantly improving the quality of reconstructed images (with higher PSNR and SSIM indices compared to existing tensor decomposition techniques).

[0031] The shared factor matrix projects the original high-dimensional data into a low-dimensional latent space, enabling subsequent block decomposition to be performed in the low-dimensional space. This greatly reduces the number of parameters to be optimized and the computational complexity, allowing the present invention to efficiently process large-scale high-dimensional signals and solving the bottleneck problem of the traditional BTD method having huge computational resource requirements and being difficult to put into practical use. Attached Figure Description

[0032] To more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly described below. It should be understood that the following drawings only show some embodiments of the present invention and should not be considered as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort. In the drawings:

[0033] Figure 1 This is a schematic diagram of the block term tensor decomposition technique;

[0034] Figure 2 This is a flowchart of a high-dimensional signal reconstruction method based on cooperative block term tensor decomposition;

[0035] Figure 3 This is a schematic diagram of the collaborative block term tensor decomposition technique;

[0036] Figure 4 This is a comparison of the multispectral image reconstruction results based on cooperable block term tensor decomposition and block term tensor decomposition;

[0037] Figure 5 This is a comparison chart of the visual effects of different tensor decomposition techniques on grayscale video reconstruction. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of this invention are only for explaining this invention and are not intended to limit this invention.

[0039] It should be noted that the terms "comprising" and "having" and any variations thereof in the specification, claims, and accompanying drawings of this invention are intended to cover non-exclusive inclusion, for example, a process, method, system, product, or device that includes a series of steps or units is not necessarily limited to other steps or units inherent in the device.

[0040] The terminology used in the various embodiments of the invention is for the purpose of describing particular embodiments only and is not intended to limit the various embodiments of the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which the various embodiments of the invention pertain. The terms (such as those defined in commonly used dictionaries) are to be interpreted as having the same meaning as in the context of the relevant technical field and are not to be interpreted as having an idealized or overly formal meaning, unless clearly defined in the various embodiments of the invention.

[0041] Tensor decomposition techniques, by decomposing the original tensor (high-dimensional signal) into low-dimensional factor tensors or factor matrices, can uncover the underlying structure of high-dimensional signals and are widely used in high-dimensional signal reconstruction problems. The most classic tensor decomposition techniques are CP decomposition and Tucker decomposition. CP decomposition decomposes the original tensor into the sum of several rank tensors, but optimizing CP decomposition is often an NP-hard problem, hindering its application to real-world data. Tucker decomposition decomposes the original tensor into a form where a core tensor is multiplied by factor matrices along each mode. The Tucker rank derived from Tucker decomposition can be easily used to construct its relaxed form and optimize the model.

[0042] Tensor network decomposition techniques (such as tensor chain decomposition, tensor ring decomposition, and fully connected tensor network decomposition) are some of the new tensor decomposition techniques that have emerged in recent years and have achieved significant success in the field of signal processing. Tensor network decomposition decomposes a tensor into several low-dimensional factors and connects these factors through contraction, making it suitable for tensor data of order greater than 3. Benefiting from its favorable algebraic properties, tensor singular value decomposition (SVD) decomposes a tensor into two orthogonal tensors and an f-diagonal tensor. This can also be understood as performing singular value decomposition on each front slice of the tensor after a mode 3 transformation, and it has received increasing attention in the field of 3rd-order tensor processing.

[0043] Block term tensor decomposition (BTD) decomposes a tensor into a sum of multiple block terms, enabling the characterization of different components of the tensor. Compared to other tensor decomposition techniques, BTD has stronger representational power and essential uniqueness, demonstrating great potential in high-dimensional signal processing, such as source separation, blind deconvolution, spectral mapping, and image reconstruction tasks.

[0044] like Figure 1The diagram illustrates the principle of Block Term Tensor Decomposition (BTD). Traditional BTD decomposes a tensor into the sum of multiple blocks (i.e., low-rank Tucker tensors). Each block consists of a core tensor and a set of factor matrices, and each block independently represents a component of the tensor. Specifically, for a third-order tensor, the traditional BTD model can be represented as:

[0045]

[0046] in, For the original tensor, Let r be the core tensor of the r-th low-rank term. , , These represent the shared factor matrices for the three modes, , , Representing tensors respectively ( Modular product.

[0047] While this independent processing approach allows each block to focus on representing different components in the data, it ignores the inherent relationships that may exist between different components, causing the model to fail to capture collaborative features across components.

[0048] Despite its numerous advantages, block term tensor decomposition (BTD) still suffers from several significant limitations that hinder its wider application. First, because BTD processes each term independently, it neglects the interactions between different terms. Second, since BTD inherently requires the computation of multiple Tucker decomposition factors, its accompanying algorithms (such as alternating least squares for BTD) are computationally expensive, limiting its application in reconstructing large-scale real high-dimensional signals.

[0049] Based on this, the present invention proposes a high-dimensional signal reconstruction technique based on cooperative block term tensor decomposition. Through a sharing mechanism, different low-dimensional terms can interact with each other, thereby improving the reconstruction effect.

[0050] like Figure 2 As shown, the image reconstruction method based on cooperative block term tensor decomposition includes the following steps.

[0051] S1, obtain the original tensor of the image to be reconstructed.

[0052] In this implementation, the original tensor is the image data to be reconstructed, i.e., the observation data, which serves as the foundational data for the image reconstruction task. This image data can be two-dimensional or higher-dimensional, including but not limited to visible light images, infrared images, radar images, and video frame images.

[0053] S2 decomposes the original tensor into the sum of multiple low-rank terms, and decomposes each low-rank term based on the tensor of cooperating block terms to obtain the low-rank decomposition model of the original tensor.

[0054] The decomposition method based on the cooperative block term tensor is as follows:

[0055] S2-1 represents each low-rank term along the N patterns of the original tensor as the product of N factor matrices and the core tensor, with the N factor matrices corresponding to the N patterns respectively.

[0056] S2-2, for each low-rank term, the nth factor matrix is ​​represented as the product of the nth shared factor matrix and the nth independent factor matrix, n∈[1,N]; the nth shared factor matrix uses the same parameters in all low-rank terms.

[0057] In this implementation, N is an integer greater than or equal to 2, meaning the original tensor is a high-dimensional vector of order two or higher.

[0058] like Figure 3 As shown, the original tensor For a third-order tensor, such as a multispectral image, it has three modes: spatial × spatial × spectral, which are respectively represented by... , , This indicates that the original tensor This can be represented as the summation of R block term tensors, a step based on block term tensor decomposition. However, unlike traditional block term tensor decomposition, each block term is decomposed using a core tensor. Independent factor matrix representing the three modes , , And the shared factor matrix representing the three modes , , The shared factor matrix is ​​identical across all block term tensors, meaning it shares the same matrix parameters. This achieves two key effects: first, as a common foundation for all block terms, the shared factor matrix captures common features among different components, promoting collaborative representation among terms; second, by projecting the original high-dimensional data into a low-dimensional space, the shared factor matrix significantly reduces the computational complexity of subsequent block term decomposition, as the independent factor matrix and core tensor of each block term are optimized in the low-dimensional space, thus reducing the overall number of parameters and computational resource requirements.

[0059] For a third-order tensor The rank of its R terms The low-rank decomposition model constructed based on the collaborative block term tensor decomposition is expressed as follows:

[0060]

[0061] in, , , Let each represent a shared factor matrix of the three modes, satisfying... , , , The dimension is The identity matrix, The dimension is The identity matrix, The dimension is The identity matrix; , , Let each of the three modes be an independent factor matrix representing the r-th low-rank term; Let r be the core tensor of the r-th low-rank term, and , and .

[0062] Furthermore, in the low-rank decomposition part of step S2-1, Tucker decomposition, tensor ring decomposition, tensor singular value decomposition, and fully connected tensor network decomposition can be used. Taking Tucker decomposition as an example, each term in the block term tensor decomposition is a Tucker decomposition tensor. Similarly, each term can also be replaced by a tensor ring decomposition tensor, a tensor singular value decomposition tensor, and a fully connected tensor network decomposition tensor.

[0063] S3. A reconstruction task model is constructed based on a low-rank decomposition model, and the reconstruction task model is solved by an optimization algorithm to obtain the solutions of each factor matrix.

[0064] Based on collaborative block term tensor decomposition, high-dimensional signal reconstruction models for specific tasks can be constructed. Specifically, according to the type of reconstruction task, a reconstruction task model corresponding to the task type is constructed. Each reconstruction task model can be uniformly constructed as a fidelity term and a regularization term. Among them, the fidelity term is configured according to the task type and is used to measure the consistency between the reconstructed image and the original tensor; the regularization term is constructed based on the low-rank decomposition model of the original tensor.

[0065] Taking the high-dimensional signal denoising task as an example, the reconstruction task model is constructed as follows:

[0066]

[0067] After constructing the specific task model, the various components in the model are iteratively updated through a factor learning process until convergence. Here, we take the proximal alternating minimization algorithm as an example; the specific solution process is as follows:

[0068] First, let's introduce the indicator function:

[0069]

[0070] In the formula, Represents any matrix variable that needs to satisfy column orthogonality constraints.

[0071] Then, the original model is converted into an unconstrained model using a semi-quadratic splitting technique:

[0072]

[0073] in, It is a penalty parameter; when it is large enough, the unconstrained model is equivalent to the original model.

[0074] The learning method for each factor is given below, which is the solution to each factor subproblem.

[0075] Learning steps:

[0076]

[0077] in, , Let be the matrix formed by expanding the core tensor of the r-th low-rank term along modulo 1;

[0078]

[0079] express A matrix expanded modulo 1. They represent respectively to The left singular value matrix, diagonal matrix, and right singular value matrix obtained by performing singular value decomposition on the matrix. is the proximal regularization coefficient.

[0080] Learning steps:

[0081]

[0082] in, , , , They represent respectively to The left singular value matrix, diagonal matrix, and right singular value matrix are obtained by performing singular value decomposition on the matrix. Let be the matrix formed by expanding the core tensor of the r-th low-rank term along modulo 2.

[0083] .

[0084] express A matrix expanded along modulo 2.

[0085] Learning steps:

[0086]

[0087] in, , , , They represent respectively to The left singular value matrix, diagonal matrix, and right singular value matrix are obtained by performing singular value decomposition on the matrix. Let be the matrix formed by expanding the core tensor of the r-th low-rank term along modulo 3;

[0088]

[0089] express A matrix expanded along modulo 2.

[0090] Learning steps:

[0091] make ,have:

[0092]

[0093] Learning steps:

[0094]

[0095] Learning steps:

[0096]

[0097] in, , , , They represent respectively to The left singular value matrix, diagonal matrix, and right singular value matrix obtained by performing singular value decomposition on the matrix. , express A matrix expanded modulo 1.

[0098] Learning steps:

[0099]

[0100] in, , , , They represent respectively to The left singular value matrix, diagonal matrix, and right singular value matrix obtained by performing singular value decomposition on the matrix. express A matrix expanded along modulo 2.

[0101] Learning steps:

[0102]

[0103] in, , , , They represent respectively to The left singular value matrix, diagonal matrix, and right singular value matrix obtained by performing singular value decomposition on the matrix. express The matrix is ​​expanded along modulo 3. By learning the above components, each component is continuously updated until convergence or the maximum number of iterations is reached, optimizing the factors of the co-block tensor decomposition, and finally reconstructing the signal using the factors.

[0104] In addition, other learning algorithms can be used for optimization, such as the alternating direction multiplier method, alternating least squares method, and Adam algorithm. For constraints, matrix F-norm constraints, column sum-to-1 constraints, and sparsity constraints can also be employed.

[0105] S4. Substitute the solutions of each factor matrix into the low-rank decomposition model to obtain the reconstructed image.

[0106] The sharing mechanism allows different low-dimensional terms to interact, improving reconstruction results. Simultaneously, this mechanism reduces the computational resource requirements of the technique. For specific reconstruction tasks, a reconstruction is constructed in step S3 (e.g., for denoising and completion tasks, an irregular low-rank tensor restoration model is constructed). The model represents the potential reconstruction signal based on the cooperative block term tensor decomposition in step S2. Only the fidelity-preserving terms need to be replaced for specific restoration tasks to make it applicable to various tasks such as denoising, interpolation, source separation, and blind deconvolution.

[0107] By decoupling the decomposition model from the specific optimization algorithm, it can be compatible with a variety of mature optimization algorithms. This shows that the implementation of the present invention does not depend on a specific algorithm, has good robustness and engineering feasibility, and is easy to deploy on different computing platforms and scenarios.

[0108] Furthermore, the shared factor matrix employs a single-layer matrix, i.e., a simple linearization method. It can be generated using multi-layer nonlinear techniques, such as multilayer perceptrons and implicit neural representations.

[0109] By using a single-layer matrix as the shared factor matrix, the model's simplicity is maintained to the maximum extent while ensuring performance improvement. This avoids overfitting and training difficulties that may arise from introducing complex structures, which is conducive to the rapid implementation and convergence of the method.

[0110] See Figure 4 As shown, this figure compares the performance of the proposed method with traditional block term tensor decomposition in multispectral image reconstruction tasks. It can be observed that, compared to block term tensor decomposition, the collaborative block term tensor decomposition technique based on this invention achieves improved reconstruction results with a higher peak signal-to-noise ratio (PSNR). Furthermore, it significantly reduces the time cost compared to block term tensor decomposition, thus significantly lowering the computational resource requirements and meeting the needs of large-scale data reconstruction tasks.

[0111] Table 1 compares the performance of the proposed method (CBTD method) with several other tensor decomposition techniques for grayscale video denoising. The methods compared include high-dimensional signal reconstruction techniques based on tensor CP decomposition, tensor Tucker decomposition, tensor LL1-type block term tensor decomposition (LL1), and block term tensor decomposition (BTD). Reconstruction performance metrics include peak signal-to-noise ratio (PSNR) and structural similarity (SSIM); higher metric values ​​indicate better reconstruction performance.

[0112] Table 1

[0113]

[0114] As can be seen, in most cases, the method proposed in this invention achieves better reconstruction results in terms of metrics and retains more visual details, such as... Figure 5 As shown. Meanwhile, BTD cannot operate when the data scale reaches a certain level, while the method proposed in this invention has very low time costs.

[0115] Embodiments of the present invention also provide an image reconstruction apparatus based on cooperative block term tensor decomposition, used to execute the image reconstruction method based on cooperative block term tensor decomposition of any embodiment of the present invention, the apparatus comprising:

[0116] The data acquisition module is used to acquire the original tensor, which is the image data to be reconstructed;

[0117] The block term tensor decomposition module is used to decompose the original tensor into a sum of multiple low-rank terms, and to decompose each low-rank term based on the collaborative block term tensor to obtain the low-rank decomposition model of the original tensor.

[0118] The decomposition method based on the cooperating block term tensor is as follows: each low-rank term is represented as the product of N factor matrices and the core tensor along the N patterns of the original tensor, and the nth factor matrix is ​​represented as the product of the nth shared factor matrix and the nth independent factor matrix, where n∈[1,N]; the nth shared factor matrix uses the same parameters in all low-rank terms;

[0119] The model solving module is used to construct a reconstruction task model based on the low-rank decomposition model, and solve the reconstruction task model through an optimization algorithm to obtain the solutions of each factor matrix;

[0120] The reconstruction output module is used to substitute the solutions of each factor matrix into the low-rank decomposition model to obtain the reconstructed image and output it.

[0121] Embodiments of the present invention also provide an electronic device comprising a processor and a memory, wherein the number of processors may be one or more. The memory, as a computer-readable storage medium, can be used to store software programs, computer-executable programs, and modules. The processor executes various functional applications and data processing of the electronic device by running the software programs, instructions, and modules stored in the memory, thereby implementing the image reconstruction method based on cooperative block term tensor decomposition of any of the above embodiments of the present invention.

[0122] The memory may primarily comprise a program storage area and a data storage area. The program storage area may store the operating system and at least one application program required for a given function; the data storage area may store data created based on terminal usage. Furthermore, the memory may include high-speed random access memory (RAM) and non-volatile memory, such as at least one disk storage device, flash memory, or other non-volatile solid-state storage device. In some instances, the memory may further include memory remotely located relative to the processor, which can be connected to the electronic device via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks (LANs), mobile communication networks, and combinations thereof.

[0123] Embodiments of the present invention also provide a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the image reconstruction method based on cooperative block term tensor decomposition of any embodiment of the present invention.

[0124] The computer storage medium of this invention can be any combination of one or more computer-readable media. A computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. A computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of computer-readable storage media (a non-exhaustive list) include: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this invention, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0125] Computer-readable signal media may include data signals propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. Computer-readable signal media may also be any computer-readable medium other than computer-readable storage media, capable of sending, propagating, or transmitting programs for use by or in connection with an instruction execution system, apparatus, or device.

[0126] Embodiments of the present invention also provide a computer program product that, when run on a computer, causes the computer to execute the image reconstruction method based on cooperative block term tensor decomposition of any of the above embodiments of the present invention.

[0127] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for image reconstruction based on a synergistic block term tensor decomposition, characterized in that, include: Obtain the original tensor, which is the image data to be reconstructed; The original tensor is decomposed into a sum of multiple low-rank terms, and each low-rank term is decomposed based on a cooperating block term tensor to obtain a low-rank decomposition model of the original tensor. The decomposition method based on the cooperating block term tensor is as follows: each low-rank term is represented as the product of N factor matrices and the core tensor along the N patterns of the original tensor, where the nth factor matrix is ​​represented as the product of the nth shared factor matrix and the nth independent factor matrix, n∈[1,N]; the nth shared factor matrix uses the same parameters in all low-rank terms; A reconstruction task model is constructed based on the low-rank decomposition model, and the reconstruction task model is solved by an optimization algorithm to obtain the solutions of each factor matrix. Substituting the solutions of each factor matrix into the low-rank decomposition model yields the reconstructed image.

2. The image reconstruction method based on cooperative block term tensor decomposition according to claim 1, characterized in that, N≥2。 3. The image reconstruction method based on cooperative block term tensor decomposition according to claim 1, characterized in that, The low-rank decomposition model of the original tensor is expressed as: in, For the original tensor, Let r be the core tensor of the r-th low-rank term. , , These represent the shared factor matrices for the three modes, , , Let R represent the independent factor matrices of the three modes of the r-th low-rank term, where R is the number of terms. , , Represent the first and second edges along the tensor, respectively. Each pattern is multiplied by a matrix.

4. The image reconstruction method based on cooperative block term tensor decomposition according to claim 1, characterized in that, Constructing a reconstruction task model based on the low-rank decomposition model includes: constructing a corresponding reconstruction task model according to the type of reconstruction task; The reconstruction task model includes a fidelity term and a regularization term; the fidelity term is configured according to the task type and is used to measure the consistency between the reconstructed image and the original tensor; the regularization term is constructed based on the low-rank decomposition model of the original tensor.

5. The image reconstruction method based on cooperative block term tensor decomposition according to claim 4, characterized in that, The types of reconstruction tasks include denoising, interpolation, source separation, and blind deconvolution.

6. The image reconstruction method based on cooperative block term tensor decomposition according to claim 1, characterized in that, The optimization algorithms include the proximal alternating minimization algorithm, the alternating direction multiplier method, the alternating least squares method, and the Adam algorithm.

7. The image reconstruction method based on cooperative block term tensor decomposition according to any one of claims 1-6, characterized in that, The shared factor matrix is ​​a single-layer matrix.

8. An image reconstruction apparatus based on cooperative block term tensor decomposition, characterized in that, include: The data acquisition module is used to acquire the original tensor, which is the image data to be reconstructed; The block term tensor decomposition module is used to decompose the original tensor into a sum of multiple low-rank terms, and to decompose each low-rank term based on the collaborative block term tensor to obtain the low-rank decomposition model of the original tensor. The decomposition method based on the cooperating block term tensor is as follows: each low-rank term is represented as the product of N factor matrices and the core tensor along the N patterns of the original tensor, where the nth factor matrix is ​​represented as the product of the nth shared factor matrix and the nth independent factor matrix, n∈[1,N]; the nth shared factor matrix uses the same parameters in all low-rank terms; The model solving module is used to construct a reconstruction task model based on the low-rank decomposition model, and solve the reconstruction task model through an optimization algorithm to obtain the solutions of each factor matrix; The reconstruction output module is used to substitute the solutions of each factor matrix into the low-rank decomposition model to obtain the reconstructed image.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the image reconstruction method based on cooperative block term tensor decomposition as described in any one of claims 1-7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the image reconstruction method based on cooperative block term tensor decomposition as described in any one of claims 1-7.

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