Global reconstruction method of natural images based on co-sparse representation

Abstract

The present invention discloses a method for global reconstruction of natural images based on co-sparse representation, including a method for modeling image blocks co-sparse representation for global reconstruction of natural images using a sparse decomposition model. The method also includes a fast decomposition and sparse reconstruction algorithm for realizing image block co-sparse degree adaptation for image reconstruction. The method also includes an alternating minimization fast decomposition dictionary learning algorithm for image reconstruction. The present invention solves the problems generated in the natural image reconstruction process, ensures that global reconstruction using co-sparse representation of image blocks is feasible, and also ensures high-quality reconstruction of images, which has theoretical innovation and practical significance for application.

Description

Technical Field

[0001] The present invention belongs to the field of image processing, and more precisely, is a method for global reconstruction of natural images, and specifically is a method for global reconstruction of natural images based on co-sparse representation, which is applied to the field of image reconstruction. Background Art

[0002] Research based on sparse synthesis model is one of the hottest topics in the past decade. Many of its algorithms are relatively mature, and some results have appeared in industrial applications. However, another model of "sparseness" - sparse decomposition model, can be said to have just been unveiled. The sparse decomposition model directly takes signal x as the research object, while the sparse synthesis model uses sparse coding z as the transition calculation signal x. In this way, the sparse decomposition model provides richer feature representation information. Compared with the sparse synthesis model, the sparse decomposition model is equally effective and has better performance. For this reason, more and more scholars are paying attention to the sparse decomposition model for natural image processing applications. At present, the research based on sparse decomposition model focuses more on the optimization and reconstruction process of co-sparse priors, while image modeling and compressed sensing applications, as well as the decomposition and sparse reconstruction of the model and decomposition dictionary learning, have not been deeply studied, and there are even fewer specific applications. At this stage, there is still great research potential. This research direction is generally aimed at applications that are closely related to reality, such as image processing and pattern recognition.

[0003] The key to achieving global image reconstruction by sparse representation of image blocks is to establish a sparse representation model for image blocks, realize decomposition and sparse reconstruction of the entire image, and solve the technical gap between the reconstruction of the entire image and key technologies of sparse decomposition models such as decomposition and sparse reconstruction and decomposition dictionary learning. Therefore, it is necessary not only to ensure that the sparse decomposition model is feasible to achieve sparse representation of image blocks, but also to ensure the quality of global reconstruction by sparse representation of image blocks. Specifically, the key issues involved include the following two points:

[0004] (1) Image block co-sparse representation model achieves high-quality global reconstruction of the entire image

[0005] One of the biggest challenges facing image reconstruction using co-sparse representation is how to design a co-sparse representation model for image blocks that avoids overfitting and large computational complexity. The root of the problem is that traditional local methods divide the entire image in an overlapping manner, resulting in oversized overlapping image blocks. In addition, excessive efforts to solve the overfitting problem can easily lead to underfitting, so how to find a balance strategy in the co-sparse representation model for image blocks is a key issue that the present invention aims to address. At the same time, how to eliminate grid line artifacts and block effects when the entire image is composed of co-sparse representation of image blocks to ensure high quality of global image reconstruction is also a major challenge for the present invention, and this is a key issue that needs to be addressed.

[0006] (2) A fast image reconstruction method based on co-sparse representation model of image blocks to achieve co-sparse degree adaptation

[0007] How to design a fast, easy-to-implement and co-sparse adaptive decomposition and reconstruction algorithm framework based on the signal characteristics of the co-sparse representation coefficients of the image blocks is another difficult problem that needs to be solved in global image reconstruction. The problem can be understood from two levels: first, the traditional image sparse representation model focuses on the sparse representation coefficients, and various fast sparse reconstruction algorithms are designed based on the characteristics of the sparse coefficients; second, in the sparse decomposition model, co-sparseness is a result-oriented attribute, which exists in the objective function of co-sparse representation, but is not the core concern of the optimization problem like in the sparse synthesis model. Summary of the invention

[0008] The purpose of this invention is to study the global co-sparse representation modeling method for natural image reconstruction using a sparse decomposition model, design a fast numerical calculation method for decomposition sparse reconstruction and decomposition dictionary learning in global reconstruction, and form a natural image global reconstruction algorithm framework suitable for a sparse decomposition model. Figure 1 shown.

[0009] The sparse decomposition model is a relatively new research direction. This paper takes the sparse decomposition model as the center and the natural image reconstruction application as the starting point, and explores the image block co-sparse representation model to achieve a fast global reconstruction method for co-sparse degree adaptation. At the same time, the image representation model and two core issues of decomposition sparse reconstruction and decomposition dictionary learning of this model are studied respectively, which is expected to promote the overall development in this direction and ensure the integrity and systematicness of the research content.

[0010] The technical solution of the present invention is as follows:

[0011] The global reconstruction method of natural images based on co-sparse representation includes:

[0012] S1. Sparse decomposition model realizes the image block co-sparse representation modeling method for global reconstruction of natural images;

[0013] S2, a fast decomposition and sparse reconstruction algorithm for image block co-sparseness adaptation to achieve image reconstruction;

[0014] S3. Implement the alternating minimization fast decomposition dictionary learning algorithm for image reconstruction.

[0015] Furthermore, the sparse decomposition model of S1 implements an image block co-sparse representation modeling method for global reconstruction of natural images: image reconstruction is divided into multiple sub-problems, each sub-problem processes non-overlapping image blocks covering the entire image, and finally the reconstruction results of multiple sub-problems are averaged to obtain the final image reconstruction result.

[0016] Furthermore, the number of image blocks obtained by global modeling is ceil(W / w)*ceil(H / h), and the image can be reconstructed globally, that is, all image blocks of one partition can be reconstructed at a time.

[0017] Furthermore, the fast decomposition and sparse reconstruction algorithm of S2 comprises the following steps:

[0018] S2.1 Common support detection:

[0019] Detect the co-support Λ of the signal of interest x, that is, the rows of the decomposition dictionary Ω make the decomposition signal of interest x equal to 0 or the rows of the decomposition dictionary Ω make it orthogonal to the signal of interest x;

[0020] S2.2 Signal estimation:

[0021] Update the signal x to be reconstructed by solving the least squares problem on the common support set Λ:

[0022]

[0023] Where Ω Λ represents the co-support set, and Λ indicates the sub-row matrix.

[0024] Furthermore, the reference design method of the common support set of S2.1 is to use the negative gradient of the least squares: x (t) =x (t-1) +μM T (y-Mx (t-1) ), where μ is the step size.

[0025] Furthermore, a common support set detection method is designed based on the signal estimation features of 2.2: hard thresholding is performed on the common sparse representation coefficient Ωx, that is, the l values ​​with the smallest absolute value are assigned 0 to obtain the common support set Λ; specifically:

[0026] A threshold parameter greater than 0 and less than or equal to 1 is introduced to dynamically monitor the ratio of the absolute value of the common sparse representation coefficient Ωx to obtain the support set, and then the complement set is solved to obtain the common support set Λ.

[0027] The thresholding parameter is determined by balancing the reconstruction result and the reconstruction time.

[0028] Furthermore, the S3 implements an alternating minimization fast decomposition dictionary learning algorithm for image reconstruction, which includes two parts: decomposition sparse reconstruction and decomposition dictionary update.

[0029] Furthermore, the decomposition sparse reconstruction is to solve the signal set X by the training sample set Y when the decomposition dictionary Ω is known, and the implementation method is completed by the algorithm as claimed in claim 4.

[0030] Furthermore, the decomposition dictionary is updated by updating the decomposition dictionary with the signal set X and the training sample set Y, and each atom (row of Ω) of the decomposition dictionary Ω is calculated step by step to update the dictionary. The constraint here is that the rows of Ω on the common branch set I are orthogonal to the columns of X, that is, Ω I X I Ω I X I =0, (here Ω I , X I Take the row submatrix of Ω and the column submatrix of X respectively), and get the optimization problem:

[0031]

[0032] Furthermore, it also includes: adding a constraint ||Ω i ||2=1, find the singular vector corresponding to the smallest singular value, Ω i =d:

[0033]

[0034] Beneficial effects of the present invention:

[0035] The present invention focuses on the research of a fast method for achieving global reconstruction through co-sparse representation of image blocks, and uses co-sparse representation model and greedy sparse learning as the main technical means to solve the problems arising in the process of natural image reconstruction. It not only ensures that global reconstruction through co-sparse representation of image blocks is feasible, but also ensures that the image reconstruction process is efficient. Its theoretical innovative significance and practical significance in application are very obvious. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 The present invention is a natural image global reconstruction algorithm framework applicable to the sparse decomposition model;

[0037] Figure 2 These are the results of local and global reconstruction based on the sparse synthesis model of the present invention;

[0038] Figure 3 The decomposition and sparse reconstruction ICSD algorithm framework for image reconstruction of the present invention;

[0039] Figure 4 The present invention decomposes the alternating minimization algorithm flow of dictionary learning. DETAILED DESCRIPTION

[0040] The present invention will be further described below in conjunction with the accompanying drawings.

[0041] like Figure 1 As shown, the method of the present invention includes the following three parts (1)-(3).

[0042] (1) A sparse decomposition model is proposed to achieve a sparse representation modeling method for image blocks to achieve global reconstruction of natural images.

[0043] In order to avoid the defects of traditional local modeling methods, the present invention intends to adopt a global modeling method based on the divide-and-conquer idea, dividing the image reconstruction into multiple sub-problems, each sub-problem processes a non-overlapping image block covering the entire image, and finally the final image reconstruction result is obtained by averaging the reconstruction results of multiple sub-problems. The sub-problem here is a division of the entire image, which is divided into non-overlapping image blocks covering the entire image.

[0044] Different from the traditional local overlapping image block method, each pixel here belongs to only one image block. The present invention takes an image of size 50*50 as an example to generate an 8*8 image block. According to set theory, theoretically there are at most wh=64 partitions, w and h represent the length and width of the image block respectively. The present invention only selects several typical partitions. Different from the traditional local image modeling, the number of image blocks obtained by global modeling is ceil(W / w)*ceil(H / h), where the ceil function represents rounding up, W and H represent the length and width of the entire image respectively, that is, the scale of the number of image blocks is only about 1 / wh of the local method (that is, the number of image blocks covering the entire image in this example is 49, and if local overlapping image blocks are used, there are 1849). Therefore, the present invention can globally reconstruct the image, that is, reconstruct all image blocks of one partition at a time, thus avoiding the overfitting problem of the traditional local method and improving the time efficiency of image reconstruction.

[0045] The non-overlapping image block method is prone to produce artifacts and block effects at the image block boundaries. In order to eliminate this problem, the global modeling method proposed in the present invention can be solved by solving multiple sub-problems (each partition can be calculated in parallel) and then averaging them. For example, randomly selecting 3-5 image blocks to partition can also avoid underfitting problems. Figure 2 The preliminary experimental results of reconstructing the pepper image in the sparse synthesis model using the above modeling method are given. To avoid special cases of image size, the image size is adjusted from 512*512 to 308*308, and the image block size is 8*8. (1) is reconstructed by the traditional local method, and (2)-(4) are reconstructed by the global method using 20% ​​compressed sampling.

[0046] (2) A fast decomposition and sparse reconstruction algorithm based on the co-sparseness of image blocks is proposed to achieve image reconstruction.

[0047] In order to achieve fast image reconstruction and co-sparity adaptation, the present invention "dually" draws on the greedy algorithm for sparse synthesis model proposed by our research group before, and designs a greedy algorithm framework for solving problem (1). According to the algorithm idea, it is called iterative co-support detection (ICSD: Iterative Co-Support Dectecion). The decomposition sparse reconstruction algorithm iteratively calculates the following two steps (the algorithm flow is as follows Figure 3 shown):

[0048] (a) Common support detection:

[0049] The co-support Λ of the signal of interest x is detected, that is, which rows of the decomposition dictionary Ω are used to decompose the signal of interest x to obtain 0, or which rows of the decomposition dictionary Ω are orthogonal to the signal of interest x.

[0050] (b) Signal estimation:

[0051] Update the signal x to be reconstructed by solving the least squares problem on the common support set Λ:

[0052]

[0053] Where Ω Λ represents the common support set, Λ indicates the sub-row matrix, and M is the measurement matrix. Similar to the sparse reconstruction algorithm of the sparse synthesis model, the above proposal is an algorithm framework, and the specific implementation depends on the common support set detection method.

[0054] Designing a new algorithm involves two aspects:

[0055] a) Select the reference for common support detection

[0056] The present invention adopts the negative gradient of least squares: x (t) =x (t-1) +μM T (y-Mx (t-1) ), where μ is the step size and t is the number of iterations. Unlike greedy algorithms such as GAP, the reference of common support detection does not need to solve the pseudo-inverse matrix. Algorithms such as GAP refer to the correlation between the decomposition dictionary Ω and the residual signal, while the ICSD algorithm refers to the common sparse representation coefficient Ωx after gradient descent, which not only accelerates the convergence of the algorithm but also provides richer information for subsequent common support detection.

[0057] b) Design a common support detection method based on the characteristics of the signal

[0058] Drawing on the greedy algorithm of the sparse synthesis model, the present invention designs a detection method, namely, hard thresholding the common sparse representation coefficient Ωx (assigning the l values ​​with the smallest absolute value to 0) to obtain the common support set Λ. The hard thresholding method, like the greedy algorithm such as GAP, needs to specify an input parameter l (common sparsity). Therefore, different methods must be designed to achieve common sparsity adaptation. Since the common sparse representation coefficient of the natural image block is a (approximately) rapidly decaying sparse signal, the present invention can "dually" draw on the thresholding greedy strategy for the sparse synthesis model proposed by this research group before. Here, a thresholding parameter greater than 0 and less than or equal to 1 is introduced to dynamically detect the ratio of the absolute value of the common sparse representation coefficient Ωx to obtain the support set, and then solve the complement to obtain the common support set Λ, thus solving the common sparsity adaptation problem. In practical applications, the thresholding parameter can be determined by balancing the reconstruction result and the reconstruction time.

[0059] (3) Propose an alternating minimization fast decomposition dictionary learning algorithm for image reconstruction

[0060] In order to find a fast algorithm, the present invention adopts an alternating minimization method different from the convex relaxation algorithm and designs a decomposition dictionary learning algorithm to solve problem (2). The algorithm is divided into two steps: decomposition sparse reconstruction and decomposition dictionary update, such as Figure 4 As shown, decomposition sparse reconstruction is to solve the signal set X by the training sample set Y when the decomposition dictionary Ω is known. The present invention adopts the decomposition sparse reconstruction ICSD algorithm designed in (2) above. In the decomposition dictionary update, the decomposition dictionary is updated by the signal set X and the training sample set Y. Different from the literature that updates the entire dictionary at one time, the present invention implements the step-by-step calculation of each atom (row of Ω) of the decomposition dictionary Ω to update the dictionary. The constraint here is that the rows of Ω on the common branch set I are orthogonal to the columns of X, that is, Ω I X I Ω I X I =0, (here Ω I , X I are the row submatrix of Ω and the column submatrix of X respectively), and the optimization problem is:

[0061]

[0062] Among them, Y is the training sample set and e is the error constant.

[0063] The present invention adds a constraint ||Ω i ||2=1, so we can use the same dictionary learning as the sparse synthesis model, using singular value decomposition SVD (Singular Value Decomposition), but here we solve the singular vector corresponding to the smallest singular value, Ω i = d, d is the training sample set Y indexed by I IThe singular vector corresponding to the smallest singular value:

[0064]

[0065] By comparing and analyzing the alternating minimization dictionary learning of the sparse synthesis model, the present invention adopts the ICSD algorithm in the decomposition and sparse reconstruction step, so that the common support set I can be directly obtained without an additional thresholding step, and the decomposition dictionary update solves the least squares problem of orthogonal constraints by using SVD, which avoids pseudo-inverse matrix operations.

[0066] Feasibility analysis of the implementation of the present invention

[0067] The solution to achieve global image reconstruction by using the sparse representation model of image blocks is based on the analysis of traditional local methods combined with the understanding of the image reconstruction task of the sparse decomposition model. The method of covering non-overlapping image blocks is based on the theoretical basis of block-based classical image processing. It is theoretically feasible, and there are also many image covering division methods provided technically, such as MATLAB's image processing toolbox. Figure 2 As shown, preliminary experiments show that the present invention can well achieve the goal of the scheme in the sparse synthesis model; through theoretical analysis, it can also be applied to the sparse decomposition model. Therefore, the above overall scheme has sufficient theoretical basis and method guidance and is feasible.

[0068] The biggest challenge for the image block co-sparse representation model to achieve co-sparse adaptive fast image reconstruction comes from the gap from image sparse representation to image co-sparse representation. The technical solution of the present invention to resolve the above challenges is to understand the image sparse representation coefficients in a "dual" way based on the image co-sparse representation coefficients. The support detection is smoothly transitioned to the co-support detection, and the alternating minimization of the dictionary atoms corresponding to the maximum singular values ​​is transitioned to the decomposition dictionary atoms corresponding to the minimum singular values. The statistical sparse signal characteristic analysis and calculation methods involved have relatively complete theories and algorithms, which provide the necessary theoretical basis and implementation means for the present invention to explore the sparse decomposition model to realize the fast image reconstruction method. Therefore, the above scheme is feasible both in theory and in practice.

[0069] Therefore, based on the co-sparse representation characteristics of images, the present invention studies the image block co-sparse representation model to realize a fast global image reconstruction method with co-sparse degree adaptation. The expected goal has sufficient theoretical basis and technical support. In addition, the present invention has conducted preliminary research on simple Shepp-Logan images and achieved the expected results in image co-sparse degree adaptive representation, laying the foundation for further in-depth research in combination with the global image block co-sparse representation model.

[0070] The series of detailed descriptions listed above are only specific descriptions of feasible implementation methods of the present invention. They are not intended to limit the scope of protection of the present invention. All equivalent methods or changes that do not deviate from the technical creation of the present invention should be included in the scope of protection of the present invention.

Claims

1. A global reconstruction method of natural images based on co-sparse representation, characterized in that: include: S1. Sparse decomposition model realizes the image block co-sparse representation modeling method for global reconstruction of natural images; S2, a fast decomposition and sparse reconstruction algorithm for image block co-sparseness adaptation to achieve image reconstruction; S3, an alternating minimization fast decomposition dictionary learning algorithm for image reconstruction; The sparse decomposition model of S1 implements a co-sparse representation modeling method for image blocks of global reconstruction of natural images: image reconstruction is divided into multiple sub-problems, each sub-problem processes non-overlapping image blocks covering the entire image, and finally the reconstruction results of multiple sub-problems are averaged to obtain the final image reconstruction result; The number of image blocks obtained by global modeling is ceil(W / w)*ceil(H / h), and the image can be globally reconstructed, that is, all image blocks of one partition can be reconstructed at a time; where the ceil function represents rounding up, W and H represent the length and width of the entire image, respectively, and w and h represent the length and width of the image block, respectively; The fast decomposition and sparse reconstruction algorithm of S2 comprises the following steps: S2.1 Common support detection: Detect the co-support Λ of the signal of interest x, that is, the rows of the decomposition dictionary Ω make the decomposition signal of interest x equal to 0 or the rows of the decomposition dictionary Ω make it orthogonal to the signal of interest x; S2.2 Signal estimation: The signal to be reconstructed is updated by solving the least squares problem on the common support set Λ: Where Ω Λ represents the sub-row matrix of the common support set Λ, M is the measurement matrix, and y represents the observed measurement value; The reference design method of the common support set of S2.1 is to use the negative gradient of least squares: Where μ is the step size, t is the number of iterations, and T is the transposition operation. According to the signal estimation feature of S2.2, a common support set detection method is designed: the common sparse representation coefficient Ωx is hard-thresholded, that is, the l values ​​with the smallest absolute value are assigned 0 to obtain the common support set Λ; specifically: A threshold parameter greater than 0 and less than or equal to 1 is introduced to dynamically monitor the ratio of the absolute value of the common sparse representation coefficient Ωx to obtain the support set, and then the complement set is solved to obtain the common support set Λ; Among them, the thresholding parameter is determined by balancing the reconstruction result and the reconstruction time; The S3 implements an alternating minimization fast decomposition dictionary learning algorithm for image reconstruction, which includes two parts: decomposition sparse reconstruction and decomposition dictionary update; The decomposition sparse reconstruction is to solve the signal set X by the training sample set Y, given the decomposition dictionary Ω; The decomposition dictionary is updated by updating the decomposition dictionary with the signal set X and the training sample set Y, and each atom of the decomposition dictionary Ω is calculated step by step to update the dictionary. The constraint here is that the rows of Ω on the common branch set I are orthogonal to the columns of X, that is, Ω I X I =0, here Ω I I, X I are the row submatrix of Ω and the column submatrix of X, respectively, and the optimization problem is: Where, e is the error constant; It also includes: adding a constraint ||Ωi||2=1, solving the singular vector corresponding to the smallest singular value, Ωi=d: 。

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