A noisy image processing method based on robust matrix feature learning

Abstract

The present invention provides a noise image processing method based on robust matrix feature learning, comprising the following steps: S1: obtaining a noise image to be processed, and converting the noise image into a matrix form to obtain a sample matrix, and forming a sample matrix set; S2: performing matrix normalization processing on the sample matrix set to obtain a normalized sample matrix set; S3: constructing a weight graph matrix according to the similarity relationship of matrices in the normalized sample matrix set; S4: constructing a matrix feature learning model according to the weight graph matrix, and introducing a matrix recovery term and a constraint error term to obtain a joint learning model; S5: optimizing the joint learning model, and outputting an optimal recovery matrix set after dimensionality reduction as a noise image processing result. The present invention provides a noise image processing method based on robust matrix feature learning, which realizes denoising and dimensionality reduction of noise images, and solves the problem that images obtained in actual scenes may have noise information and it is difficult to obtain high-quality image data.

Description

Technical Field

[0001] The present invention relates to the technical field of image processing, and more specifically, to a noise image processing method based on robust matrix feature learning. Background Art

[0002] In recent years, with the rapid development of image information technology and image information acquisition tools (cameras, sensors), people can now easily obtain the image data they want through various information channels, regardless of region and time. For example, in power operation scenarios, operators can obtain a large number of images at different times and regions to perform learning tasks such as operating environment classification and equipment fault detection. However, although image data can be easily obtained, when faced with massive amounts of image data, people cannot meet the real-time and effectiveness of image data processing by relying solely on manpower, so artificial intelligence and machine learning are needed to replace manpower to learn and process massive amounts of image data.

[0003] For image classification tasks, the common method is to first pull the image into a vector and then use the classic classification algorithm to process it. However, pulling the image data into a vector will cause the generated image data to have too high a dimension and destroy the spatial position information of the image data itself. Based on these problems, a dimensionality reduction method based on matrix expression has been proposed. The purpose of dimensionality reduction is to remove redundant information in the data and retain the most effective feature data. Since the image is directly expressed using a matrix, the dimension of the image data is significantly reduced, which not only improves the learning efficiency, but also retains the essential spatial structure of the image, and can obtain better learning results. Feature learning is one of the dimensionality reduction methods. This method achieves dimensionality reduction by projecting the original high-dimensional data space into an ideal low-dimensional feature space. However, in the application process of actual scenes, many images obtained on site will have noise information due to noise, lighting, occlusion, angle, etc., making it difficult to obtain high-quality image data. If noisy images are directly used for learning tasks such as scene classification and equipment fault detection, it will be difficult to obtain high-quality learning results in the learning tasks. Summary of the invention

[0004] In order to overcome the technical defect that images obtained in actual scenes may contain noise information and it is difficult to obtain high-quality image data, the present invention provides a noise image processing method based on robust matrix feature learning.

[0005] In order to solve the above technical problems, the technical solution of the present invention is as follows:

[0006] A noisy image processing method based on robust matrix feature learning comprises the following steps:

[0007] S1: Obtain a noise image to be processed, and convert the noise image into a matrix form to obtain a sample matrix, thereby forming a sample matrix set;

[0008] S2: performing matrix normalization processing on the sample matrix set to obtain a normalized sample matrix set;

[0009] S3: construct a weight graph matrix according to the similarity relationship of matrices in the normalized sample matrix set;

[0010] S4: construct a matrix feature learning model according to the weight map matrix, and introduce matrix recovery terms and constraint error terms to obtain a joint learning model;

[0011] S5: Optimize the joint learning model and output the optimal recovery matrix set after dimensionality reduction as the noisy image processing result.

[0012] In the above scheme, the noisy image is first converted into a matrix form, and the correlation information between matrices is effectively reflected through the weight map matrix. Then, the matrix feature learning is combined, and the matrix recovery term and the constrained error term are introduced, so as to integrate the image recovery and dimensionality reduction. The final output of the reduced-dimensional optimal recovery matrix set removes the noise information and redundant information in the noisy image, retains only the most essential image features, and reduces the data dimension, thereby realizing denoising and dimensionality reduction of the noisy image.

[0013] Preferably, in step S1, the noise image is converted into a matrix form by:

[0014] The matrix is ​​constructed according to the position of each pixel in the noise image corresponding to a matrix element, and the corresponding matrix element is assigned a value according to the color of the pixel.

[0015] In the above scheme, the noise image includes the image data of the work site taken under different lighting conditions (including cloudy conditions, sunny conditions, daytime conditions, night conditions, etc.) and different shooting angles (including looking down angle, looking up angle, looking straight angle, side angle, etc.), and the shooting objects may be workers, electrical equipment, working environment, etc. Noise includes image noise generated by partial occlusion, impulse noise, Gaussian noise, etc.

[0016] Preferably, the matrix normalization process in step S2 is specifically as follows:

[0017] For the sample matrix set X′=[(X1)′,(X2)′,…(X i )′,…,(X n )′] are divided by their own F norms to obtain the normalized sample matrix set X = [X1, X2, …X i ,…,X n ]Right now:

[0018]

[0019] Among them, (X i )′ represents the i-th sample matrix, the dimension of the sample matrix is ​​m×l, ‖(X i )′‖ F Indicates (X i )′, X i Represents the i-th normalized sample matrix.

[0020] In the above scheme, each element in the sample matrix can be mapped to the interval between (-1, 1) through matrix normalization processing, so that different sample matrices are in the same dimension.

[0021] Preferably, the elements in the weight map matrix are assigned values ​​in the following manner:

[0022]

[0023] Among them, s ij represents the element in the i-th row and j-th column of the weighted graph matrix S. Each element in the weighted graph matrix S represents the similarity relationship between the two normalized sample matrices; A = [A1, A2, ... A i ,…,A n ] represents the recovery matrix set, A i Represents the normalized sample matrix X i The restoration matrix; N k (A j ) represents the jth recovery matrix A j The k nearest neighbor set of ; represents the distance between the two matrices; t represents the bandwidth of the Gaussian kernel function;

[0024] The normalized sample matrix set X and the recovery matrix set A have the following relationship:

[0025] X=A+E

[0026] Where E=[E1,E2,...,E i ,...,E n ] represents the error matrix set, E i Represents the normalized sample matrix X i And the recovery matrix A i The deviation between.

[0027] In the above scheme, the elements in the weight map matrix are assigned values ​​by the Gaussian kernel function method.

[0028] Preferably, the elements in the weight map matrix are assigned values ​​in the following manner:

[0029]

[0030]

[0031] Among them, s ij represents the element in the i-th row and j-th column of the weighted graph matrix S. Each element in the weighted graph matrix S represents the similarity relationship between the two normalized sample matrices. A=[A1,A2,…A i ,…,A n ] represents the recovery matrix set, A i Represents the normalized sample matrix X i The recovery matrix, N k (A j ) represents the jth recovery matrix A j The k nearest neighbor set of , t represents the bandwidth of the Gaussian kernel function;

[0032] The normalized sample matrix set X and the recovery matrix set A have the following relationship:

[0033] X=A+E

[0034] Where E=[E1,E2,...,E i ,...,E n ] represents the error matrix set, E i Represents the normalized sample matrix X i And the recovery matrix A i The deviation between.

[0035] In the above scheme, the elements in the weight map matrix are assigned values ​​through a local linear reconstruction method.

[0036] Preferably, in step S4, the mathematical formula of the matrix feature learning model is:

[0037]

[0038] sP T AMA T P=I

[0039] Where P is a linear projection matrix with a dimension of m×d, d is the dimension of the set low-dimensional space, d<m; (·) T Represents the transpose of a matrix; represents the i-th recovery matrix A i and j

[0040] The recovery matrix A j The distance information between T A represents the set obtained after the dimensionality reduction of the recovery matrix set A, M is a diagonal matrix, and I represents the identity matrix;

[0041] In order to facilitate the solution, the mathematical formula of the matrix feature learning model is derived as follows:

[0042]

[0043] sP T AMA T P=I

[0044] Tr(·) represents the trace of the matrix, and the Laplace matrix L=MS.

[0045] Preferably,

[0046] use ||P T A i -P T A j || 2，1 or ||P T A i -P T A j || * To calculate the distance of the matrix,

[0047] in, represents the square of the F-norm of the matrix, ||·|| 2，1 represents the L2,1 norm of the matrix, ||·|| * Represents the nuclear norm of the matrix.

[0048] Preferably, the mathematical formulas of the introduced matrix recovery term and constraint error term are:

[0049]

[0050] stX=A+E

[0051] Among them, φ(E) is the prior constraint on the error matrix set E, such as ||E||1, ||E|| 2，1 、||E|| * ,||·||1 represents the L1 norm of the matrix,||·|| 2，1 represents the L2,1 norm of the matrix, ||·|| * represents the nuclear norm of the matrix; α and β represent different norm term weight balancing variables, X represents the normalized sample matrix set, and A represents the recovery matrix set.

[0052] In the above scheme, different bias constraints are introduced to explore the impact of error on feature learning. Among them, the L1 norm and L2,1 norm can provide sparsity constraints on the error, while the nuclear norm can provide low-rank constraints on the error.

[0053] Preferably, the mathematical formula of the joint learning model is as follows:

[0054]

[0055] stX=A+E,P T AMA T P=I

[0056] Where P is a linear projection matrix of dimension m×d, represents the i-th recovery matrix A i and the jth recovery matrix A j The distance information between T A represents the set obtained after the dimensionality reduction of the recovery matrix set A, s ij represents the element in the i-th row and j-th column of the weight graph matrix S, α and β represent weight balancing variables of different norm terms, X represents the set of normalized sample matrices, ||·|| * represents the nuclear norm of the matrix, φ(E) is the prior constraint on the error matrix set E, M is a diagonal matrix, and I represents the identity matrix.

[0057] In the above scheme, the essential image features are further obtained by integrating the two-dimensional feature learning and the matrix recovery process into a whole for joint learning.

[0058] Preferably, step S5 specifically includes the following steps:

[0059] S5.1: According to the augmented Lagrange multiplier method, the joint learning model is re-expressed as:

[0060]

[0061] sP T AMA T P=I

[0062]

[0063] sP T AMA T P=I

[0064] Among them, Q and B represent different Lagrange multipliers, H represents the intermediate variable, μ represents the step size coefficient, Represents the square of the F norm of the matrix;

[0065] S5.2: Fix the variables in the formula of step S5.1 that are not related to E and obtain:

[0066]

[0067] Find E based on the specific prior constraints of φ(E);

[0068] Fixing the variables that are not related to A in the formula of step S5.1 yields:

[0069]

[0070] Use matrix differentiation to directly derive A;

[0071] Fixing the variables in the formula of step S5.1 that are not related to H yields:

[0072]

[0073] Use Singular Value Thresholding (SVT) decomposition to find H;

[0074] Fixing the variables in the formula of step S5.1 that are not related to P yields:

[0075]

[0076] sP T AMA T P=I

[0077] Use generalized eigenvalue decomposition to find P;

[0078] S5.3: Update model parameters Q, B, μ:

[0079]

[0080] Among them, ρ is used to adjust the convergence speed of the iterative optimization process, 1<ρ<2;

[0081] S5.4: Determine whether the difference between two consecutive output values ​​of the optimized joint learning model is less than a preset threshold.

[0082] If so, the convergence condition is met, and the optimal recovery matrix set is obtained. The optimal recovery matrix set is reduced in dimension and output as the result of noise image processing;

[0083] If not, return to step S5.2 to iteratively update and optimize the joint learning model.

[0084] In the above scheme, the augmented Lagrange multiplier method (ADMM) is used to split the joint learning model that cannot be directly solved into several easy-to-solve sub-optimization problems. The joint learning model is gradually optimized by iteratively updating different variables, and the optimal recovery matrix set is obtained. T The optimal recovery matrix set is projected into a low-dimensional space to obtain the most essential image features, that is, the output optimal recovery matrix set after dimensionality reduction.

[0085] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0086] The present invention provides a noisy image processing method based on robust matrix feature learning. The noisy image is first converted into a matrix form, and the correlation information between matrices is effectively reflected through a weight map matrix. Then, matrix feature learning is combined to introduce matrix recovery terms and constraint error terms, thereby integrating image recovery and dimensionality reduction. The optimal recovery matrix set after dimensionality reduction that is finally outputted removes noise information and redundant information in the noisy image, retains only the most essential image features, and reduces the data dimension, thereby achieving denoising and dimensionality reduction of the noisy image. BRIEF DESCRIPTION OF THE DRAWINGS

[0087] Figure 1 It is a flowchart of the implementation steps of the technical solution of the present invention;

[0088] Figure 2 This is a flow chart of the steps for optimizing the joint learning model in the present invention. DETAILED DESCRIPTION

[0089] The drawings are for illustrative purposes only and should not be construed as limiting the present patent;

[0090] In order to better illustrate the present embodiment, some parts in the drawings may be omitted, enlarged or reduced, and do not represent the size of the actual product;

[0091] It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0092] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0093] Example 1

[0094] like Figure 1 As shown, a noisy image processing method based on robust matrix feature learning includes the following steps:

[0095] S1: Obtain a noise image to be processed, and convert the noise image into a matrix form to obtain a sample matrix, thereby forming a sample matrix set;

[0096] S2: performing matrix normalization processing on the sample matrix set to obtain a normalized sample matrix set;

[0097] S3: construct a weight graph matrix according to the similarity relationship of matrices in the normalized sample matrix set;

[0098] S4: construct a matrix feature learning model according to the weight map matrix, and introduce matrix recovery terms and constraint error terms to obtain a joint learning model;

[0099] S5: Optimize the joint learning model and output the optimal recovery matrix set after dimensionality reduction as the noisy image processing result.

[0100] In the specific implementation process, the noisy image is first converted into a matrix form, and the correlation information between matrices is effectively reflected through the weight map matrix. Then, the matrix feature learning is combined, and the matrix recovery term and the constrained error term are introduced to integrate the image recovery and dimensionality reduction. The final output of the reduced-dimensional optimal recovery matrix set removes the noise information and redundant information in the noisy image, retains only the most essential image features, and reduces the data dimension, thereby achieving denoising and dimensionality reduction of the noisy image.

[0101] Example 2

[0102] A noisy image processing method based on robust matrix feature learning comprises the following steps:

[0103] S1: Obtain a noise image to be processed, and convert the noise image into a matrix form to obtain a sample matrix, thereby forming a sample matrix set;

[0104] S2: performing matrix normalization processing on the sample matrix set to obtain a normalized sample matrix set;

[0105] S3: construct a weight graph matrix according to the similarity relationship of matrices in the normalized sample matrix set;

[0106] S4: construct a matrix feature learning model according to the weight map matrix, and introduce matrix recovery terms and constraint error terms to obtain a joint learning model;

[0107] S5: Optimize the joint learning model and output the optimal recovery matrix set after dimensionality reduction as the noisy image processing result.

[0108] More specifically, in step S1, the noise image is converted into a matrix form by:

[0109] The matrix is ​​constructed according to the position of each pixel in the noise image corresponding to a matrix element, and the corresponding matrix element is assigned a value according to the color of the pixel.

[0110] In the specific implementation process, the noise image includes the image data of the work site taken under different lighting conditions (including cloudy conditions, sunny conditions, daytime conditions, night conditions, etc.) and different shooting angles (including looking down angle, looking up angle, looking straight angle, side angle, etc.), and the shooting objects can be workers, electrical equipment, working environment, etc. Noise includes image noise generated by partial occlusion, impulse noise, Gaussian noise, etc.

[0111] More specifically, the matrix normalization process in step S2 is as follows:

[0112] For the sample matrix set X′=[(X1)′,(X2)′,…(X i )′,…,(X n )′] are divided by their own F norms to obtain the normalized sample matrix set X = [X1, X2, …X i ,…,X n ]Right now:

[0113]

[0114] Among them, (X i )′ represents the i-th sample matrix, the dimension of the sample matrix is ​​m×l, ‖(X i )′‖ F Indicates (X i )′, X i Represents the i-th normalized sample matrix.

[0115] In the specific implementation process, each element in the sample matrix can be mapped to the interval between (-1, 1) through matrix normalization processing, so that different sample matrices are in the same dimension.

[0116] More specifically, the elements in the weight map matrix are assigned as follows:

[0117]

[0118] Among them, s ij represents the element in the i-th row and j-th column of the weighted graph matrix S. Each element in the weighted graph matrix S represents the similarity relationship between the two normalized sample matrices; A = [A1, A2, ... A i ,…,A n ] represents the recovery matrix set, A i Represents the normalized sample matrix X i The restoration matrix; N k (A j ) represents the jth recovery matrix A j The k nearest neighbor set of ; Represents the distance between the two matrices; t represents the bandwidth of the Gaussian kernel function, and its size can be adjusted to control the local range of the Gaussian kernel function;

[0119] The normalized sample matrix set X and the recovery matrix set A have the following relationship:

[0120] X=A+E

[0121] Where E=[E1,E2,...,E i ,...,E n ] represents the error matrix set, E iRepresents the normalized sample matrix X i And the recovery matrix A i The deviation between.

[0122] In the specific implementation process, the elements in the weight map matrix are assigned values ​​through the Gaussian kernel function method.

[0123] More specifically, in step S4, the mathematical formula of the matrix feature learning model is:

[0124]

[0125] sP T AMA T P=I

[0126] Where P is a linear projection matrix with a dimension of m×d, d is the dimension of the set low-dimensional space, d<m; (·) T Represents the transpose of a matrix; represents the i-th recovery matrix A i and j

[0127] The recovery matrix A j The distance information between T A represents the set obtained after the dimensionality reduction of the recovery matrix set A, M is a diagonal matrix whose diagonal elements are m ii =∑ j s ij , I represents the identity matrix;

[0128] In order to facilitate the solution, the mathematical formula of the matrix feature learning model is derived as follows:

[0129]

[0130] sP T AMA T P=I

[0131] Tr(·) represents the trace of the matrix, and the Laplace matrix L=MS.

[0132] More specifically,

[0133] use ||P T A i -P T A j || 2，1 or ||P T A i -P T A j || * To calculate the distance of the matrix,

[0134] in, represents the square of the F-norm of the matrix, ||·|| 2，1 represents the L2,1 norm of the matrix, ||·|| * Represents the nuclear norm of the matrix.

[0135] In the specific implementation process, by introducing three different metrics: the square of the F norm, the L2,1 norm, and the nuclear norm, using different norms to calculate the loss function can avoid overfitting of the model during training, improve the robustness of the model, and reflect the sample correlation information from different angles. By selecting the optimal solution under the model framework, an optimal linear projection matrix is ​​learned.

[0136] More specifically, the mathematical formulas of the introduced matrix recovery term and constraint error term are:

[0137]

[0138] stX=A+E

[0139] Among them, φ(E) is the prior constraint on the error matrix set E, such as ||E||1, ||E||2, 1, ||E||*, ||·||1 represents the L1 norm of the matrix, ||·|| 2，1 represents the L2,1 norm of the matrix, ||·|| * represents the nuclear norm of the matrix; α and β represent weight balancing variables of different norm items. By changing the size of the two variables, we can explore the influence of each norm item on the model and achieve better learning effect. X represents the normalized sample matrix set, and A represents the recovery matrix set.

[0140] In the specific implementation process, different deviation constraints are introduced to explore the impact of errors on feature learning. Among them, the L1 norm and L2,1 norm can provide sparsity constraints on the error, while the nuclear norm can provide low-rank constraints on the error, thereby improving the robustness of the learned recovery matrix.

[0141] More specifically, the mathematical formula of the joint learning model is as follows:

[0142]

[0143] stX=A+E,P T AMA T P=I

[0144] Where P is a linear projection matrix of dimension m×d, represents the i-th recovery matrix A i and the jth recovery matrix A j The distance information between TA represents the set obtained after the dimensionality reduction of the recovery matrix set A, s ij represents the element in the i-th row and j-th column of the weight graph matrix S, α and β represent weight balancing variables of different norm terms, X represents the set of normalized sample matrices, ||·|| * represents the nuclear norm of the matrix, φ(E) is the prior constraint on the error matrix set E, M is a diagonal matrix, and I represents the identity matrix.

[0145] In the specific implementation process, the two-dimensional feature learning and matrix recovery process are integrated into a whole for joint learning to further obtain the essential image features.

[0146] More specifically, Figure 2 As shown, step S5 specifically includes the following steps:

[0147] S5.1: According to the augmented Lagrange multiplier method, the joint learning model is re-expressed as:

[0148]

[0149] sP T AMA T P=I

[0150]

[0151] sP T AMA T P=I

[0152] Among them, Q and B represent different Lagrange multipliers respectively; since it is difficult to solve the nuclear norm, an intermediate variable H is introduced, and H = A is used to approximate each other to achieve the solution; μ represents the step size coefficient, Represents the square of the F norm of the matrix;

[0153] S5.2: Fix the variables in the formula of step S5.1 that are not related to E and obtain:

[0154]

[0155] Find E based on the specific prior constraints of φ(E);

[0156] Fixing the variables that are not related to A in the formula of step S5.1 yields:

[0157]

[0158] Use matrix differentiation to directly derive A;

[0159] Fixing the variables in the formula of step S5.1 that are not related to H yields:

[0160]

[0161] Use Singular Value Thresholding (SVT) decomposition to find H;

[0162] Fixing the variables in the formula of step S5.1 that are not related to P yields:

[0163]

[0164] sP T AMA T P=I

[0165] Use generalized eigenvalue decomposition to find P;

[0166] S5.3: Update model parameters Q, B, μ:

[0167]

[0168] Among them, ρ is used to adjust the convergence speed of the iterative optimization process, 1<ρ<2;

[0169] S5.4: Determine whether the difference between two consecutive output values ​​of the optimized joint learning model is less than a preset threshold.

[0170] If so, the convergence condition is met, and the optimal recovery matrix set is obtained. The optimal recovery matrix set is reduced in dimension and output as the result of noise image processing;

[0171] If not, return to step S5.2 to iteratively update and optimize the joint learning model.

[0172] In the specific implementation process, the augmented Lagrange multiplier method (ADMM) is used to split the joint learning model that cannot be directly solved into several easy-to-solve sub-optimization problems. The method of iteratively updating different variables is adopted to gradually optimize the joint learning model, obtain the optimal recovery matrix set, and use P T The optimal recovery matrix set is projected into a low-dimensional space to obtain the most essential image features, that is, the output optimal recovery matrix set after dimensionality reduction.

[0173] The output optimal recovery matrix set after dimensionality reduction is used as sample data for subsequent learning tasks, such as classifying the environment of the power operation site, detecting and analyzing the faults of power equipment, and other image learning tasks, which can effectively improve the learning effect and efficiency of the algorithm.

[0174] Example 3

[0175] A noise image processing method based on robust matrix feature learning is basically the same as the noise image processing method based on robust matrix feature learning in Example 2, except that the method of assigning values ​​to the elements in the weight map matrix is ​​different. In this embodiment, the elements in the weight map matrix are assigned values ​​in the following manner:

[0176]

[0177]

[0178] Among them, s ij represents the element in the i-th row and j-th column of the weighted graph matrix S. Each element in the weighted graph matrix S represents the similarity relationship between the two normalized sample matrices. A=[A1,A2,…A i ,…,A n ] represents the recovery matrix set, A i Represents the normalized sample matrix X i The recovery matrix, N k (A j ) represents the jth recovery matrix A j The k nearest neighbor set of , t represents the bandwidth of the Gaussian kernel function;

[0179] The normalized sample matrix set X and the recovery matrix set A have the following relationship:

[0180] X=A+E

[0181] Where E=[E1,E2,...,E i ,...,E n ] represents the error matrix set, E i Represents the normalized sample matrix X i And the recovery matrix A i The deviation between.

[0182] In the specific implementation process, the elements in the weight map matrix are assigned values ​​through a local linear reconstruction method.

[0183] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the embodiments here. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A noisy image processing method based on robust matrix feature learning, characterized in that: The following steps are involved: S1: Obtain a noise image to be processed, and convert the noise image into a matrix form to obtain a sample matrix, thereby forming a sample matrix set; S2: performing matrix normalization processing on the sample matrix set to obtain a normalized sample matrix set; S3: construct a weight graph matrix according to the similarity relationship of matrices in the normalized sample matrix set; S4: construct a matrix feature learning model according to the weight map matrix, and introduce matrix recovery terms and constraint error terms to obtain a joint learning model; S5: Optimize the joint learning model and output the optimal recovery matrix set after dimension reduction as the noisy image processing result; The mathematical formula of the joint learning model is as follows: s.t.X=A+E,P T AMA T P=I Where P is a linear projection matrix with a dimension of m×d, d is the dimension of the set low-dimensional space, d<m, (·) T represents the transpose of a matrix, represents the i-th recovery matrix A i and the jth recovery matrix A j The distance information between T A represents the set obtained after the dimensionality reduction of the recovery matrix set A, s ij represents the element in the i-th row and j-th column of the weight graph matrix S, α and β represent weight balancing variables of different norm terms, X represents the set of normalized sample matrices, ||·|| * represents the nuclear norm of the matrix, φ(E) is the prior constraint on the error matrix set E, M is a diagonal matrix, and I represents the identity matrix; S5 specifically includes the following steps: S5.1: According to the augmented Lagrange multiplier method, the joint learning model is re-expressed as: s.t.P T AMA T P=I s.t.P T AMA T P=I Among them, Q and B represent different Lagrange multipliers, H represents the intermediate variable, μ represents the step size coefficient, represents the square of the F-norm of the matrix, φ(E) is the prior constraint on the error matrix set E; S5.2: Fix the variables in the formula of step S5.1 that are not related to E and obtain: Find E based on the specific prior constraints of φ(E); Fixing the variables that are not related to A in the formula of step S5.1 yields: Where Tr(·) represents the trace of the matrix, and the Laplace matrix L = MS; Use matrix differentiation to directly derive A; Fixing the variables in the formula of step S5.1 that are not related to H yields: Use singular value threshold decomposition to find H; Fixing the variables in the formula of step S5.1 that are not related to P yields: s.t.P T AMA T P=I Use generalized eigenvalue decomposition to find P; S5.3: Update model parameters Q, B, μ: Among them, ρ is used to adjust the convergence speed of the iterative optimization process, 1<ρ<2; S5.4: Determine whether the difference between two consecutive output values ​​of the optimized joint learning model is less than a preset threshold. If so, the convergence condition is met, and the optimal recovery matrix set is obtained. The optimal recovery matrix set is reduced in dimension and output as the result of noise image processing; If not, return to step S5.2 to iteratively update and optimize the joint learning model.

2. The method for processing noisy images based on robust matrix feature learning according to claim 1, characterized in that: In step S1, the noisy image is converted into a matrix form by: The matrix is ​​constructed according to the position of each pixel in the noise image corresponding to a matrix element, and the corresponding matrix element is assigned a value according to the color of the pixel.

3. The method for processing noisy images based on robust matrix feature learning according to claim 1, characterized in that: The matrix normalization process in step S2 is specifically as follows: For the sample matrix set X′=[(X1)′,(X2)′,…(X i )′,…,(X n )′] are divided by their own F norms to obtain the normalized sample matrix set X = [X1, X2, …X i ,…,X n ]Right now: Among them, (X i )′ represents the i-th sample matrix, the dimension of the sample matrix is ​​m×l, ‖(X i )′‖ F Indicates (X i )′, X i Represents the i-th normalized sample matrix.

4. The method for processing noisy images based on robust matrix feature learning according to claim 1, characterized in that: The elements in the weight map matrix are assigned as follows: Among them, s ij represents the element in the i-th row and j-th column of the weighted graph matrix S. Each element in the weighted graph matrix S represents the similarity relationship between the two normalized sample matrices; A = [A1, A2, ... A i ,…,A n ] represents the recovery matrix set, A i Represents the normalized sample matrix X i The restoration matrix; N k (A j ) represents the jth recovery matrix A j The k nearest neighbor set of ; represents the distance between the two matrices; t represents the bandwidth of the Gaussian kernel function; The normalized sample matrix set X and the recovery matrix set A have the following relationship: X=A+E Where E=[E1,E2,...,E i ,...,E n ] represents the error matrix set, E i Represents the normalized sample matrix X i And the recovery matrix A i The deviation between.

5. The method for processing noisy images based on robust matrix feature learning according to claim 1, characterized in that: The elements in the weight map matrix are assigned as follows: Among them, s ij represents the element in the i-th row and j-th column of the weighted graph matrix S. Each element in the weighted graph matrix S represents the similarity relationship between the two normalized sample matrices. A=[A1,A2,…A i ,…,A n ] represents the recovery matrix set, A i Represents the normalized sample matrix X i The recovery matrix, N k (A j ) represents the jth recovery matrix A j The k nearest neighbor set of , t represents the bandwidth of the Gaussian kernel function; The normalized sample matrix set X and the recovery matrix set A have the following relationship: X=A+E Where E=[E1,E2,...,E i ,...,E n ] represents the error matrix set, E i Represents the normalized sample matrix X i And the recovery matrix A i The deviation between.

6. The method for processing noisy images based on robust matrix feature learning according to claim 1, characterized in that: In step S4, the mathematical formula of the matrix feature learning model is: s.t.P T AMA T P=I Among them, P is a linear projection matrix of dimension m×d, d is the dimension of the set low-dimensional space, d<m;(·) T Represents the transpose of a matrix; represents the i-th recovery matrix A i and j The recovery matrix A j The distance information between T A represents the set obtained after the dimensionality reduction of the recovery matrix set A. M is a diagonal matrix, I represents the identity matrix; In order to facilitate the solution, the mathematical formula of the matrix feature learning model is derived as follows: m P inTr(P T THAT T P) s.t.P T AMA T P=I Tr(·) represents the trace of the matrix, and the Laplace matrix L=MS.

7. The method for processing noisy images based on robust matrix feature learning according to claim 6, characterized in that: use ||P T A i -P T A j || 2，1 or ||P T A i -P T A j || * To calculate the distance of the matrix, in, represents the square of the F-norm of the matrix, ||·|| 2，1 represents the L2,1 norm of the matrix, ||·|| * Represents the nuclear norm of the matrix.

8. The method for processing noisy images based on robust matrix feature learning according to claim 1, characterized in that: The mathematical formulas of the introduced matrix recovery term and constraint error term are: stX=A+E Among them, φ(E) is the prior constraint on the error matrix set E, such as ||E||1, ||E|| 2，1 、||E|| * ,||·||1 represents the L1 norm of the matrix,||·|| 2，1 represents the L2,1 norm of the matrix, ||·|| * represents the nuclear norm of the matrix; α and β represent different norm term weight balancing variables, X represents the normalized sample matrix set, and A represents the recovery matrix set.

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