Hyperspectral image restoration method integrating sparse and low-rank prior

Abstract

The invention discloses a hyperspectral image restoration method integrating sparse and low-rank prior. The method comprises the following steps: identifying image information; inputting codes into an optimization model: extracting image features, inputting the extracted features into an encoder, arranging the encoded features into an observation matrix, and inputting the observation matrix into the optimization model to obtain an optimization model; the optimization model is used for decomposing the observation matrix into a low-rank matrix L for capturing a data basic structure and a sparse matrix S for capturing an abnormal value; calculating and recovering by using an algorithm; and output image recovery: analyzing the noisy hyperspectral image data and decomposing the noisy hyperspectral image data to obtain a low-rank underlying structure L and a sparse anomaly S, then respectively recovering a low-rank part L and a sparse part S, and finally combining the low-rank part L and the sparse part S to generate a final recovery result, namely the processed image. The method not only can better process a complex data set, but also can improve the quality of image restoration.

Description

Technical Field

[0001] The invention relates to the technical field of data dimensionality reduction and restoration, and in particular to a hyperspectral image restoration method integrating sparse and low-rank priors. Background Art

[0002] In the past 20 years, the world has entered the "big data era". The amount and dimension of data have reached an unprecedented scale and are still growing at an unprecedented rate. In the information industry, more and more tasks require processing and analyzing large amounts of data every day. In the past, people collected corresponding data and signals according to the needs of the task in most cases, and did not contain much redundant or irrelevant information except for some uncontrollable noise. However, the continuous development of technologies such as the Internet and high-quality imaging has fundamentally changed the way data is collected and analyzed. The world is moving from an era of "data scarcity" to an era of "data abundance".

[0003] However, “data rich” does not necessarily mean “information rich”. When faced with tasks that require obtaining specific information from a highly redundant sampled data set containing a large amount of irrelevant data, scholars have found through research [7] that in a large number of application scenarios, the specific information required for the task is usually encoded as some low-dimensional structure beneath the data.

[0004] Principal component analysis (PCA) is a main method for dimensionality reduction, which aims to find the best low-dimensional linear subspace of high-dimensional data in Euclidean space. PCA has a wide range of applications in many fields, including computer vision, bioinformatics, and signal and image processing, because in many real-world data, most of the information exists in low-dimensional subspaces. However, due to the uncontrollable data collection process, the quality of the collected data is uneven and often inevitably contains different degrees of interference.

[0005] Robust Principal Component Analysis (RPCA): RPCA is a robust version of PCA, which enhances the robustness of data analysis by decomposing the data into low-rank and sparse matrices, effectively isolating outliers and capturing the underlying data structure.

[0006] Existing methods include RPCA algorithms such as RPCA-HQF, Accelerated Alternating Projection (AccAltProj), TNNR-APGL and RCPA-CUR. These algorithms are all proposed to solve the problem of RPCA, but they may face some challenges when dealing with complex data sets. For example, when different materials are closely located together, the resulting spectrum may be a highly nonlinear combination of end members, resulting in model anomalies. The following is a brief description of the existing technology:

[0007] 1) RPCA-HQF is an algorithm for processing data, especially for cases with outliers. The RPCA-HQF algorithm combines the ideas of sparse representation and low-rank representation, aiming to decompose the data into a combination of a low-rank matrix and a sparse matrix.

[0008] The core idea of ​​this algorithm is to decompose the data matrix into low-rank components and sparse components in order to better capture the structural information of the data. Low-rank components usually represent the main structure in the data, while sparse components represent outliers or noise. By decomposing the data into these two parts, RPCA-HQF can more accurately separate the real signal and outliers, thereby improving the quality and efficiency of data processing.

[0009] The advantages of the RPCA-HQF algorithm include strong robustness to different types of outliers in the data and the ability to provide high-quality fitting results, which makes it have broad application prospects in fields such as image processing, video analysis, and signal processing.

[0010] 2) AccAltProj is an iterative algorithm for solving convex optimization problems. The main goal of the algorithm is to reduce the value of the objective function as much as possible in each iteration, so as to gradually approach the optimal solution. It is mainly used to solve convex optimization problems containing linear constraints, such as linear programming problems, least squares problems, etc. Its basic idea is to search for the optimal solution in the feasible solution set by alternating projections. In each iteration, the AccAltProj algorithm projects the objective function according to the current solution to obtain a new solution, and ensures that the new solution meets the constraints of the problem.

[0011] The "acceleration" part of the algorithm usually refers to the use of some acceleration techniques or improvement strategies based on the standard alternating projection algorithm, such as the use of momentum terms, adaptive step sizes, etc., to improve the convergence speed and stability of the algorithm.

[0012] It has certain advantages in practical applications, especially for large-scale convex optimization problems. It can effectively handle linear constraints and gradually approach the optimal solution during the iteration process, so it has been widely used in the field of optimization.

[0013] 3) TNNR-APGL is an algorithm for processing tensor data, especially for cases with missing values ​​or outliers. The TNNR-APGL algorithm combines tensor nuclear norm regularization and alternating direction multiplication method, aiming to decompose tensor data into a combination of a low-rank tensor and a sparse tensor.

[0014] Its core idea is to better capture the structural information of the data by decomposing the tensor into low-rank components and sparse components. The low-rank components usually represent the main structure in the data, while the sparse components represent outliers or noise. By decomposing the data into these two parts, the TNNR-APGL algorithm can more accurately separate the real signal and outliers, thereby improving the quality and efficiency of data processing.

[0015] The advantages of this algorithm include strong robustness to different types of outliers in the data and the ability to provide high-quality fitting results, which makes it have broad application prospects in fields such as image processing, video analysis, and signal processing.

[0016] 4) RCPA-CUR is a matrix decomposition and data dimension reduction algorithm that combines the ideas of sparse decomposition and low-rank approximation. Through column selection and row selection, the most representative columns and rows of the original data are selected to reduce the data dimension. Then, the selected row and column data are processed using robust decomposition to obtain the results of low-rank approximation and sparse representation, and finally these results are used to reconstruct the original data. This method can effectively extract key information and reduce data dimensions, and is suitable for fields such as data dimension reduction, feature selection and signal processing.

[0017] Although existing robust principal component analysis (RPCA) techniques, such as RPCA-HQF, AccAltProj, TNNR-APGL and RPCA-CUR, have achieved certain results in dealing with RPCA problems, they still have some problems and shortcomings.

[0018] Limited processing power for complex data sets: When dealing with complex data sets, such as when different materials are located closely together, the resulting spectra may be highly nonlinear combinations of end members, which may lead to model anomalies. This is because these algorithms are mainly based on linear models and have limited processing power for nonlinear data structures.

[0019] Image restoration quality needs to be improved: When performing image restoration, these algorithms do not perform well in terms of color restoration and image reconstruction quality. For example, some algorithms may not be able to effectively restore image details and colors when dealing with high noise or low signal-to-noise ratio situations.

[0020] Computational efficiency issues: Some existing RPCA algorithms, such as TNNR-APGL and AccAltProj, may face computational efficiency issues when processing large-scale datasets. This may be due to the fact that these algorithms require a large number of iterations and calculations during the optimization process, which may lead to computational inefficiency when processing large-scale datasets. Summary of the invention

[0021] In order to solve the problems existing in the prior art, the purpose of the present invention is to provide a hyperspectral image restoration method integrating sparse and low-rank priors, which can not only better process complex data sets, but also improve the quality of image restoration.

[0022] To achieve the above object, the technical solution adopted by the present invention is: a hyperspectral image restoration method integrating sparse and low-rank priors, comprising the following steps:

[0023] Step 1: Identify image information;

[0024] Step 2, encoding input optimization model: extract image features, input the extracted features into the encoder, arrange the encoded features into a measurement matrix, and input the measurement matrix into the optimization model, the optimization model is used to decompose the measurement matrix into a low-rank matrix L that captures the basic structure of the data and a sparse matrix S that captures outliers;

[0025] Step 3: Use the algorithm to calculate the recovery;

[0026] Step 4: Restore the output image: Analyze the noisy hyperspectral image data and decompose it to obtain the low-rank underlying structure L and the sparse anomaly S, then restore the low-rank part L and the sparse part S respectively, and finally combine the low-rank part L and the sparse part S to generate the final restored result, that is, the processed image.

[0027] As a further improvement of the present invention, step 2 specifically comprises the following steps:

[0028] Step 2.1, use robust principal component analysis to decompose the observation matrix into a low-rank matrix and a sparse matrix:

[0029] min L,S rank(L)+λ‖S‖ 0 stD=L+S

[0030] Represents the observation matrix, which is a low-rank matrix and sparse matrices The sum of, cardinality ‖S‖ 0 represents the number of non-zero elements in S;

[0031] Step 2.2: Replace the rank function with the nuclear norm and change L 0 Norm replaced by L 1 Norm:

[0032]

[0033] Step 2.3: Extend the robust principal component analysis to projected robust principal component analysis:

[0034]

[0035] Where P and Q are row smoothers and column smoothers respectively;

[0036] Step 2.4: Expand the nuclear norm in the projected robust principal component analysis to the truncated nuclear norm, which is as follows:

[0037]

[0038] Step 2.5: L in the projected robust principal component analysis 1 The norm is extended to the logarithmic hyperbolic cosine function as follows:

[0039] g(x)=ln[cosh(αx)]

[0040] Where α is a scaling factor;

[0041] Step 2.6: Integrate the semi-quadratic function and the truncated kernel to obtain a robust integrated sparse and low-order prior:

[0042]

[0043] Step 2.7. Optimize the robust ensemble sparse and low-order priors by using alternating minimization:

[0044] Keeping S constant and minimizing the objective function with respect to another variable L, we get the first subproblem:

[0045]

[0046] Keep L constant and minimize S through the second subproblem:

[0047]

[0048] Step 2.8: For any given matrix and matrix AA T =I,BB T =I, where r≤min(m,n), the first subproblem is rewritten as follows:

[0049]

[0050] As a further improvement of the present invention, step 3 specifically includes the following steps:

[0051] Step 3.1. Input regularization parameter λ 1 ,λ 2 , scaling factor α, highly non-convex regularized data matrix D to be decomposed, tolerance ∈, parameter δ;

[0052] Step 3.2: Initialize L(0) For D, S (1) is 0, and the following steps are repeated until the convergence condition is met;

[0053] Step 3.3: Fix S (k) And update L (k+1) ;

[0054] Step 3.4, fix L (k+1) ,use

[0055] Step 3.5: Check whether the convergence condition || L is met (k+1) -L (k) || F ≤∈; if satisfied, proceed to the next step; otherwise return to the step to continue updating;

[0056] Step 3.6: Output L (k+1) ,S (k+1) ;

[0057] As a further improvement of the present invention, step 3.3 specifically includes the following steps:

[0058] Step 3.3.1: Given L (k) , calculate L (k) The singular value decomposition of U (k) ,Σ (k) ,V (k) ;

[0059] Step 3.3.2, define A (k) ,B (k) For U (k) and V (k) The transpose of the first r columns of ;

[0060] Step 3.3.3, solve the optimization problem:

[0061]

[0062] Get L (k+1) , using the accelerated proximal gradient method;

[0063]

[0064] Step 3.3.5: Output L (k+1) .

[0065] The beneficial effects of the present invention are:

[0066] The present invention proposes a hyperspectral image restoration method integrating sparse and low-rank prior (RPCA-LHCF), which can not only better process complex data sets, but also improve the quality of image restoration, and adopts the proximal gradient algorithm to improve the computational efficiency; this makes RPCA-LHCF have great potential in processing complex data sets, especially in the fields of computational hyperspectral imaging. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 is a flow chart of an embodiment of the present invention;

[0068] Figure 2 A flow chart of an optimization model in an embodiment of the present invention;

[0069] Figure 3 Schematic diagram of relative recovery error of the algorithm under different signal-to-noise ratios (SNR) in an embodiment of the present invention;

[0070] Figure 4 Schematic diagram of relative recovery errors of algorithms under different ranks in an embodiment of the present invention;

[0071] Figure 5 RGB renderings of hyperspectral images restored by different algorithms in embodiments of the present invention;

[0072] Figure 6 ] are the spatial PSNR values ​​of the hyperspectral images restored by different algorithms in the embodiments of the present invention. DETAILED DESCRIPTION

[0073] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0074] Example

[0075] A hyperspectral image restoration method integrating sparse and low-rank priors includes: receiving a complex data set to be analyzed; selecting appropriate low-rank and sparse information according to data characteristics to determine the corresponding low-rank module and sparse module in the RPCA-LHCF method; using the low-rank module to restore the complex data to be analyzed to obtain a preliminary low-rank data representation; using the sparse module to restore the complex data to be analyzed to obtain a preliminary sparse data representation; combining the preliminary low-rank data and the preliminary sparse data to obtain the final data recovery result of the RPCA-LHCF method. Through this method, RPCA-LHCF can process complex data sets more specifically, thereby improving the processing capability of complex data sets. Compared with using only a single module, RPCA-LHCF can better extract low-rank structure and sparse information in the data by considering both data and low-rank structural information, thereby improving the accuracy of data recovery. In addition, different low-rank and sparse combinations are flexibly selected according to data characteristics and features, so that the RPCA-LHCF method is more effective in processing different types of data, which further improves the accuracy of data recovery.

[0076] like Figure 1 As shown, the specific steps include:

[0077] Step S101, identifying image information;

[0078] Step S102, encoding input optimization model;

[0079] Among them, image feature extraction is a key step in image processing, which aims to extract representative features from the original image for subsequent analysis and processing. This process can be achieved through traditional image processing methods (such as edge detection, corner detection, texture feature extraction and color feature extraction) and deep learning methods (such as convolutional neural networks). Traditional methods focus on extracting obvious visual features from images, while deep learning methods automatically extract abstract features by learning feature representations from large amounts of data. These extracted features can be further used in application fields such as image classification, target detection, and image retrieval, which are of great significance for image processing and analysis.

[0080] Next, an encoder is used to convert the extracted image features into a more compact representation. This step is to reduce the dimension of the features and extract their most representative information. The choice of encoder can be flexibly adjusted according to specific tasks and requirements. Common encoders include autoencoders, variational autoencoders (VAE), generative adversarial networks (GANs), etc. The autoencoder learns to map the input image to a hidden representation space and reconstructs the original image, so that the encoded features contain the key information of the input image. The variational autoencoder generates data by learning the distribution of hidden variables, which can be used to generate diverse feature representations. The generative adversarial network trains the generator and discriminator in a game-based manner to generate an encoder with high-quality feature representations. These encoded features usually have lower dimensions and contain key information of the input image, providing a more effective data representation for subsequent image processing and analysis.

[0081] The encoded features are arranged into an observation matrix. The rows of the observation matrix usually correspond to different samples, and the columns correspond to the feature dimensions. This process can be regarded as reorganizing the original data into a matrix for subsequent processing and analysis.

[0082] Finally, the observation matrix is ​​input to the optimization model. The optimization model aims to decompose the observed matrix D into two parts: a low-rank matrix L that captures the basic structure of the data, and a sparse matrix S that captures outliers. By using the nuclear norm and L 1 The norm or semi-quadratic function is used as a regularization term to improve the robustness and sparsity of the model. The original non-convex problem is handled by a convex relaxation method, and the optimization problem is solved by an alternating minimization algorithm, providing an efficient computational solution suitable for a variety of signal processing and machine learning tasks.

[0083] Step S103, using an algorithm to calculate and restore;

[0084] Step S104, restoring the output image;

[0085] The noisy hyperspectral image data is analyzed and decomposed to obtain the low-rank underlying structure L and sparse anomalies S. This step aims to separate the basic structure of the image from the noise and outliers. Subsequently, the algorithm recovers the low-rank part L and the sparse part S separately to more accurately reconstruct the intrinsic features and outliers of the image. Finally, the low-rank part L and the sparse part S are combined to generate the final recovery result, which is the processed image.

[0086] Species Figure 2 As shown, step S102 specifically includes:

[0087] Step S1021, RPCA decomposes the matrix into a low-rank and sparse matrix, which can be directly expressed mathematically as:

[0088] min L,S rank(L)+λ‖S‖ 0 stD=L+S. (1)

[0089] Step S1022: In this model, the matrix Represents the observed matrix, which is a low-rank matrix and a sparse matrix The goal of the model is to decompose X into its low-rank part L and sparse part S. The cardinality ‖S‖ 0 represents the number of nonzero elements in S, which is a measure of its sparsity.

[0090] A straightforward approach to this decomposition involves solving an optimization problem that minimizes the rank and cardinality. However, since the rank function and L 0 The norms are both non-convex and discrete in the rank case, making the problem computationally intractable.

[0091] To overcome this computational challenge, the problem is reformulated by replacing the rank function with the nuclear norm (the sum of the matrix singular values) and L 0 Norm replaced by L 1 norm (the sum of the absolute values ​​of the matrix elements). This substitution leads to a convex relaxation of the original problem, making it computationally feasible to solve:

[0092]

[0093] Step S1023: Extend RPCA to projected robust principal component analysis (PRPCA):

[0094]

[0095] where P and Q are some row and column smoothers, respectively;

[0096] Step S1024: In order to further mine low-rank priors, the nuclear norm in PRPCA is extended to the truncated nuclear norm. The truncated nuclear norm is a variant of the nuclear norm, which is used to improve the performance of low-rank matrix recovery in various signal processing and machine learning tasks. However, the nuclear norm treats all singular values ​​equally, which may not always be ideal, especially when some singular values ​​are significantly larger than other singular values, indicating that there is important structural information in the matrix that should be retained. The truncated nuclear norm is defined as:

[0097]

[0098] Step S1025, this method aims to focus on the lower part of the singular value spectrum, under the premise that the smallest singular value contributes more to the noise or redundancy in the data, while the largest singular value carries the most important structural information about the matrix. By truncating or omitting a certain number of the largest singular values ​​from the summation, the truncated nuclear norm attempts to provide a more refined approximation of the matrix rank, which can better recover the low-rank components by reducing the influence of the largest singular value that is assumed to represent the basic characteristics of the data. On the other hand, the L in PRPCA 1 The norm is extended to the log-hyperbolic cosine function to achieve robustness and sparsity. The log-hyperbolic cosine function is defined as:

[0099] g(x)=ln[cosh(αx)]

[0100] Here, α is a scaling factor.

[0101] Step S1026, parameter δ can be adjusted to approximate the L1 norm. Finally, the semi-quadratic function and the truncated kernel are integrated, and a model, robust PCA integrated sparse and low-order prior (RPCA-LHCF), is proposed, as shown below:

[0102]

[0103] Step S1027. In (6), it is tractable to optimize both L and S simultaneously, so (6) is optimized by using alternating minimization. Alternating minimization is an optimization technique used to solve problems involving minimizing a function with respect to two (or more) sets of variables by alternately fixing one set of variables and optimizing the other set of variables. This approach is particularly useful when one set of variables is kept constant, where the optimization problem can be simplified or made more tractable. Alternating minimization of (6) involves two main steps that are repeated iteratively:

[0104] Step 1: Keep S constant and minimize the objective function with respect to another variable L. Therefore, there are sub-problems:

[0105]

[0106] Step 2: Keep L constant and minimize S by the following subproblems

[0107]

[0108] Step S1028, Lemma 1. For any given matrix and matrix AA T =I,BB T =I, where r≤min(m,n), (7) can be rewritten as follows:

[0109]

[0110] Step S103 of this embodiment specifically includes:

[0111] Step S1031: input regularization parameter λ 1 ,λ 2 , scaling factor α, highly non-convex regularized data matrix D to be decomposed, tolerance ∈, parameter δ;

[0112] Step S1032: Initialize L (0) For D, S (1) is 0, and the following steps are repeated until the convergence condition is met;

[0113] Step S1033: Fix S (k) , use Algorithm 1 to update L (k+1) , the L matrix is ​​gradually optimized by iterative solution of singular value decomposition and accelerated proximal gradient method. The steps are simple and clear, and the L matrix optimization in the RPCA-LHCF model is effectively realized. Step S1033 specifically includes:

[0114] Obtain L through Algorithm 1 (k+1) Step S10331 specifically includes:

[0115] Step S103311: Given L (k) , calculate L (k) The singular value decomposition of U (k) ,Σ (k) ,V (k) ;

[0116] Step S103312: Define A (k) ,B (k) For U (k) and V (k) The transpose of the first r columns of ;

[0117] Step S103313, solving the optimization problem:

[0118]

[0119] Get L (k+1) , using the accelerated proximal gradient method;

[0120]

[0121]

[0122] Step S103314, until the convergence condition ‖L is met (k+1) -L (k) ‖ F ≤∈;

[0123] Step S103315: Output L (k+1) ;

[0124] Step S1034: Fix L (k+1) ,use

[0125] Step S1035: Check whether the convergence condition ‖L is satisfied (k+1) -L (k) ‖ F If ≤∈ is satisfied, proceed to the next step; otherwise, return to step S1033 to continue updating;

[0126] Step S1036: Output L (k+1) ,S (k+1) ;

[0127]

[0128] This flow describes in detail the RPCA-LHCF method that combines Algorithm 1 and Algorithm 2. By alternately optimizing L and S, efficient data decomposition and anomaly detection are achieved.

[0129] Figure 3 and Figure 4 This is an experiment on simulation data, from which we can see that the proposed RPCA-LHCF algorithm:

[0130] Processing ability for complex data sets: The relative error of RPCA-LHCF decreases at high signal-to-noise ratio, showing its robustness to noise. Under different ranks r, the relative error of RPCA-LHCF grows slowly, indicating that it has strong processing ability for complex data.

[0131] Image restoration quality: The relative error of RPCA-LHCF is relatively low at high signal-to-noise ratio, indicating that its image restoration quality is improved. When the rank r increases, the restoration effect of RPCA-LHCF decreases more slowly than other algorithms, which also indicates that its image restoration quality is improved.

[0132] Computational efficiency: From the perspective of denoising effect with fewer iterations, the RPCA-LHCF algorithm has higher computational efficiency.

[0133] Figure 5 and Figure 6 is an experiment conducted on hyperspectral images. Figure 5 Among them, (a) is RPCA-LHCF, (b) is RPCA-HQF, (c) is TNNR-APGL, (d) is AccAltProj, and (e) is RPCA-CUR; Figure 6In the experiment, (a) is RPCA-LHCF, (b) is RPCA-HQF, (c) is TNNR-APGL, (d) is AccAltProj, and (e) is RPCA-CUR. From this experiment, we can see that the proposed RPCA-LHCF algorithm:

[0134] Ability to process complex data sets: RPCA-LHCF can effectively process complex data sets such as hyperspectral images. It can extract useful information from multispectral imaging, generate a spectral response vector for each pixel, and obtain information in the form of a third-order tensor. This experimental result confirms that RPCA-LHCF has made improvements in processing such complex structured data.

[0135] Image restoration quality: In Figure 6, we can see that the heat map of algorithm (a) RPCA-LHCF is mainly blue, indicating that most images have high PSNR values. This means that among various algorithms, this method has the highest image restoration quality. Compared with other competing algorithms, RPCA-LHCF performs better in restoring low-rank native images.

[0136] Computational efficiency: It is able to achieve excellent results in effective operations on practical ultra-low-rank and ultra-large-scale hyperspectral images, which means that the algorithm is computationally efficient and practical.

[0137] In general, the experimental results support that RPCA-LHCF has improved the limitations of complex dataset processing capabilities, image restoration quality, and computational efficiency to a certain extent.

[0138] The above-mentioned embodiments only express the specific implementation of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the present invention. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A hyperspectral image restoration method integrating sparse and low-rank priors, characterized in that: The following steps are involved: Step 1: Identify image information; Step 2, encoding input optimization model: extract image features, input the extracted features into the encoder, arrange the encoded features into a measurement matrix, and input the measurement matrix into the optimization model, the optimization model is used to decompose the measurement matrix into a low-rank matrix L that captures the basic structure of the data and a sparse matrix S that captures outliers; Step 3: Use the algorithm to calculate the recovery; Step 4: Restore the output image: Analyze the noisy hyperspectral image data and decompose it to obtain the low-rank underlying structure L and the sparse anomaly S, then restore the low-rank part L and the sparse part S respectively, and finally combine the low-rank part L and the sparse part S to generate the final restored result, that is, the processed image.

2. The hyperspectral image restoration method integrating sparse and low-rank priors according to claim 1, characterized in that: Step 2 specifically includes the following steps: Step 2.1, use robust principal component analysis to decompose the observation matrix into a low-rank matrix and a sparse matrix: bad L，S rank(L)+λ||S||0s.tD=L+S Represents the observation matrix, which is a low-rank matrix and sparse matrices The sum of , the cardinality ||S||0 represents the number of non-zero elements in S; Step 2.2, replace the rank function with the nuclear norm, and replace the L0 norm with the L1 norm: Step 2.3: Extend the robust principal component analysis to projected robust principal component analysis: Where P and Q are row smoothers and column smoothers respectively; Step 2.4: Expand the nuclear norm in the projected robust principal component analysis to the truncated nuclear norm, which is as follows: Step 2.5: Extend the L1 norm in the projected robust principal component analysis to the logarithmic hyperbolic cosine function as follows: g(x)=ln[cosh(αx)] Where α is a scaling factor; Step 2.6: Integrate the semi-quadratic function and the truncated kernel to obtain a robust integrated sparse and low-order prior: Step 2.

7. Optimize the robust ensemble sparse and low-order priors by using alternating minimization: Keeping S constant and minimizing the objective function with respect to another variable L, we get the first subproblem: Keep L constant and minimize S through the second subproblem: Step 2.8: For any given matrix and matrix AA T =I, BB T =I, where r≤min(m,n), the first subproblem is rewritten as follows:

3. The hyperspectral image restoration method integrating sparse and low-rank priors according to claim 2, characterized in that: Step 3 specifically includes the following steps: Step 3.1, input regularization parameters λ1, λ2, scaling factor α, highly non-convex regularized data matrix D to be decomposed, tolerance ∈, parameter δ; Step 3.2, initialize L( 0 ) is D, S( 1 ) is 0, and the following steps are repeated until the convergence condition is met; Step 3.3, fix S( k ) and update L( k+1 ); Step 3.4, fix L (k+1) ,use Update S (k+1) ; Step 3.5: Check whether the convergence condition || L is met (k+1) -L (k) || F ≤∈; if satisfied, proceed to the next step; otherwise return to the step to continue updating; Step 3.6: Output L (k+1) , S (k+1) .

4. The hyperspectral image restoration method integrating sparse and low-rank priors according to claim 3, characterized in that: Step 3.3 specifically includes the following steps: Step 3.3.1: Given L (k) , calculate L (k) The singular value decomposition of U (k) ,∑ (k) , V (k) ; Step 3.3.2, define A (k) , B (k) For U (k) and V (k) The transpose of the first r columns of ; Step 3.3.3, solve the optimization problem: Get L (k+1) , using the accelerated proximal gradient method; Step 3.3.4, until the convergence condition ||L is met (k+1) -L (k) || F ≤∈; Step 3.3.5: Output L (k+1) .

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