Hyperspectral Image Restoration Method Integrating Sparse and Low-Rank Priors

Abstract

This invention discloses a hyperspectral image restoration method integrating sparse and low-rank priors, comprising: identifying image information; encoding input to 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 an optimization model, wherein the optimization model is used to decompose the observation matrix into a low-rank matrix L capturing the basic structure of the data and a sparse matrix S capturing outliers; calculating restoration using an algorithm; restoring the output image: by analyzing noisy hyperspectral image data and decomposing it to obtain the low-rank underlying structure L and sparse outliers S, then restoring the low-rank part L and the sparse part S respectively, and finally combining the low-rank part L and the sparse part S to generate the final restoration result, i.e., the processed image; this invention can not only better handle complex datasets, but also improve the quality of image restoration.

Description

Technical Field

[0001] This invention relates to the field of data dimensionality reduction and restoration technology, and in particular to a hyperspectral image restoration method that integrates sparseness and low-rank priors. Background Technology

[0002] Over the past 20 years, the world has entered the "Big Data Era," with the quantity and dimensions of data reaching unprecedented levels and continuing to grow at an unprecedented rate. In the information industry, an increasing number of tasks require the processing and analysis of massive amounts of data daily. In the past, data and signals were mostly collected according to the needs of the task, containing little redundant or irrelevant information beyond 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, “rich data” does not necessarily mean “rich information”. When faced with tasks that require obtaining specific information from highly redundant sampled datasets containing a large amount of irrelevant data, scholars have found through research [7] that in many application scenarios, the specific information required by the task is usually encoded as some low-dimensional structure under the data.

[0004] Principal Component Analysis (PCA) is a leading method for dimensionality reduction, aiming to find the optimal low-dimensional linear subspace of high-dimensional data within Euclidean space. PCA has wide applications in various fields, including computer vision, bioinformatics, and signal and image processing, because much of the information in real-world data resides in low-dimensional subspaces. However, due to the uncontrollable nature of the data acquisition process, the quality of the acquired data varies considerably, often inevitably containing varying degrees of interference.

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

[0006] Existing methods include RPCA-HQF, Accelerated Alternating Projection (AccAltProj), TNNR-APGL, and RCPA-CUR, among other RPCA algorithms. These algorithms were proposed to address the RPCA problem, but they may face challenges when dealing with complex datasets. For example, when different materials are closely packed together, the resulting spectra may exhibit highly nonlinear combinations of endmembers, leading to model anomalies. The following is a brief description of the existing techniques:

[0007] 1) RPCA-HQF is an algorithm for processing data, particularly suitable 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 and sparse components to better capture the structural information of the data. Low-rank components typically represent the main structure of the data, while sparse components represent outliers or noise. By decomposing the data into these two parts, RPCA-HQF can more accurately separate true signals from outliers, thereby improving the quality and efficiency of data processing.

[0009] The advantages of the RPCA-HQF algorithm include its strong robustness to different types of outliers in the data and its ability to provide high-quality fitting results. This makes it a promising candidate for applications in fields such as image processing, video analysis, and signal processing.

[0010] 2) AccAltProj is an iterative algorithm for solving convex optimization problems. Its main objective is to minimize the value of the objective function in each iteration, thereby gradually approaching the optimal solution. It is primarily used to solve convex optimization problems with linear constraints, such as linear programming and least squares problems. Its basic idea is to search for the optimal solution in the feasible solution set through alternating projections. In each iteration, the AccAltProj algorithm projects the objective function based on the current solution to obtain a new solution, ensuring that the new solution satisfies the problem's constraints.

[0011] The "acceleration" part of this algorithm usually refers to the use of some speed-up techniques or improvement strategies on the basis of the standard alternating projection algorithm, such as using 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, thus it has been widely used in the field of optimization.

[0013] 3) TNNR-APGL is an algorithm for processing tensor data, particularly suitable for cases with missing or outlier values. The TNNR-APGL algorithm combines tensor kernel norm regularization and alternating direction multiplication methods, 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 data by decomposing tensors into low-rank and sparse components. Low-rank components typically represent the main structure in the data, while sparse components represent outliers or noise. By decomposing the data into these two parts, the TNNR-APGL algorithm can more accurately separate true signals from outliers, thereby improving the quality and efficiency of data processing.

[0015] The algorithm's advantages include strong robustness to different types of outliers in the data and the ability to provide high-quality fitting results. This makes it a promising candidate for applications in fields such as image processing, video analysis, and signal processing.

[0016] 4) RCPA-CUR is a matrix factorization and dimensionality reduction algorithm that combines the ideas of sparse decomposition and low-rank approximation. It selects the most representative columns and rows from the original data through column and row selection to reduce data dimensionality. Then, robust decomposition is used to process the selected rows and columns, obtaining low-rank approximation and sparse representation results. Finally, these results are used to reconstruct the original data. This method effectively extracts key information and reduces data dimensionality, making it suitable for fields such as dimensionality reduction, feature selection, and signal processing.

[0017] Existing robust principal component analysis (RPCA) techniques, such as RPCA-HQF, AccAltProj, TNNR-APGL, and RPCA-CUR, have achieved certain results in handling RPCA problems, but still have some problems and shortcomings.

[0018] Limited processing power for complex datasets: When dealing with complex datasets, such as those where different materials are closely packed together, the resulting spectra may be highly nonlinear combinations of endmembers, potentially leading to model anomalies. This is because these algorithms are primarily based on linear models, and their processing power is limited for nonlinear data structures.

[0019] Image restoration quality needs improvement: These algorithms do not perform ideally in terms of color restoration and image reconstruction quality during image restoration. For example, some algorithms may fail to effectively restore image details and colors when dealing with high noise or low signal-to-noise ratio conditions.

[0020] Computational efficiency issues: Some existing RPCA algorithms, such as TNNR-APGL and AccAltProj, may face computational efficiency problems when processing large-scale datasets. This is likely because these algorithms require a large number of iterations and calculations during optimization, which can lead to low computational efficiency when dealing with large datasets. Summary of the Invention

[0021] To address the problems existing in the prior art, the purpose of this invention is to provide a hyperspectral image restoration method that integrates sparseness and low-rank priors. This invention can not only better handle complex datasets, but also improve the quality of image restoration.

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

[0023] Step 1: Recognize image information;

[0024] Step 2, Encode Input Optimization Model: Extract image features, input the extracted features into the encoder, arrange the encoded features into an observation matrix, and input the observation matrix into the optimization model. The optimization model is used to decompose the observation 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: Calculate the recovery using an algorithm;

[0026] Step 4: Restore the output image: By analyzing the noisy hyperspectral image data and decomposing it to obtain the low-rank underlying structure L and the sparse anomaly S, the low-rank part L and the sparse part S are restored separately. Finally, the low-rank part L and the sparse part S are combined to generate the final restored result, i.e., the processed image.

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

[0028] Step 2.1: Decompose the observation matrix into a low-rank matrix and a sparse matrix using robust principal component analysis:

[0029] min L,S rank(L)+λ‖S‖0s.tD=L+S

[0030] The observation matrix is ​​a low-rank matrix. sparse matrix The sum, and the 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 replace the L0 norm with the L1 norm:

[0032]

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

[0034]

[0035] Where P and Q are the row smoother and column smoother, respectively;

[0036] Step 2.4: Extend the nuclear norm in projective robust principal component analysis to a truncated nuclear norm, as follows:

[0037]

[0038] Step 2.5: Extend the L1 norm in projective robust principal component analysis to the log-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 robust integrated sparsity and low-order priors:

[0042]

[0043] Step 2.7: Optimize robust integration of 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 obtain the first subproblem:

[0045]

[0046] By keeping L constant and minimizing S through the second subproblem:

[0047]

[0048] Step 2.8: For any given matrix sum matrix That is, 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 parameters λ1, λ2, scaling factor α, the high-level non-convex regularized data matrix D to be decomposed, tolerance ∈, parameter δ;

[0052] Step 3.2, Initialize L (0) For D, S (1) If the value is 0, repeat the following steps 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 if the convergence condition is met ||L (k+1) -L (k) || F If ≤∈; if satisfied, proceed to the next step; otherwise, return to step 1 and 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 yields (k) ,Σ (k) V (k) ;

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

[0060] Step 3.3.3: Solve the optimization problem:

[0061]

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

[0063]

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

[0065] The beneficial effects of this invention are:

[0066] This invention proposes a hyperspectral image restoration method integrating sparse and low-rank priors (RPCA-LHCF), which can not only better handle complex datasets but also improve the quality of image restoration. Furthermore, it employs a proximal gradient algorithm to improve computational efficiency. This makes RPCA-LHCF a promising approach for handling complex datasets, especially in computational hyperspectral imaging. Attached Figure Description

[0067] Figure 1 This is a flowchart of an embodiment of the present invention;

[0068] Figure 2 This is a flowchart of the optimization model in an embodiment of the present invention;

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

[0070] Figure 4 This is a schematic diagram illustrating the relative recovery error of the algorithm at different ranks in an embodiment of the present invention;

[0071] Figure 5 These are RGB renderings of hyperspectral images recovered by different algorithms in embodiments of the present invention.

[0072] Figure 6 These are the spatial PSNR values ​​of hyperspectral images recovered by different algorithms in the embodiments of the present invention. Detailed Implementation

[0073] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0074] Example

[0075] A hyperspectral image restoration method integrating sparse and low-rank priors includes: receiving a complex dataset to be analyzed; selecting appropriate low-rank and sparse information based on data features to determine the corresponding low-rank and sparse modules in the RPCA-LHCF method; using the low-rank module to restore the complex data to obtain a preliminary low-rank data representation; using the sparse module to restore the complex data to obtain a preliminary sparse data representation; and combining the preliminary low-rank and preliminary sparse data to obtain the final data restoration result of the RPCA-LHCF method. This method allows RPCA-LHCF to process complex datasets more effectively, thereby improving its processing capabilities. Compared to using only a single module, RPCA-LHCF, by simultaneously considering data and low-rank structure information, can better extract low-rank structure and sparse information from the data, improving the accuracy of data restoration. Furthermore, the flexible selection of different combinations of low-rank and sparse priors based on data features and characteristics makes the RPCA-LHCF method more effective in processing different types of data, further improving the accuracy of data restoration.

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

[0077] Step S101: Recognize image information;

[0078] Step S102: Encode input optimization model;

[0079] Image feature extraction is a crucial step in image processing, aiming 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) as well as 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 applications such as image classification, object detection, and image retrieval, and are of great significance for image processing and analysis.

[0080] Next, an encoder is used to transform the extracted image features into a more compact representation. This step aims to reduce the dimensionality of the features and extract their most representative information. The choice of encoder can be flexibly adjusted according to specific tasks and needs. Common encoders include autoencoders, variational autoencoders (VAEs), and generative adversarial networks (GANs). Autoencoders learn to map the input image to a hidden representation space and reconstruct the original image, thus ensuring that the encoded features contain the key information of the input image. Variational autoencoders generate data by learning the distribution of latent variables and can be used to generate diverse feature representations. Generative adversarial networks train the generator and discriminator through a game-like approach to generate encoders with high-quality feature representations. These encoded features typically have lower dimensionality and contain the key information of the input image, providing a more efficient data representation for subsequent image processing and analysis.

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

[0082] Finally, the observation matrix is ​​input into the optimization model. This model aims to decompose the observed matrix D into two parts: a low-rank matrix L capturing the basic structure of the data, and a sparse matrix S capturing outliers. The robustness and sparsity of the model are improved by using the kernel norm and L1 norm or semi-quadratic functions as regularization terms. A convex relaxation method is employed to handle the original non-convex problem, and the optimization problem is solved using an alternating minimization algorithm, providing an efficient computational solution suitable for various signal processing and machine learning tasks.

[0083] Step S103: Calculate the recovery using an algorithm;

[0084] Step S104: Restore the output image;

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

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

[0087] Step S1021, RPCA, by decomposing the matrix into low-rank and sparse matrices, 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 The matrix representing the observations is a low-rank matrix. and a sparse matrix The sum of these components, where the sparse matrix captures outliers or isolated points in the data. The goal of the model is to decompose X into its low-rank part L and its sparse part S. The cardinality ||S||0 represents the number of non-zero elements in S, which is a measure of its sparsity.

[0090] Directly implementing this decomposition involves solving an optimization problem that minimizes the rank and cardinality. However, this problem is computationally difficult to handle because both the rank function and the L0 norm are non-convex, and discrete in the case of the rank.

[0091] To overcome this computational challenge, the problem is reformulated by replacing the rank function with the nuclear norm (the sum of the singular values ​​of the matrix) and the L0 norm with the L1 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 and solvable.

[0092]

[0093] Step S1023: Extend RPCA to Projection Robust Principal Component Analysis (PRPCA):

[0094]

[0095] Where P and Q are certain row smoothers and column smoothers, respectively;

[0096] Step S1024: To further explore low-rank priors, the nuclear norm in PRPCA is extended to a truncated nuclear norm. The truncated nuclear norm is a variant of the nuclear norm 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 others, indicating the presence of important structural information in the matrix that should be preserved. The truncated nuclear norm is defined as:

[0097]

[0098] Step S1025: This method aims to focus on the lower portion of the singular value spectrum, presumably because the smallest singular values ​​contribute more to noise or redundancy in the data, while the largest singular values ​​carry 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 finer approximation of the matrix rank, which can better recover the low-rank components by reducing the influence of the largest singular values ​​assumed to represent the fundamental characteristics of the data. On the other hand, the L1 norm in PRPCA 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] In step S1026, the parameter δ can be adjusted to approximate the L1 norm. Finally, the semi-quadratic function and the truncation kernel are integrated, and a model—Robust PCA Integration of Sparseness and Low-Order Priors (RPCA-LHCF)—is proposed, as shown below:

[0102]

[0103] Step S1027: In (6), optimizing L and S simultaneously is tractable, so (6) is optimized by using alternating minimization. Alternating minimization is an optimization technique used to solve problems involving minimizing a function relative to two (or more) sets of variables by alternately fixing one set of variables and optimizing another set. This approach is particularly useful when the optimization problem can be simplified or become more tractable, as one set of variables remains constant. Alternating minimization of (6) involves two iteratively repeated main steps:

[0104] Step 1: Keep S constant and minimize the objective function with respect to another variable L. Therefore, we have the following subproblems:

[0105]

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

[0107]

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

[0109]

[0110] Step S103 in this embodiment specifically includes:

[0111] Step S1031: Input regularization parameters λ1, λ2, scaling factor α, the high-level non-convex regularized data matrix D to be decomposed, tolerance ∈, parameter δ;

[0112] Step S1032, Initialize L (0) For D, S (1) If the value is 0, repeat the following steps until the convergence condition is met;

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

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

[0115] Step S103311, given L (k) Calculate L (k) The singular value decomposition of U yields (k) ,Σ (k) V (k) ;

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

[0117] Step S103313, Solve the optimization problem:

[0118]

[0119] Get L(k+1) Use 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 if the convergence condition is met. ||L (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 process details the RPCA-LHCF method, which 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 The experiment was conducted using simulation data, and the results demonstrate the proposed RPCA-LHCF algorithm:

[0130] Capability to handle complex datasets: RPCA-LHCF exhibits reduced relative error at high signal-to-noise ratios, demonstrating robustness against noise. At different ranks r, the relative error of RPCA-LHCF increases slowly, indicating strong capability in handling complex data.

[0131] Image restoration quality: RPCA-LHCF exhibits relatively low relative error at high signal-to-noise ratios, indicating improved image restoration quality. As the rank r increases, the restoration performance of RPCA-LHCF decreases more slowly compared to other algorithms, further demonstrating its improved image restoration quality.

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

[0133] Figure 5 and Figure 6 It is an experiment conducted on hyperspectral images. Figure 5 In the table, (a) is RPCA-LHCF, (b) is RPCA-HQF, (c) is TNNR-APGL, (d) is AccAltProj, and (e) is RPCA-CUR; Figure 6 In the diagram, (a) represents RPCA-LHCF, (b) represents RPCA-HQF, (c) represents TNNR-APGL, (d) represents AccAltProj, and (e) represents RPCA-CUR. This experiment demonstrates the effectiveness of the proposed RPCA-LHCF algorithm.

[0134] Capability to handle complex datasets: RPCA-LHCF can effectively handle complex datasets such as hyperspectral images. It can extract useful information from multispectral imaging, generate spectral response vectors for each pixel, and obtain information in the form of third-order tensors. These experimental results confirm that RPCA-LHCF has achieved improvements in processing such complex data structures.

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

[0136] Computational efficiency: It can achieve excellent results in efficient computation of real-world ultra-low rank and ultra-large-scale hyperspectral images, which means that the algorithm has high computational efficiency and is practical.

[0137] Overall, the experimental results support the fact that RPCA-LHCF improves upon the limitations of complex dataset processing capabilities, image restoration quality, and computational efficiency to some extent.

[0138] The embodiments described above are merely illustrative of specific implementations of the present invention, and while the descriptions are detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

Claims

1. A hyperspectral image restoration method integrating sparse and low-rank priors, characterized in that, The method comprises the following steps: Step 1, identifying image information; Step 2, encoding input 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 an optimization model, the optimization model being used to decompose the observation matrix into a low-rank matrix L capturing the basic structure of the data and a sparse matrix S capturing outliers; Step 2 specifically comprises the following steps: Step 2.1, decomposing the observation matrix into a low-rank matrix and a sparse matrix capturing outliers by using robust principal component analysis: min L,S rank(L) + λ‖S‖0 s.t. D = L + S denotes the observation matrix, which is a low-rank matrix and a sparse matrix that captures outliers the sum of the norms, where the cardinality ||S||0denotes the number of non-zero elements in S; Step 2.2, replacing the rank function with the nuclear norm and replacing the L0 norm with the L1 norm: Step 2.3, extending the robust principal component analysis to projected robust principal component analysis: Where P and Q are row and column smoothers, respectively; Step 2.4, extending the nuclear norm in the projected robust principal component analysis to the truncated nuclear norm, which is as follows: Step 2.5, extending 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, integrating the semi-quadratic function and the truncated kernel to obtain the robust integrated sparse and low-order prior: Step 2.7, optimizing the robust integrated sparse and low-order prior by using alternating minimization: Keeping S constant and minimizing the objective function with respect to another variable L to obtain the first subproblem: Keeping L constant and minimizing S through the second subproblem: Step 2.8, for any given matrix and matrix i.e. AA T = I, BB T = I, where r < min(m,n), the first subproblem is rewritten as follows: Step 3, calculating recovery with an algorithm; Step 4, outputting the recovered image: by analyzing the noisy hyperspectral image data and decomposing to obtain the low-rank matrix L and the sparse matrix S capturing outliers, then recovering the low-rank matrix L and the sparse matrix S capturing outliers respectively, and finally combining the recovered low-rank matrix L' and sparse matrix S' to generate the final recovery result, i.e. the processed image.

2. The hyperspectral image restoration method integrating sparse and low-rank priors according to claim 1, characterized in that, Step 3 specifically comprises the following steps: Step 3.1, inputting regularization parameters λ1, λ2, scaling factor α, high non-convex regularization data matrix D to be decomposed, tolerance ∈, and parameter δ; Step 3.2, initialize L (0) for D, S (1) for 0, repeat the following steps until a convergence condition is met; Step 3.3, fix S (k) L (k) and update L (k+1) ; Step 3.4, fixing L (k+1) , using update S (k+1) ; Step 3.5, check if convergence condition ||L (k+1) -L (k) ‖ F ≤∈;‖L (k+1) -L (k) ‖ F ≤∈If yes, go to next step; otherwise, go back to step 3.3 to continue updating. Step 3.6, output L (k+1) S (k+1) .

3. The hyperspectral image restoration method integrating sparse and low-rank priors according to claim 2, characterized in that, Step 3.3 specifically comprises the following steps: Step 3.3.1, Given L (k) S (k) , compute the singular value decomposition of L (k) to obtain U (k) ,∑ (k) ,V (k) ; Step 3.3.2, Definition A (k) ,B (k) is the transpose of the first r columns of U (k) and V (k) . Step 3.3.3, solving the optimization problem: L is obtained (k+1) using an accelerated proximal gradient method; Step 3. 3.4, until the convergence condition ||L (k+1) - L (k) ‖ F ≤ ∈; Step 3.3.5, output L (k+1) .

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