A sparse unmixing method based on hypergraph denoising and superpixel weighting

Abstract

The application discloses a sparse unmixing method based on hypergraph denoising and superpixel weighting, and comprises the following steps: step 1, hypergraph smoothing filtering and denoising of a hyperspectral image; step 2, constructing a spatial weighting matrix based on superpixels; and step 3, weighted sparse unmixing of the hyperspectral image. The method combines hypergraph learning and hypergraph smoothing filtering and denoising to obtain a denoised image, and can effectively preserve the spatial structure of the original image; the denoised image is segmented by using the SLIC superpixel segmentation method, the superpixel structure of the image can be more accurately extracted, and the method has better robustness to Gaussian noises with various signal-to-noise ratios. Therefore, the application has the characteristics of strong practical application value and good reliability, and is suitable for promotion and use.

Description

Technical Field

[0001] This invention belongs to the research field of remote sensing technology and relates to a sparse demixing method, specifically a sparse demixing method based on supergraph denoising and superpixel weighting. Background Technology

[0002] Remote sensing technology originated in the late 1960s, with the first human landing on the moon as a significant milestone, and has undergone continuous development over the past century. Remote sensing technology utilizes electromagnetic radiation as an interaction medium to acquire data remotely without direct contact with the object of study, and then analyzes this data to obtain the desired information—a comprehensive Earth observation technology. With the continuous development of remote sensing technology, breakthroughs have been achieved in remote sensing platforms, sensors, remote sensing information processing, and applications, leading to widespread attention in numerous fields such as information science, environmental science, biological science, and earth science.

[0003] Hyperspectral remote sensing technology has wide applications in agriculture, environmental monitoring, and geological exploration. Its images contain a wealth of information about the spectral characteristics of ground features, providing crucial support for ground feature identification and quantitative analysis in remote sensing applications. However, due to the limited spatial resolution of hyperspectral imaging systems and the complexity of ground feature distribution in scenes, a large number of mixed pixels exist in hyperspectral images, affecting the accurate identification and analysis of surface materials and thus significantly limiting its application in related fields. Hyperspectral unmixing technology is an effective way to solve this problem, making it a hot research topic in the field of remote sensing. Hyperspectral unmixing technology involves decomposing mixed pixels in a hyperspectral image to obtain the spectral information and compositional proportions of various substances in the scene. The spectral information of a substance is called an endmember, and the corresponding proportion is called abundance. The abundance obtained using hyperspectral unmixing technology is not only important for understanding the distribution and composition of surface cover and its background features, but also can further improve the accuracy of tasks such as ground feature classification and target detection, providing strong technical support for the reanalysis of hyperspectral images, and thus promoting the development and innovation of related fields. Summary of the Invention

[0004] This invention addresses the presence of noise and spatial relationships between pixels in observed hyperspectral remote sensing images, providing a sparse unmixing method based on supergraph denoising and superpixel weighting. This method jointly optimizes supergraph learning and supergraph smoothing filtering to obtain a denoised image, effectively preserving the spatial structure of the original image. Utilizing the SLIC superpixel segmentation method to segment the denoised image allows for more accurate extraction of the superpixel structure and exhibits better robustness to Gaussian noise at various signal-to-noise ratios. Therefore, this invention possesses strong practical application value and high reliability, making it suitable for widespread use.

[0005] The objective of this invention is achieved through the following technical solution:

[0006] A sparse demixing method based on supergraph denoising and superpixel weighting includes the following steps:

[0007] Step 1: Hypergraph smoothing filtering and noise reduction of hyperspectral images:

[0008] Step 1.1, let Representation and observation of hyperspectral images The corresponding clean image, where each pixel is treated as a node in the hypergraph, utilizes... - The nearest neighbor method selects each hyperedge of the hypergraph. The nearest neighbor node, at the th nearest neighbor node, in the th ... In the next iteration, the hyperedge weights of the hypergraph Calculate using the following formula:

[0009]

[0010] in, This represents the diagonal operations of a matrix, and the diagonal vector. elements For super-edge The weights can be calculated using the following formula:

[0011]

[0012] in, It is an exponential function. For Gaussian kernel scaling parameters, and Representing images respectively The and the 1 pixel, express The square of the norm;

[0013] Step 1.2, in the... In the next iteration, the hypergraph Laplacian matrix Calculate using the following formula:

[0014]

[0015] Among them, superscript For matrix inversion, superscript This is the transpose operation of a matrix. Indicates by and The correlation matrix formed by the elements and Let the node degree and hyperedge degree matrices represent the matrix respectively, and calculate them using the following formula:

[0016]

[0017] in, Indicates all elements are Column vectors;

[0018] Step 1.3, in the... In the next iteration, the image Calculate using the following formula:

[0019]

[0020] in, For regularization parameters, Representing dimension and The same unit matrix, Indicates the first During the next iteration value, Indicates the first The newly calculated value in the next iteration value;

[0021] Step 1.4, if the number of iterations... Then terminate the iteration and output. ,in Set the maximum number of iterations for the image denoising process. Otherwise, proceed to step 1.1.

[0022] Step 2: Construct a spatial weighted matrix based on superpixels:

[0023] Based on the SLIC superpixel segmentation algorithm, the denoised hyperspectral image output in step 1 is processed. Superpixel segmentation is performed, and a spatial weighting matrix is ​​further constructed. and The specific steps are as follows:

[0024] Step 2.1, let Indicates the image The first segment generated after segmentation using the SLIC algorithm One superpixel, vector For superpixels A pixel in a superpixel is then in the superpixel. The spectral average of all pixels Calculate using the following formula:

[0025]

[0026] in, For the first Superpixels The number of pixels in The number of superpixels; then, the spectral average value is used within each superpixel region. The spectral values ​​of the original pixels are replaced to obtain a coarsely reconstructed hyperspectral image. ;

[0027] Step 2.2: Based on the coarse image Estimating a rough abundance matrix By introducing auxiliary variables and Lagrangian multipliers Perform alternating optimization solutions;

[0028] In the During the next iteration, the fixed variable and Then the rough abundance Calculate using the following formula:

[0029]

[0030] in, Given a known spectral library matrix, Representing dimension and The same unit matrix, For penalty parameters, Indicates the first During the next iteration The value;

[0031] fixed and Auxiliary variables Calculate using the following formula:

[0032]

[0033] in, , Represents a symbolic function. This represents element-based absolute value operations. For regularization parameters;

[0034] Lagrangian multipliers Calculate using the following formula:

[0035]

[0036] If the number of iterations Then terminate the iteration and output the coarse abundance. ;

[0037] Step 2.3: Based on the rough abundance obtained in Step 2.2 Constructing a spatial weighted matrix and ,matrix and Calculate using the following formula:

[0038]

[0039] in, For hyperparameters, Indicates the rough abundance The A row vector composed of row elements. For rough abundance The number of rows, Indicates rough abundance The OK The absolute value of the elements in the column. Representation of space matrix The OK Column elements;

[0040] Step 3: Weighted sparse unmixing of hyperspectral images:

[0041] Step 3.1: Utilize the spatial weighting matrix obtained in Step 2. and Constraint estimation of abundance matrix ;

[0042] Step 3.2: Introduce auxiliary variables and Lagrangian multipliers The denoised hyperspectral images were processed using an alternating optimization strategy following these steps. Perform weighted sparse demixing:

[0043] Step 3.2.1, in the... In the next iteration, the variables during the unmixing process Calculate using the following formula:

[0044]

[0045] in, Penalty parameters set for the unmixing process;

[0046] Step 3.2: In the first... In the next iteration, auxiliary variables during the unmixing process Calculate using the following formula:

[0047]

[0048] in, For the regularization parameters of the unmixing process, " is an element-based product operation;

[0049] Step 3.2.3, in the... In the next iteration, the Lagrangian multipliers Calculate using the following formula:

[0050]

[0051] Step 3.2.4, if the number of iterations... Then terminate the iteration and output. ,in The maximum number of iterations is set for the unmixing process; otherwise, proceed to step 3.2.1. When iteration stops according to step 3.2.4, the output is... This is the abundance matrix that needs to be estimated.

[0052] Compared with the prior art, the present invention has the following advantages:

[0053] 1. This invention optimizes hypergraph learning and hypergraph smoothing filtering denoising by jointly optimizing the hypergraph learning and hypergraph smoothing filtering denoising problem, and can obtain a denoised hyperspectral image with the same spatial structure information as the original hyperspectral image, which can then be used for subsequent demixing tasks.

[0054] 2. The present invention uses the SLIC superpixel segmentation algorithm to segment the denoised image, which can obtain a spatial weighted matrix containing the superpixel structure in the hyperspectral image, so as to promote the spatial consistency of abundance estimation during the unmixing process.

[0055] 3. In both the construction of the spatial weighting matrix and the unmixing process, this invention decomposes the original problem into several simple subproblems that are alternately optimized and solved. Therefore, this invention has strong practical application value and good reliability, making it suitable for widespread use. Attached Figure Description

[0056] Figure 1 This is a flowchart of the sparse unmixing method proposed in this invention;

[0057] Figure 2 The sparse unmixing method proposed in this invention, along with six other similar sparse unmixing methods—SUnSAL, DRSU-TV, ReHGSU, SUnCNN, WSRSSU, and SGLRWRSU—achieves a signal-to-noise ratio of [value missing] in Gaussian noise. Under these circumstances, the performance of each method in obtaining the estimated abundance map is compared.

[0058] Figure 3 The sparse unmixing method proposed in this invention, along with six other similar sparse unmixing methods—SUnSAL, DRSU-TV, ReHGSU, SUnCNN, WSRSSU, and SGLRWRSU—achieves a signal-to-noise ratio of [value missing] in Gaussian noise. Under these circumstances, the performance of each method in obtaining the estimated abundance map is compared. Detailed Implementation

[0059] The technical solution of the present invention will be further described below with reference to the accompanying drawings, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention that do not depart from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention.

[0060] This invention provides a sparse unmixing method based on hypergraph denoising and superpixel weighting. First, hypergraph learning and hypergraph smoothing filtering denoising are jointly optimized to denoise observed hyperspectral images while ensuring that the denoised image retains the same spatial structure as the original image. Then, the SLIC superpixel segmentation algorithm is used to segment the denoised image into superpixels, and a spatial weighting matrix is ​​further constructed based on the superpixels, which can be used to promote spatial consistency of abundance during the unmixing process. Furthermore, the sparse unmixing model proposed in this invention can be solved quickly based on the ADMM algorithm framework by introducing appropriate auxiliary variables and using an alternating optimization strategy. Finally, experiments are conducted on a simulated hyperspectral dataset to verify the method described in this invention. The results show that the method of this invention is significantly superior to several other advanced sparse unmixing methods of the same type. Figure 1 As shown, the specific steps are as follows:

[0061] Step 1: Hypergraph smoothing filtering and noise reduction of hyperspectral images:

[0062] In the hypergraph smoothing filtering and denoising process of hyperspectral images, the initialization method and parameter settings of relevant variables are as follows:

[0063] Clean image Initialization settings: ;

[0064] In signal-to-noise ratio When setting the number of neighboring nodes Gaussian kernel scale parameters Regular expression parameters Number of iterations ;

[0065] In signal-to-noise ratio When setting the number of neighboring nodes Gaussian kernel scale parameters Regular expression parameters Number of iterations .

[0066] The specific implementation steps are as follows:

[0067] To ensure that the denoised hyperspectral image has the same spatial structure information as the original observation image, the denoising process of the hyperspectral image needs to be implemented in the following steps:

[0068] Step 1.1, let Representation and observation of hyperspectral images The corresponding clean image, where each pixel is treated as a node in the hypergraph, utilizes... - The nearest neighbor method selects each hyperedge of the hypergraph. The nearest neighbor node. In the next iteration, the hyperedge weights of the hypergraph Calculate using the following formula:

[0069] (1)

[0070] in, This represents the diagonal operations of a matrix, and the diagonal vector. elements For super-edge The weights can be calculated using the following formula:

[0071] (2)

[0072] in, It is an exponential function. For Gaussian kernel scaling parameters, and Representing images respectively The and the 1 pixel, express The square of the norm.

[0073] Step 1.2, in the... In the next iteration, the hypergraph Laplacian matrix Calculate using the following formula:

[0074] (3)

[0075] Among them, superscript For matrix inversion, superscript This is the transpose operation of a matrix. Indicates by and The correlation matrix formed by the elements and Let the node degree and hyperedge degree matrices represent the matrix respectively, and calculate them using the following formula:

[0076] (4)

[0077] in, Indicates all elements are Column vectors.

[0078] Step 1.3, in the... In the next iteration, the image Calculate using the following formula:

[0079] (5)

[0080] in, For regularization parameters, Representing dimension and The same unit matrix, Indicates the first During the next iteration value, Indicates the first The newly calculated value in the next iteration value.

[0081] Step 1.4, if the number of iterations... Then terminate the iteration and output. ,in Set the maximum number of iterations for the image denoising process. Otherwise, proceed to step 1.1.

[0082] Step 2: Construct a spatial weighted matrix based on superpixels:

[0083] In constructing the spatial weighted matrix based on superpixels, the initialization methods for relevant variables and the necessary parameter settings are as follows:

[0084] primitive variables Initialization settings: ;

[0085] Auxiliary variables Initialization settings: ;

[0086] Lagrangian multipliers Initialization settings: ;

[0087] In signal-to-noise ratio When setting the number of superpixels Regular expression parameters Penalty parameters Number of iterations Hyperparameters ;

[0088] In signal-to-noise ratio When setting the number of superpixels Regular expression parameters Penalty parameters Number of iterations Hyperparameters .

[0089] The specific implementation steps are as follows:

[0090] To further utilize the spatial structure information of hyperspectral images, this invention uses the SLIC superpixel segmentation algorithm to process the denoised hyperspectral image output in step 1. Superpixel segmentation is performed, and a spatial weighting matrix is ​​further constructed. and Next, follow these steps to construct the spatial weighted matrix based on superpixels:

[0091] Step 2.1, let Indicates the image The first segment generated after segmentation using the SLIC algorithm One superpixel, vector For superpixels A pixel in the superpixel is then in the superpixel. The average spectral value of all pixels can be obtained. Calculate using the following formula:

[0092] (6)

[0093] in, For the first Superpixels The number of pixels in This represents the number of superpixels. Then, the spectral average is used within each superpixel region. The spectral values ​​of the original pixels are replaced to obtain a coarsely reconstructed hyperspectral image. .

[0094] Step 2.2: Based on the coarse image Estimating a rough abundance matrix By introducing appropriate auxiliary variables and Lagrangian multipliers Alternating optimization methods are used to solve the problem. In the... In the next iteration, by fixing the variables and Then the rough abundance Calculate using the following formula:

[0095] (7)

[0096] in, Given a known spectral library matrix, Representing dimension and The same unit matrix, For penalty parameters, Indicates the first During the next iteration The value. By fixing and Auxiliary variables Calculate using the following formula:

[0097] (8)

[0098] in, , Represents a symbolic function. This represents element-based absolute value operations. Regularization parameters. Lagrangian multipliers. Calculate using the following formula:

[0099] (9)

[0100] If the number of iterations Then terminate the iteration and output the coarse abundance. .

[0101] Step 2.3: Based on the rough abundance obtained in Step 2.2 Constructing a spatial weighted matrix and This effectively preserves the superpixel structure from step 2.1, which can be further used to promote spatial consistency of abundance during the unmixing process. Finally, the matrix... and Calculate using the following formula:

[0102] (10)

[0103] in, For hyperparameters, Indicates the rough abundance The A row vector composed of row elements. For rough abundance The number of rows, Indicates rough abundance The OK The absolute value of the elements in the column. Representation of space matrix The OK The elements of the column.

[0104] Step 3: Weighted sparse unmixing of hyperspectral images:

[0105] In the weighted sparse demixing process of hyperspectral images, the initialization methods of relevant variables and the settings of necessary parameters are as follows:

[0106] primitive variables Initialization settings: ;

[0107] Auxiliary variables Initialization settings: ;

[0108] Lagrangian multipliers Initialization settings: ;

[0109] In signal-to-noise ratio When setting regular expression parameters Penalty parameters Number of iterations ;

[0110] In signal-to-noise ratio When setting regular expression parameters Penalty parameters Number of iterations .

[0111] The specific implementation steps are as follows:

[0112] By utilizing the spatial weighting matrix obtained in step 2 and To constrain the estimation of the abundance matrix This can further improve the spatial consistency of the estimated abundance matrix. Next, appropriate auxiliary variables are introduced. and Lagrangian multipliers The denoised hyperspectral images were processed using an alternating optimization strategy following these steps. Perform weighted sparse demixing:

[0113] Step 3.1, in the... In the next iteration, the variables during the unmixing process Calculate using the following formula:

[0114] (11)

[0115] in, The penalty parameter set for the unmixing process.

[0116] Step 3.2, in the... In the next iteration, auxiliary variables during the unmixing process Calculate using the following formula:

[0117] (12)

[0118] in, For the regularization parameters of the unmixing process, " is an element-based product operation.

[0119] Step 3.3, in the... In the next iteration, the Lagrangian multipliers Calculate using the following formula:

[0120] (13)

[0121] Step 3.4, if the number of iterations... Then terminate the iteration and output. ,in The maximum number of iterations set for the unmixing process. Otherwise, proceed to step 3.1. When iteration stops according to step 3.4, the output is... This is the abundance matrix that needs to be estimated.

[0122] To verify the effectiveness of the weighted sparse unmixing method proposed in this invention, six similar unmixing methods—SUnSAL, DRSU-TV, ReHGSU, SUnCNN, WSRSSU, and SGLRWRSU—and the method described in this invention (Proposed) were used to add signal-to-noise ratio to simulated hyperspectral image data. and The experiment was conducted using Gaussian noise. This simulated hyperspectral dataset contains... Each band contains [number] bands. Each pixel, by It consists of squares arranged in a grid, where each square represents a homogeneous region and its pixels are composed of the same abundance.

[0123] The experimental results show the abundance maps corresponding to all endmembers in the dataset, where Reference is the reference abundance map. Figure 2 and 3 As shown in the figure, the abundance maps corresponding to each endmember estimated by the method proposed in this invention have a clearer spatial structure compared with other methods. This indicates that the method proposed in this invention can effectively utilize the superpixel structure information of hyperspectral images. Furthermore, the abundance maps estimated by each method also show that the demixing method described in this invention effectively suppresses Gaussian noise at various signal-to-noise ratios, which fully verifies the robustness of the method against Gaussian noise.

[0124] Furthermore, to further illustrate the effectiveness of the proposed method, SRE and RMSE are used to measure the unmixing accuracy of each method. These two metrics are widely used to measure the performance of hyperspectral unmixing methods. The signal reconstruction error SRE is defined as:

[0125] (12)

[0126] in, and These represent the reference abundance and the estimated abundance, respectively. Generally, a higher SRE value indicates better performance of the unmixing method. The root mean square error (RMSE) is defined as:

[0127] (13)

[0128] in, and Each is a matrix and The There are several column vectors. Generally, the smaller the RMSE value, the better the performance of the unmixing method. As can be seen from the experimental results in Table 1, the SRE and RMSE values ​​obtained by the method described in this invention are far superior to other similar comparative methods, which further verifies the effectiveness of the method described in this invention.

[0129]

Claims

1. A sparse unmixing method based on supergraph denoising and superpixel weighting, characterized in that... The method includes the following steps: Step 1: Hypergraph smoothing filtering and noise reduction of hyperspectral images: Step 1.1, let Representation and observation of hyperspectral images The corresponding clean image, where each pixel is treated as a node in the hypergraph, utilizes... - The nearest neighbor method selects each hyperedge of the hypergraph. The nearest neighbor node, at the th nearest neighbor node, in the th ... In the next iteration, the hyperedge weights of the hypergraph Calculate using the following formula: in, This represents the diagonal operations of a matrix, and the diagonal vector. elements For super-edge The weights; Step 1.2, in the... In the next iteration, the hypergraph Laplacian matrix Calculate using the following formula: Among them, superscript For matrix inversion, superscript This is the transpose operation of a matrix. Indicates by and The correlation matrix formed by the elements and These represent the node degree and hyperedge degree matrices, respectively; Step 1.3, in the... In the next iteration, the image Calculate using the following formula: in, For regularization parameters, Representing dimension and The same unit matrix, Indicates the first During the next iteration value, Indicates the first The newly calculated value in the next iteration value; Step 1.4, if the number of iterations... Then terminate the iteration and output. ,in Set the maximum number of iterations for the image denoising process; otherwise, proceed to step 1.1 to continue execution. Step 2: Construct a spatial weighted matrix based on superpixels: Based on the SLIC superpixel segmentation algorithm, the denoised hyperspectral image output in step 1 is processed. Superpixel segmentation is performed, and a spatial weighting matrix is ​​further constructed. and ; Step 3: Weighted sparse unmixing of hyperspectral images: Step 3.1: Utilize the spatial weighting matrix obtained in Step 2. and Constraint estimation of abundance matrix ; Step 3.2: Introduce auxiliary variables and Lagrangian multipliers The denoised hyperspectral images were processed using an alternating optimization strategy following these steps. Perform weighted sparse demixing: Step 3.2.1, in the... In the next iteration, the variables during the unmixing process Calculate using the following formula: in, Given a known spectral library matrix, Representing dimension and The same unit matrix, Penalty parameters set for the unmixing process; Step 3.2.2: In the first... In the next iteration, auxiliary variables during the unmixing process Calculate using the following formula: in, For the regularization parameters of the unmixing process, " is an element-based product operation; Step 3.2.3, in the... In the next iteration, the Lagrangian multipliers Calculate using the following formula: Step 3.2.4, if the number of iterations... Then terminate the iteration and output. ,in The maximum number of iterations is set for the unmixing process; otherwise, proceed to step 3.2.

1. When iteration stops according to step 3.2.4, the output is... This is the abundance matrix that needs to be estimated.

2. The sparse demixing method based on supergraph denoising and superpixel weighting according to claim 1, characterized in that... The Calculate using the following formula: in, It is an exponential function. For Gaussian kernel scaling parameters, and Representing images respectively The and the 1 pixel, express The square of the norm.

3. The sparse demixing method based on supergraph denoising and superpixel weighting according to claim 1, characterized in that... The and Calculated by the following formula: in, Indicates all elements are Column vectors.

4. The sparse demixing method based on supergraph denoising and superpixel weighting according to claim 1, characterized in that... The specific steps of step 2 are as follows: Step 2.1, let Indicates the image The first segment generated after segmentation using the SLIC algorithm One superpixel, vector For superpixels A pixel in the superpixel is then in the superpixel. The spectral average of all pixels Calculate using the following formula: in, For the first Superpixels The number of pixels in The number of superpixels; then, the spectral average value is used within each superpixel region. The spectral values ​​of the original pixels are replaced to obtain a coarsely reconstructed hyperspectral image. ; Step 2.2: Based on the coarse image Estimating a rough abundance matrix By introducing auxiliary variables and Lagrangian multipliers Perform alternating optimization solutions; In the During the next iteration, the fixed variable and Then the rough abundance Calculate using the following formula: in, Given a known spectral library matrix, Representing dimension and The same unit matrix, For penalty parameters, Indicates the first During the next iteration The value; fixed and Auxiliary variables Calculate using the following formula: in, , Represents a symbolic function. This represents element-based absolute value operations. For regularization parameters; Lagrangian multipliers Calculate using the following formula: If the number of iterations Then terminate the iteration and output the coarse abundance. ; Step 2.3: Based on the rough abundance obtained in Step 2.2 Constructing a spatial weighted matrix and ,matrix and Calculate using the following formula: in, For hyperparameters, Indicates the rough abundance The A row vector composed of row elements. For rough abundance The number of rows, Indicates rough abundance The OK The absolute value of the elements in the column. Representation of space matrix The OK The elements of the column.

5. The sparse demixing method based on supergraph denoising and superpixel weighting according to claim 1, characterized in that... In step 1, the variable initialization and related parameter settings are as follows: Clean image Initialization settings: ; In signal-to-noise ratio When setting the number of neighboring nodes Gaussian kernel scale parameters Regular expression parameters Number of iterations ; In signal-to-noise ratio When setting the number of neighboring nodes Gaussian kernel scale parameters Regular expression parameters Number of iterations .

6. The sparse demixing method based on supergraph denoising and superpixel weighting according to claim 1, characterized in that... In step 2, the variable initialization and related parameter settings are as follows: primitive variables Initialization settings: ; Auxiliary variables Initialization settings: ; Lagrangian multipliers Initialization settings: ; In signal-to-noise ratio When setting the number of superpixels Regular expression parameters Penalty parameters Number of iterations Hyperparameters , For penalty parameters; In signal-to-noise ratio When setting the number of superpixels Regular expression parameters Penalty parameters Number of iterations Hyperparameters .

7. The sparse demixing method based on supergraph denoising and superpixel weighting according to claim 1, characterized in that... In step 3, the variable initialization and related parameter settings are as follows: primitive variables Initialization settings: ; Auxiliary variables Initialization settings: ; Lagrangian multipliers Initialization settings: ; In signal-to-noise ratio When setting regular expression parameters Penalty parameters Number of iterations ; In signal-to-noise ratio When setting regular expression parameters Penalty parameters Number of iterations .

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