Hyperspectral image sparse unmixing method based on multi-scale superpixel low-rank representation

Abstract

The present invention discloses a sparse unmixing method for hyperspectral images based on multi-scale superpixel low-rank representation, comprising the following specific steps: introducing the Frobenius norm to calculate the difference between the reconstructed hyperspectral image and the original hyperspectral image, taking the minimum difference as the data fidelity term of the objective function; introducing the L1 norm to adaptively construct the spectral weighting factor and spatial weighting factor of the abundance matrix to obtain the sparse regularization term of the objective function; obtaining multiple segmentation maps of different segmentation scales based on the superpixel segmentation algorithm; introducing the weighted nuclear norm constraint on the superpixel region of each segmentation map to obtain the low-rank representation regularization term of the objective function; constructing the objective function; and solving the objective function using the alternating direction multiplier method. By constructing a multi-scale superpixel-guided low-rank regularization term, the present invention adaptively integrates complementary information from multiple segmentation scales, thereby improving the performance of the unmixing algorithm and the accuracy of the results.

Description

Technical Field

[0001] The present invention relates to the technical field of sparse unmixing of hyperspectral images, and in particular to a sparse unmixing method for hyperspectral images based on multi-scale superpixel low-rank representation. Background Art

[0002] Hyperspectral images consist of three-dimensional data cubes containing a large number of channels. This rich spectral information is crucial for interpreting ground-based targets and has been widely used in fields such as agriculture, food safety, geological exploration, and environmental protection. However, in real-world scenarios, the diverse distribution of targets and the limited spatial resolution of hyperspectral image sensors cause hyperspectral image pixels to appear as a mixture of multiple endmembers. The presence of mixed pixels limits the accurate interpretation and further exploration of hyperspectral images. To address this issue, a hyperspectral unmixing method has been proposed that decomposes mixed pixels into their pure material components and their corresponding proportions.

[0003] Hyperspectral unmixing algorithms can generally be divided into unsupervised and semi-supervised methods. Unsupervised unmixing algorithms may extract endmembers that have no actual physical meaning from hyperspectral images, resulting in unmixing results that do not meet the requirements. Semi-supervised unmixing methods are also called sparse unmixing, which uses a known spectral library as an endmember matrix and estimates the abundance of each target. However, existing sparse unmixing algorithms only consider the correlation of abundance within homogeneous regions at a single segmentation scale. Although this method is effective in some cases, since the objects in hyperspectral images usually exhibit spatial characteristics at different scales, the homogeneous regions at a single scale cannot fully capture the spatial information of the hyperspectral image, thereby reducing the unmixing accuracy of the sparse unmixing algorithm. Summary of the Invention

[0004] In order to solve the above-mentioned technical problems, the present invention provides a sparse unmixing method for hyperspectral images based on multi-scale superpixel low-rank representation.

[0005] The technical solution adopted by the present invention is:

[0006] A sparse unmixing method for hyperspectral images based on multi-scale superpixel low-rank representation includes the following steps:

[0007] S1. Introduce the Frobenius norm to calculate the difference between the reconstructed hyperspectral image and the original hyperspectral image, and take the minimum difference as the data fidelity term of the objective function;

[0008] S2. Based on the abundance matrix in the original hyperspectral image, the L1 norm is introduced to adaptively construct the spectral weighting factor and the spatial weighting factor of the abundance matrix to obtain a sparse regularization term of the objective function;

[0009] S3. Setting the superpixel size of the original hyperspectral image, obtaining multiple segmentation maps of different segmentation scales based on the superpixel segmentation algorithm, and calculating the Calinski-Harabasz index of each segmentation map to obtain the weighting factor of each segmentation map;

[0010] S4. Introducing a weighted nuclear norm constraint into the superpixel region of each segmentation map to obtain a low-rank representation regularization term of the objective function;

[0011] S41, obtaining multiple segmentation maps of different segmentation scales;

[0012] S42, introducing a weighted nuclear norm constraint into the superpixel region of each segmentation image to obtain similar abundance matrices corresponding to mixed pixels in the same superpixel region;

[0013] S43, introduce the weight of the segmentation map and adaptively fuse multiple segmentation map features of different segmentation scales;

[0014] S44. A multi-scale superpixel guided low-rank representation regularization term of the objective function is obtained based on the weighted nuclear norm constraint and the weight of the segmentation map;

[0015] Specifically, for the h-th segmentation map, a weighted nuclear norm constraint is added, which is specifically expressed as:

[0016]

[0017] Where, ω j is a weighting factor that imposes a larger penalty on smaller singular values, thus forcing them to be close to zero in the next iteration; X i represents the abundance matrix of mixed pixels in the i-th superpixel;

[0018] The low-rank representation regularization term of the objective function is expressed as:

[0019]

[0020] Where β represents the hyperparameter of the low-rank regularization term of the objective function;

[0021] S5. Constructing an objective function based on the data fidelity term, the sparse regularization term, and the low-rank representation regularization term;

[0022] S6. Solve the objective function by the alternating direction multiplier method to obtain the target abundance matrix.

[0023] Furthermore, the step S1 specifically includes the following steps:

[0024] S11, obtaining original hyperspectral images;

[0025] S12, using a linear mixed model to decompose the mixed pixels of the original hyperspectral image to obtain a spectral library of multiple end members and a combination coefficient corresponding to each end member to obtain a reconstructed hyperspectral image;

[0026] The reconstructed hyperspectral image is represented by Y=AX+N; Y=[y1,...,y m ]∈R l×m represents the original hyperspectral image, which contains l spectral bands and m pixels; A = [a1, ..., a p ]∈R l×p represents a spectral library with p end members; X = [x1, ..., x m ]∈R p×m Represents the combination coefficient corresponding to each end member, that is, the abundance matrix of the original hyperspectral image; AX represents the reconstructed hyperspectral image; N∈R m×l represents additional noise and error;

[0027] S13. Based on the original hyperspectral image and the reconstructed hyperspectral image, the Frobenius norm is introduced to calculate the difference between the reconstructed hyperspectral image and the original hyperspectral image, and the minimum difference is taken as the data fidelity term of the objective function; the data fidelity term of the objective function is expressed as

[0028] Where Y represents the original hyperspectral image; AX represents the reconstructed hyperspectral image; Y-AX represents the matrix of the original hyperspectral image and the reconstructed hyperspectral image; is the Frobenius norm of the matrix Y-AX.

[0029] Furthermore, the step S2 specifically includes the following steps:

[0030] S21, obtaining the abundance matrix in the original hyperspectral image;

[0031] S22, adding the L1 norm to the abundance matrix to calculate the sum of the absolute values ​​of the minimum abundance matrix;

[0032] S23. Based on the row sparsity of the abundance matrix, adaptively constructing and calculating a spectral weighting factor of the abundance matrix;

[0033] S24. Based on the sparsity of the elements of the abundance matrix, adaptively construct and calculate a spatial weighting factor of the abundance matrix;

[0034] S25. Obtaining a sparse regularization term of the objective function based on the spectral weighting factor, the spatial weighting factor, and the L1 norm of the abundance matrix;

[0035] Specifically, It is expressed as the L1 norm of the abundance matrix X; the calculation formula of the spectral weighting factor is Where i=1, ..., p, X(i,:) represents the i-th row element of the abundance matrix X; the calculation formula of the spatial weighting factor is in, Represents the mixed pixel x of the original hyperspectral image ij Neighborhood coverage; λ||W spe W spa ⊙X|| 1，1 It is expressed as the sparse regularization term of the objective function, where λ represents the parameter of the sparse regularization term, which is used to measure the importance of the sparse regularization term of the objective function.

[0036] Furthermore, it is characterized in that the step S3 specifically includes the following steps:

[0037] S31, obtaining an original hyperspectral image;

[0038] S32, setting the superpixel size of the original hyperspectral image to calculate the segmentation scale and the number of segmentation scales of the original hyperspectral image;

[0039] S33, based on the segmentation scale and the number of segmentation scales, using a superpixel segmentation algorithm to iteratively obtain multiple segmentation maps with different segmentation scales;

[0040] S34, based on multiple segmentation maps of different segmentation scales, calculating the Calinski-Harabasz index to obtain the weight of each segmentation map;

[0041] Specifically, for the hth segmentation map, the specific segmentation process is as follows:

[0042] 1) Set the superpixel size of the original hyperspectral image to S;

[0043] 2) Obtain the segmentation scale S of the original hyperspectral image by calculation h , and its calculation formula is:

[0044] S h =S+(-1) h ,h=1,2,...,H

[0045] Where H is the number of segmentation scales, S h is an integer greater than 0;

[0046] 3) Run the simple linear iterative algorithm H times to obtain H segmentation maps with different segmentation scales;

[0047] 4) Select K h seed points, among which K his the total number of superpixels in the h-th segmentation map; m is the number of pixels in the h-th segmentation map;

[0048] 5) Calculate the spectral distance and spatial distance between each mixed pixel near each seed point and the seed point; the calculation formulas for the spectral distance and spatial distance are:

[0049]

[0050] Where, d spatial and d spectral Represents the spatial distance and spectral distance between mixed pixels; (x i ,y i )、(x j ,y j ) represent the spatial coordinate information of the mixed pixels; y i ,y j represents the spectral characteristics of mixed pixels i and j;

[0051] 6) Based on the spectral distance and spatial distance, the difference between the mixed pixels is calculated; the specific calculation formula is:

[0052]

[0053] Where Dis is an indicator used to measure the difference between mixed pixels; r is a weight used to balance spectral distance and spatial distance;

[0054] 7) Comparing the spectral distance and spatial distance with the preset thresholds respectively, screening out mixed pixels whose spectral distance and spatial distance are respectively less than the preset thresholds and assigning them to seed points;

[0055] 8) The average value of all pixels of each superpixel in the segmentation map is used as the new center point, and the above steps are repeated until the number of iterations is reached or convergence is achieved;

[0056] S35, summing the weights of the multiple segmentation maps to obtain a weight factor of the segmentation map;

[0057] Specifically, for the hth segmentation map, the corresponding weight is:

[0058]

[0059] Where, C h represents the Calinski-Harabasz index of the hth segmentation map; R h is the covariance matrix between pixels of the h-th segmentation map; E h is the covariance matrix between the elements in the superpixel of the h-th segmentation map; m and K hare the number of pixels and the total number of superpixels in the h-th segmentation map, respectively.

[0060] Furthermore, step S6 specifically includes the following steps:

[0061] S61, introduce variables U, V and Lagrange multiplier D = {D1, D2, D3, D4},

[0062] S62. Construct Lagrangian function:

[0063]

[0064] in,

[0065]

[0066] μ represents the penalty parameter, μ>0;

[0067] G and B are defined as:

[0068] G=[A,I,I,I] T

[0069]

[0070] I represents the identity matrix;

[0071] S63, Lagrangian function The variables U, V, and D are solved iteratively as follows:

[0072] S631, with variables V and D fixed, the optimization problem for variable U is expressed as:

[0073]

[0074] Where d represents the number of iterations. By taking the partial derivative of the variable U in the above formula and making it equal to zero, the solution of the variable U is:

[0075] U (d+1) ←(A T A+3I) -1 (A T ζ1+ζ2+ζ3+ζ4)

[0076] in,

[0077] S632, variable V contains four sub-problems, namely V1, V2, V3 and V4:

[0078] 1) The optimization problem and solution of variable V1 are expressed as:

[0079]

[0080] 2) The optimization problem and solution of variable V2 are expressed as:

[0081]

[0082] 3) The optimization problem of variable V3 is expressed as:

[0083]

[0084] For each The solution is:

[0085]

[0086] in, The i-th superpixel region corresponding to the h-th segmentation scale; Γ w，τ (X) = U (Π - τdiag (w)) + V T ;UΠV T represents the singular value decomposition of matrix X; (x) + =max(x,0);

[0087] 4) The optimization problem and solution of variable V4 are expressed as:

[0088]

[0089] Each time the variables U, V, and D are updated, the number of iterations d increases by 1; the residual of the objective function is calculated by the variable When it is less than the predefined threshold T h = 0.0001 or when the maximum number of iterations d = 1000 is reached, the algorithm stops obtaining the target abundance matrix and then obtains the target abundance map.

[0090] Compared with the prior art, the present invention has the following beneficial effects:

[0091] 1) By adding the Frobenius norm of the abundance matrix as a regularization term in the objective function, the size of the model parameters can be effectively constrained;

[0092] 2) By introducing the L1 norm and adaptively calculating the spectral weighting factor and the spatial weighting factor, the row sparsity and element sparsity of the abundance matrix are effectively improved;

[0093] 3) By varying the superpixel segmentation scale, we obtain a multi-scale superpixel segmentation map, and then construct a multi-scale superpixel-guided low-rank regularization term to adaptively integrate complementary information from multiple segmentation scales, thereby improving the performance of the demixing algorithm and the accuracy of the results;

[0094] 4) By introducing the alternating direction multiplier method, the objective function is decomposed into multiple simple and easy-to-solve sub-problems, making the algorithm easier to solve and accelerating the convergence speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] The present invention will be further described below with reference to the accompanying drawings and specific embodiments:

[0096] Figure 1 Schematic diagram of a process of a hyperspectral image sparse unmixing method based on multi-scale superpixel low-rank representation of the present invention;

[0097] Figure 2 It is a flow chart of solving the objective function of a sparse unmixing method for hyperspectral images based on multi-scale superpixel low-rank representation of the present invention. DETAILED DESCRIPTION

[0098] Example

[0099] like Figures 1 to 2 As shown in FIG, a sparse unmixing method for hyperspectral images based on multi-scale superpixel low-rank representation includes the following specific steps:

[0100] S1. Introduce the Frobenius norm to calculate the difference between the reconstructed hyperspectral image and the original hyperspectral image, and take the minimum difference as the data fidelity term of the objective function;

[0101] S11, obtaining original hyperspectral images;

[0102] S12, using a linear mixed model to decompose the mixed pixels of the original hyperspectral image to obtain a spectral library of multiple end members and a combination coefficient corresponding to each end member to obtain a reconstructed hyperspectral image;

[0103] The reconstructed hyperspectral image is represented by Y=AX+N; Y=[y1,...,y m ]∈R l×m represents the original hyperspectral image, which contains l spectral bands and m pixels; A = [a1, ..., a p ]∈R l×p represents a spectral library with p end members; X = [x1, ..., x m ]∈R p×m Represents the combination coefficient corresponding to each end member, that is, the abundance matrix of the original hyperspectral image; AX represents the reconstructed hyperspectral image; N∈R m×l represents additional noise and error;

[0104] S13. Based on the original hyperspectral image and the reconstructed hyperspectral image, the Frobenius norm is introduced to calculate the difference between the reconstructed hyperspectral image and the original hyperspectral image, and the minimum difference is taken as the data fidelity term of the objective function; the data fidelity term of the objective function is expressed as

[0105] Where Y represents the original hyperspectral image; AX represents the reconstructed hyperspectral image; Y-AX represents the matrix of the original hyperspectral image and the reconstructed hyperspectral image; is the Frobenius norm of the matrix Y-AX.

[0106] S2. Based on the abundance matrix in the original hyperspectral image, the L1 norm is introduced to adaptively construct the spectral weighting factor and the spatial weighting factor of the abundance matrix to obtain a sparse regularization term of the objective function;

[0107] S21, obtaining the abundance matrix in the original hyperspectral image;

[0108] S22, adding the L1 norm to the abundance matrix to calculate the sum of the absolute values ​​of the minimum abundance matrix;

[0109] S23. Based on the row sparsity of the abundance matrix, adaptively constructing and calculating a spectral weighting factor of the abundance matrix;

[0110] S24. Based on the sparsity of the elements of the abundance matrix, adaptively construct and calculate a spatial weighting factor of the abundance matrix;

[0111] S25. Obtaining a sparse regularization term of the objective function based on the spectral weighting factor, the spatial weighting factor, and the L1 norm of the abundance matrix;

[0112] Specifically, It is expressed as the L1 norm of the abundance matrix X; the calculation formula of the spectral weighting factor is Where i = 1, ..., p, X(i,:) represents the i-th row element of the abundance matrix X; the calculation formula of the spatial weighting factor is in, Represents the mixed pixel x of the original hyperspectral image ij Neighborhood coverage; λ||W spe W spa ⊙X|| 1，1 It is expressed as the sparse regularization term of the objective function, where λ represents the parameter of the sparse regularization term, which is used to measure the importance of the sparse regularization term of the objective function.

[0113] S3. Setting the superpixel size of the original hyperspectral image, obtaining multiple segmentation maps of different segmentation scales based on the superpixel segmentation algorithm, and calculating the Calinski-Harabasz index of each segmentation map to obtain the weight of each segmentation map;

[0114] S31, obtaining an original hyperspectral image;

[0115] S32, setting the superpixel size of the original hyperspectral image to calculate the segmentation scale and the number of segmentation scales of the original hyperspectral image;

[0116] S33, based on the segmentation scale and the number of segmentation scales, using a superpixel segmentation algorithm to iteratively obtain multiple segmentation maps with different segmentation scales;

[0117] S34, based on multiple segmentation maps of different segmentation scales, calculating the Calinski-Harabasz index to obtain the weight of each segmentation map;

[0118] Specifically, for the hth segmentation map, the specific segmentation process is as follows:

[0119] 1) Set the superpixel size of the original hyperspectral image to S;

[0120] 2) Obtain the segmentation scale S of the original hyperspectral image by calculation h , and its calculation formula is:

[0121] S h =S+(-1) h , h=1, 2, ..., H

[0122] Where H is the number of segmentation scales, S h is an integer greater than 0;

[0123] 3) Run the simple linear iterative algorithm H times to obtain H segmentation maps with different segmentation scales;

[0124] 4) Select K h seed points, among which K h is the total number of superpixels in the h-th segmentation map; m is the number of pixels in the h-th segmentation map;

[0125] 5) Calculate the spectral distance and spatial distance between each mixed pixel near each seed point and the seed point; the calculation formulas for the spectral distance and spatial distance are:

[0126]

[0127] Where, d spatial and d spectralRepresents the spatial distance and spectral distance between mixed pixels; (x i ,y i )、(x j ,y j ) represent the spatial coordinate information of the mixed pixels; y i ,y j represents the spectral characteristics of mixed pixels i and j;

[0128] 6) Based on the spectral distance and spatial distance, the difference between the mixed pixels is calculated; the specific calculation formula is:

[0129]

[0130] Where Dis is an indicator used to measure the difference between mixed pixels; r is a weight used to balance spectral distance and spatial distance;

[0131] 7) Comparing the spectral distance and spatial distance with the preset thresholds respectively, screening out mixed pixels whose spectral distance and spatial distance are respectively less than the preset thresholds and assigning them to seed points;

[0132] 8) The average value of all pixels of each superpixel in the segmentation map is used as the new center point, and the above steps are repeated until the number of iterations is reached or convergence is achieved;

[0133] S35, summing the weights of the multiple segmentation maps to obtain a weight factor of the segmentation map;

[0134] Specifically, for the hth segmentation map, the corresponding weight is:

[0135]

[0136] Where, C h represents the Calinski-Harabasz index of the hth segmentation map; R h is the covariance matrix between pixels of the h-th segmentation map; E h is the covariance matrix between the elements in the superpixel of the h-th segmentation map; m and K h are the number of pixels and the total number of superpixels in the h-th segmentation map, respectively.

[0137] S4. Introducing a weighted nuclear norm constraint into the superpixel region of each segmentation map to obtain a low-rank representation regularization term of the objective function;

[0138] S41, obtaining multiple segmentation maps of different segmentation scales;

[0139] S42, introducing a weighted nuclear norm constraint into the superpixel region of each segmentation image to obtain similar abundance matrices corresponding to mixed pixels in the same superpixel region;

[0140] S43, introduce the weight of the segmentation map and adaptively fuse multiple segmentation map features of different segmentation scales;

[0141] S44. A multi-scale superpixel guided low-rank representation regularization term of the objective function is obtained based on the weighted nuclear norm constraint and the weight of the segmentation map;

[0142] Specifically, for the h-th segmentation map, a weighted nuclear norm constraint is added, which is specifically expressed as:

[0143]

[0144] Where, ω j is a weighting factor that imposes a larger penalty on smaller singular values, thus forcing them to be close to zero in the next iteration; X i represents the abundance matrix of mixed pixels in the i-th superpixel;

[0145] The low-rank representation regularization term of the objective function is expressed as:

[0146]

[0147] Where β represents the hyperparameter of the low-rank regularization term of the objective function.

[0148] S5. Construct an objective function based on the data fidelity term, the sparse regularization term, and the low-rank representation regularization term of the objective function, which is specifically expressed as follows:

[0149]

[0150] Where, lR + (X) indicates the non-negativity of the abundance matrix.

[0151] S6. Solve the objective function by the alternating direction multiplication method to obtain the target abundance matrix. The specific solution process is as follows:

[0152] S61, introduce variables U, V and Lagrange multiplier D = {D1, D2, D3, D4},

[0153] S62. Construct Lagrangian function:

[0154]

[0155] in,

[0156]

[0157] μ represents the penalty parameter, μ>0;

[0158] G and B are defined as:

[0159] G=[A,I,I,I] T

[0160]

[0161] I represents the identity matrix;

[0162] S63, Lagrangian function The variables U, V, and D are solved iteratively as follows:

[0163] S631, with variables V and D fixed, the optimization problem for variable U is expressed as:

[0164]

[0165] Where d represents the number of iterations. By taking the partial derivative of the variable U in the above formula and making it equal to zero, the solution of the variable U is:

[0166] U (d+1) ←(A T A+3I) -1 (A T ζ1+ζ2+ζ3+ζ4)

[0167] in,

[0168] S632, variable V contains four sub-problems, namely V1, V2, V3 and V4:

[0169] 1) The optimization problem and solution of variable V1 are expressed as:

[0170]

[0171] 2) The optimization problem and solution of variable V2 are expressed as:

[0172]

[0173] 3) The optimization problem of variable V3 is expressed as:

[0174]

[0175] For each The solution is:

[0176]

[0177] in, The i-th superpixel region corresponding to the h-th segmentation scale; Γ w，τ (X) = U (Π - τdiag (w)) + V T ;UΠVT represents the singular value decomposition of matrix X; (x) + =max(x,0);

[0178] 4) The optimization problem and solution of variable V4 are expressed as:

[0179]

[0180] Each time the variables U, V, and D are updated, the number of iterations d increases by 1; the residual of the objective function is calculated by the variable When it is less than the predefined threshold T h = 0.0001 or when the maximum number of iterations d = 1000 is reached, the algorithm stops obtaining the target abundance matrix and then obtains the target abundance map.

[0181] The present invention effectively constrains the size of model parameters by adding the Frobenius norm of the abundance matrix as a regularization term in the objective function; effectively promotes the row sparsity and element sparsity of the abundance matrix by introducing the L1 norm and adaptively calculating the spectral weighting factor and the spatial weighting factor; obtains a multi-scale superpixel segmentation map through different superpixel segmentation scales, and then constructs a multi-scale superpixel-guided low-rank regularization term, adaptively integrating complementary information from multiple segmentation scales, thereby improving the performance of the unmixing algorithm and the accuracy of the results; and introduces the alternating direction multiplier method to decompose the objective function into multiple simple and easy-to-solve sub-problems, making the algorithm easier to solve and accelerating the convergence speed.

[0182] The embodiments described above are merely descriptions of preferred implementations of the present invention and are not intended to limit the scope of the present invention. Without departing from the principles and essence of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should fall within the scope of protection determined by the claims of the present invention.

Claims

1. A sparse unmixing method for hyperspectral images based on multi-scale superpixel low-rank representation, characterized in that: The specific steps include: S1. Introduce the Frobenius norm to calculate the difference between the reconstructed hyperspectral image and the original hyperspectral image, and take the minimum difference as the data fidelity term of the objective function; S2. Based on the abundance matrix in the original hyperspectral image, the L1 norm is introduced to adaptively construct the spectral weighting factor and the spatial weighting factor of the abundance matrix to obtain a sparse regularization term of the objective function; S3. Setting the superpixel size of the original hyperspectral image, obtaining multiple segmentation maps of different segmentation scales based on the superpixel segmentation algorithm, and calculating the Calinski-Harabasz index of each segmentation map to obtain the weighting factor of each segmentation map; S4. Introducing a weighted nuclear norm constraint into the superpixel region of each segmentation map to obtain a low-rank representation regularization term of the objective function; S41, obtaining multiple segmentation maps of different segmentation scales; S42, introducing a weighted nuclear norm constraint into the superpixel region of each segmentation image to obtain similar abundance matrices corresponding to mixed pixels in the same superpixel region; S43, introduce the weight of the segmentation map and adaptively fuse multiple segmentation map features of different segmentation scales; S44. A multi-scale superpixel guided low-rank representation regularization term of the objective function is obtained based on the weighted nuclear norm constraint and the weight of the segmentation map; Specifically, for the h-th segmentation map, a weighted nuclear norm constraint is added, which is specifically expressed as: Where, ω j is a weighting factor that imposes a larger penalty on smaller singular values, thus forcing them to be close to zero in the next iteration; X i represents the abundance matrix of mixed pixels in the i-th superpixel; The low-rank representation regularization term of the objective function is expressed as: Where β represents the hyperparameter of the low-rank regularization term of the objective function; S5. Constructing an objective function based on the data fidelity term, the sparse regularization term, and the low-rank representation regularization term; S6. Solve the objective function by the alternating direction multiplier method to obtain the target abundance matrix.

2. The hyperspectral image sparse unmixing method based on multi-scale superpixel low-rank representation according to claim 1 is characterized in that: The step S1 specifically includes the following steps: S11, obtaining original hyperspectral images; S12, using a linear mixed model to decompose the mixed pixels of the original hyperspectral image to obtain a spectral library of multiple end members and a combination coefficient corresponding to each end member to obtain a reconstructed hyperspectral image; The reconstructed hyperspectral image is represented by Y=AX+N; Y=[y1,...,y m ]∈R l×m represents the original hyperspectral image, which contains l spectral bands and m pixels; A = [a1, ..., a p ]∈R l×p represents a spectral library with p end members; X = [x1, ..., x m ]∈R p×m Represents the combination coefficient corresponding to each end member, that is, the abundance matrix of the original hyperspectral image; AX represents the reconstructed hyperspectral image; N∈R m×l represents additional noise and error; S13. Based on the original hyperspectral image and the reconstructed hyperspectral image, the Frobenius norm is introduced to calculate the difference between the reconstructed hyperspectral image and the original hyperspectral image, and the minimum difference is taken as the data fidelity term of the objective function; the data fidelity term of the objective function is expressed as Where Y represents the original hyperspectral image; AX represents the reconstructed hyperspectral image; Y-AX represents the matrix of the original hyperspectral image and the reconstructed hyperspectral image; is the Frobenius norm of the matrix Y-AX.

3. The hyperspectral image sparse unmixing method based on multi-scale superpixel low-rank representation according to claim 1 is characterized in that: The step S2 specifically includes the following steps: S21, obtaining the abundance matrix in the original hyperspectral image; S22, adding the L1 norm to the abundance matrix to calculate the sum of the absolute values ​​of the minimum abundance matrix; S23. Based on the row sparsity of the abundance matrix, adaptively constructing and calculating a spectral weighting factor of the abundance matrix; S24. Based on the sparsity of the elements of the abundance matrix, adaptively construct and calculate a spatial weighting factor of the abundance matrix; S25. Obtaining a sparse regularization term of the objective function based on the spectral weighting factor, the spatial weighting factor, and the L1 norm of the abundance matrix; Specifically, It is expressed as the L1 norm of the abundance matrix X; the calculation formula of the spectral weighting factor is Where i=1, ..., p, X(i,:) represents the i-th row element of the abundance matrix X; the calculation formula of the spatial weighting factor is in, Represents the mixed pixel x of the original hyperspectral image ij Neighborhood coverage; λ||W spe W spa ⊙X|| 1，1 It is expressed as the sparse regularization term of the objective function, where λ represents the parameter of the sparse regularization term, which is used to measure the importance of the sparse regularization term of the objective function.

4. The method for sparse unmixing of hyperspectral images based on multi-scale superpixel low-rank representation according to claim 1, characterized in that: The step S3 specifically includes the following steps: S31, obtaining an original hyperspectral image; S32, setting the superpixel size of the original hyperspectral image to calculate the segmentation scale and the number of segmentation scales of the original hyperspectral image; S33, based on the segmentation scale and the number of segmentation scales, using a superpixel segmentation algorithm to iteratively obtain multiple segmentation maps with different segmentation scales; S34, based on multiple segmentation maps of different segmentation scales, calculating the Calinski-Harabasz index to obtain the weight of each segmentation map; Specifically, for the hth segmentation map, the specific segmentation process is as follows: 1) Set the superpixel size of the original hyperspectral image to S; 2) Obtain the segmentation scale S of the original hyperspectral image by calculation h , and its calculation formula is: S h =S+(-1) h ,h=1,2,...,H Where H is the number of segmentation scales, S h is an integer greater than 0; 3) Run the simple linear iterative algorithm H times to obtain H segmentation maps with different segmentation scales; 4) Select K h seed points, among which K h is the total number of superpixels in the h-th segmentation map; m is the number of pixels in the h-th segmentation map; 5) Calculate the spectral distance and spatial distance between each mixed pixel near each seed point and the seed point; the calculation formulas for the spectral distance and spatial distance are: Where, d spatial and d spectral Represents the spatial distance and spectral distance between mixed pixels; (x i ,y i )、(x j ,y j ) represent the spatial coordinate information of the mixed pixels; y i ,y j represents the spectral characteristics of mixed pixels i and j; 6) Based on the spectral distance and spatial distance, the difference between the mixed pixels is calculated; the specific calculation formula is: Where Dis is an indicator used to measure the difference between mixed pixels; r is a weight used to balance spectral distance and spatial distance; 7) Comparing the spectral distance and spatial distance with the preset thresholds respectively, screening out mixed pixels whose spectral distance and spatial distance are respectively less than the preset thresholds and assigning them to seed points; 8) The average value of all pixels of each superpixel in the segmentation map is used as the new center point, and the above steps are repeated until the number of iterations is reached or convergence is achieved; S35, summing the weights of the multiple segmentation maps to obtain a weight factor of the segmentation map; Specifically, for the hth segmentation map, the corresponding weight is: Where, C h represents the Calinski-Harabasz index of the hth segmentation map; R h is the covariance matrix between pixels of the h-th segmentation map; E h is the covariance matrix between the elements in the superpixel of the h-th segmentation map; m and K h are the number of pixels and the total number of superpixels in the h-th segmentation map, respectively.

5. The hyperspectral image sparse unmixing method based on multi-scale superpixel low-rank representation according to claim 1, characterized in that: The step S6 specifically includes the following steps: S61, introduce variables U, V and Lagrange multiplier D = {D1, D2, D3, D4}, S62. Construct Lagrangian function: in, μ represents the penalty parameter, μ>0; G and B are defined as: G=[A,I,I,I] T I represents the identity matrix; S63, Lagrangian function The variables U, V, and D are solved iteratively as follows: S631, with variables V and D fixed, the optimization problem for variable U is expressed as: Where d represents the number of iterations. By taking the partial derivative of the variable U in the above formula and making it equal to zero, the solution of the variable U is: U (d+1) ←v(A T A+3I) -1 (A T (z1+z2+z3+z4) in, S632, variable V contains four sub-problems, namely V1, V2, V3 and V4: 1) The optimization problem and solution of variable V1 are expressed as: 2) The optimization problem and solution of variable V2 are expressed as: 3) The optimization problem of variable V3 is expressed as: For each The solution is: in, The i-th superpixel region corresponding to the h-th segmentation scale; Γ w，τ (X) = U(Π-τdiag(w)) + V T ;UΠV T represents the singular value decomposition of matrix X; (x) + =max(x,0); 4) The optimization problem and solution of variable V4 are expressed as: Each time the variables U, V, and D are updated, the number of iterations d increases by 1; the residual of the objective function is calculated by the variable When it is less than the predefined threshold T h = 0.0001 or when the maximum number of iterations d = 1000 is reached, the algorithm stops obtaining the target abundance matrix and then obtains the target abundance map.

Images