A hyperspectral anomaly detection method

Abstract

The application provides a hyperspectral anomaly detection method, comprising the following steps: step 1, constructing a linear spectral mixing model of a hyperspectral image; step 2, constructing a double-space weight sparse unmixing model, and calculating an abundance matrix of each end member in a mixed pixel; step 3, introducing a spectral weighting factor and a spatial weighting factor based on spatial neighborhood information, and creating a dictionary empty spectrum low-rank decomposition model; step 4, solving the dictionary empty spectrum low-rank decomposition model to obtain an anomaly matrix; step 5, obtaining a reconstructed image through the anomaly matrix; and step 6, obtaining an anomaly target detection image according to the hyperspectral image and the reconstructed image. The application fully excavates the correlation between spectral information and spatial information of the hyperspectral image by introducing the spectral weighting factor and the spatial weighting factor based on the spatial neighborhood information, so that the accuracy of the hyperspectral image anomaly detection is improved, and the accuracy of the anomaly detection result of the application is 99.39%.

Description

Technical Field

[0001] This invention relates to a hyperspectral anomaly detection method, belonging to the field of hyperspectral image processing technology in the field of remote sensing. Background Technology

[0002] Hyperspectral images contain dozens or even hundreds of spectral bands, possessing high spectral resolution and rich spectral feature information of ground objects, which can greatly improve the ability to accurately detect and identify ground object categories. In hyperspectral images, pixels with significant spectral differences from the surrounding background are defined as anomalies. Hyperspectral image anomaly detection is a type of anomaly detection that does not require prior spectral information of the target object. It determines the presence of anomalies within a region by mining the differences in contextual information within the image itself. Hyperspectral images can utilize the unique spectral curve features of various ground objects to identify many similar ground object categories that cannot be identified by spectral images, thus making hyperspectral image anomaly detection a research hotspot.

[0003] Anomaly detection in hyperspectral images presents the following challenges: 1. Hyperspectral images have high spectral dimensions and significant data redundancy, increasing the computational complexity of anomaly detection; 2. Most areas of hyperspectral images consist of background pixels, with low anomaly frequency and small area occupied by anomalies, resulting in an uneven distribution of background and anomalies; 3. Due to the spatial resolution limitations of spectral imagers and the complexity of ground features, noise interference occurs during the acquisition of hyperspectral images, causing spectral mixing between background and anomaly spectra, resulting in hyperspectral images containing mixed pixels of various substances (endmembers).

[0004] To address the aforementioned challenges, especially in cases where background and anomalous spectral distributions intersect and hyperspectral images contain mixed pixels of multiple substances (endmembers), existing methods suffer from insufficient extraction of spectral and spatial information from hyperspectral images. Therefore, it is necessary to provide an effective method for anomaly detection that extracts spectral and spatial information from hyperspectral images to improve the accuracy of anomaly detection results. Summary of the Invention

[0005] To address the aforementioned problems, this invention provides a method for unmixing a spectral linear mixture model by constructing a dual-space weighted sparse unmixing model to obtain an abundance matrix S. Using the abundance matrix S as samples, a dictionary is generated, and a spectral weighting factor W is introduced. spe and spatial weighting factor W based on spatial neighborhood information spa A dictionary-based low-rank spatial spectrum decomposition model is created to obtain the anomaly matrix E. Using the anomaly matrix E, a reconstructed image X with the same dimension as the hyperspectral image X is obtained. r Based on hyperspectral image X and reconstructed image X rA hyperspectral anomaly detection method is developed by using the error between the two to extract anomalous targets and obtain anomalous target detection images.

[0006] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows:

[0007] A method for detecting hyperspectral anomalies includes the following steps:

[0008] Step 1: Obtain hyperspectral image data X with mixed pixels, arrange the spectral vectors of the pixels of hyperspectral image X in matrix form, and construct a linear spectral mixing model of hyperspectral image X, expressed as formula (1):

[0009] X = AS + N (1)

[0010] Where X is an L×B hyperspectral image matrix, A is an L×K endmember spectral matrix, S is a K×B abundance matrix composed of abundance vectors corresponding to B pixels, N is an L×B noise or error matrix, and L, B and K are all positive integers.

[0011] Step S2 uses the robust minimum simplex volume method to unmix the linear spectral mixing model to obtain the endmember matrix A. The endmember matrix A is fixed, and two spatial weighting factors are introduced to construct a dual spatial weighted sparse unmixing model to perform spectral unmixing on the linear spectral mixing model. The abundance matrix S of each endmember A in the mixed pixels is calculated.

[0012] Step S3: Using the abundance matrix S as a sample, introduce spectral weighting factors and spatial weighting factors based on spatial neighborhood information to construct a dictionary spatial spectrum low-rank decomposition model;

[0013] Step S4: Solve the dictionary empty spectrum low-rank decomposition model using the alternating direction multiplier method based on variable splitting to obtain the anomaly matrix;

[0014] Step S5: Obtain the reconstructed image X with the same dimensions as the hyperspectral image X using the anomaly matrix. r ;

[0015] Step S6, based on the hyperspectral image X and the reconstructed image X r The error between the two is used to extract abnormal targets and obtain an abnormal target detection image.

[0016] Preferably, step 2 specifically comprises:

[0017] S2.1 The linear spectral mixing model is unmixed using the robust minimum simplex volume method to obtain the endmember matrix A;

[0018] S2.2 With the endmember matrix A fixed, establish the initial objective function of the linear spectral mixing model, as shown in formula (2):

[0019]

[0020] S2.3 In formula (2), spatial weighting factors W1 and W2 are introduced to construct a dual-spatial-weighted sparse unmixing model, as shown in formula (3):

[0021]

[0022] S2.4 The abundance matrix S is obtained by iteratively optimizing the dual-space weighted sparse unmixing model using the alternating direction multiplier method based on variable splitting.

[0023] Where λ>0, λ1>0, λ and λ1 are regularization parameters, and min represents the minimization function, ||·|| F Denotes the F-norm of a matrix, ||·|| 1,1 L represents 1,1 Norm; ⊙ represents the Hadamard product. s represents the sum of matrix elements. n The nth row represents S.

[0024] Preferably, the spatial weighting factor W1 in step S2.3 is calculated as follows:

[0025] S2.3.1 Segment the hyperspectral image X into an approximate domain coarse hyperspectral image with a coarse spatial structure. Then, based on the similarity between adjacent superpixels, an approximate domain coarse hyperspectral image is generated. Sparse unmixing, as detailed below:

[0026] The hyperspectral image X is segmented into g superpixel blocks using the SLIC algorithm to construct a coarse hyperspectral image in the approximate domain. Constructing coarse hyperspectral images based on the approximate domain The objective function is as shown in equation (4):

[0027]

[0028] Where λ2 is L 1,1 Norm sparse constraint term, λ²>0, This represents the weighted abundance matrix after demixing.

[0029] Equation (4) is solved iteratively using the alternating direction multiplier method based on variable splitting to obtain the weighted abundance matrix.

[0030] S2.3.2 Using weights to guide the abundance matrix The spatial weighting factor W1 is calculated, and its calculation process can be expressed by formula (5):

[0031]

[0032] in, Represents the weighted abundance matrix The elements in the i-th row, ||·||2 represents the 2-norm of the matrix, ε1 is an adjustable parameter, and W 1,ij This represents the value in the i-th row and j-th column of W1.

[0033] Preferably, the result of the (t+1)th iteration of the spatial weight factor W2 in step S2.3 is... Represented as formula (6):

[0034]

[0035] Where t represents the current iteration number, ε2 represents an adjustable parameter value, and N(h) represents the element s in the i-th row and j-th column of matrix S. ij Let h∈{1,2,...,u} be the set of neighboring elements, u be the size of the neighborhood window, and S be the size of the neighborhood window. ih Let s represent the value s in the i-th row and j-th column of matrix S. ij The set of adjacent elements.

[0036] Preferably, step 3 specifically comprises:

[0037] S3.1 Using the columns of the abundance matrix S as samples, the abundance matrix S is expressed as formula (7):

[0038] S = DZ + E (7)

[0039] S3.2 Based on formula (7), a spectral weighting factor W is introduced. spe and spatial weighting factor W based on spatial neighborhood information spa Create a dictionary empty spectrum low-rank decomposition model, as shown in formula (8):

[0040]

[0041] stS=DZ+E (8)

[0042] Where D = {d1, d2, ... d 2k}∈R c×2k It is a dictionary, Z = {z1, z2, ... z} B}∈R 2k×B S is the coefficient of D, E is the anomaly matrix, ||·|| * The nuclear norm of a matrix is ​​represented by its nucleus. in Let ||·||1 represent the L1 norm, and λ3 > 0 be used to adjust the low-rank terms and ||(W). spe W spaThe parameter W that balances sparsity between terms E||1. spe It is used to improve the row sparsity of matrix E.

[0043] Preferably, the spectral weighting factor W in step 3 is... spe Result of the (t+1)th iteration Represented as formula (9):

[0044]

[0045] Where ε3 represents an adjustable parameter, E t (i,:) represents the element in the i-th row of the anomaly matrix E during the t-th iteration.

[0046] Preferably, the spatial weighting factor W based on spatial neighborhood information in step 3... spa The result of the (t+1)th iteration in the i-th row and j-th column Represented as formula (10):

[0047]

[0048] Where f(·) represents the function for mining spatial correlations through the neighborhood system, as shown in formula (11):

[0049]

[0050] Where ε4 represents an adjustable parameter, and M(o) represents the element e in the i-th row and j-th column of the anomaly matrix E. ij Let o∈{1, 2, ..., u0} be the set of neighboring elements, u0 be the size of the neighborhood window, and e be the number of neighboring elements. io Let e ​​represent the value in the i-th row and j-th column of matrix E. ij The set of neighboring elements, where ε represents the weight of the set of neighboring elements. io ε represents the value in the i-th row and j-th column of matrix ε. ij The set of adjacent elements.

[0051] Preferably, step 6 specifically includes:

[0052] S6.1 The error is calculated using formula (12):

[0053] Error(X) = ||X - Xr||2 (12)

[0054] S6.2 Obtain a grayscale image based on the error Error(X), then select a segmentation threshold δ. Pixel values ​​in the grayscale image greater than δ are marked as 1, indicating abnormal targets; otherwise, they are marked as 0, indicating background. A binary result image with only 0 and 1 is obtained, and the abnormal target detection result is obtained.

[0055] Compared with the prior art, the beneficial effects of the present invention are as follows: The present invention obtains the abundance matrix S by performing dual-space weighted sparse unmixing on the spectral linear mixture model, uses the abundance matrix S as a sample to generate a dictionary, and introduces the spectral weighting factor W. spe and spatial weighting factor W based on spatial neighborhood information spa A dictionary-based low-rank decomposition model of the hyperspectral spectrum is created to obtain the anomaly matrix E. Using the anomaly matrix E, a reconstructed image X with the same dimensions as the original hyperspectral image X is obtained. r According to the original image X and the reconstructed image X r This invention extracts anomalous targets by considering the error between the two values. It introduces a spectral weighting factor W. spe and spatial weighting factor W based on spatial neighborhood information spa This invention aims to fully exploit the correlation between spectral and spatial information in hyperspectral images to improve the accuracy of anomaly detection. Experimental results on real hyperspectral datasets show that the anomaly detection accuracy obtained by this invention is 99.39%. Attached Figure Description

[0056] Figure 1 This is a flowchart of the present invention.

[0057] Figure 2 This is an RGB pseudo-color image of the AVIRIS airport hyperspectral image according to an embodiment of the present invention.

[0058] Figure 3 This is a map showing the actual location of ground features in an AVIRIS airport hyperspectral image according to an embodiment of the present invention.

[0059] Figure 4 This is a diagram of the abnormal target detection structure of the AVIRIS airport hyperspectral image, which is a comparative example of the present invention (Method 1).

[0060] Figure 5 This is a comparison of the abnormal target detection results of the AVIRIS airport hyperspectral image (Method2).

[0061] Figure 6 This is an image showing the abnormal target detection results of an AVIRIS airport hyperspectral image according to an embodiment of the present invention. Detailed Implementation

[0062] The present invention will now be described in detail with reference to the embodiments and accompanying drawings. It should be noted that, unless otherwise specified, the embodiments and features described herein can be combined with each other.

[0063] like Figure 1As shown, a hyperspectral anomaly detection method includes the following steps: Step 1: Obtain a hyperspectral image X with mixed pixels, arrange the spectral vectors of the pixels in hyperspectral image X in matrix form, and construct a linear spectral mixing model of hyperspectral image X, expressed as formula (1):

[0064] X = AS + N (1)

[0065] Where X is an L×B hyperspectral image matrix, A is an L×K endmember spectral matrix, S is a K×B abundance matrix composed of abundance vectors corresponding to B pixels, N is an L×B noise or error matrix, and L, B and K are all positive integers.

[0066] Step S2 uses the Robust Minimum Simplex Volume (RMVSA) method to unmix the linear spectral mixing model to obtain the endmember matrix A. The endmember matrix A is fixed, and two spatial weighting factors are introduced to construct a dual spatial weighted sparse unmixing model to perform spectral unmixing on the linear spectral mixing model. The abundance matrix S of each endmember A in the mixed pixels is calculated.

[0067] Preferably, step 2 specifically comprises:

[0068] S2.1 The linear spectral mixing model is unmixed using the robust minimum simplex volume method to obtain the endmember matrix A;

[0069] S2.2 With the endmember matrix A fixed, establish the initial objective function of the linear spectral mixing model, as shown in formula (2):

[0070]

[0071] Sparsity can improve the accuracy of hyperspectral mixed pixel unmixing, so the sparse unmixing algorithm is introduced into hyperspectral image unmixing;

[0072] S2.3 In formula (2), spatial weighting factors W1 and W2 are introduced to construct a dual-spatial-weighted sparse unmixing model, as shown in formula (3):

[0073]

[0074] st:S≥0. (3)

[0075] S2.4 The abundance matrix S is obtained by iteratively optimizing the dual-space weighted sparse unmixing model using the alternating direction multiplier method based on variable splitting.

[0076] Where λ>0, λ1>0, λ and λ1 are regularization parameters, and min represents the minimization function, ||·|| F Denotes the F-norm of a matrix, ||·|| 1,1 L represents 1,1Norm; ⊙ represents the Hadamard product. Let s represent the sum of the elements of the matrix, where s n Represents the nth row of S;

[0077] Furthermore, the spatial weighting factor W1 in step S2.3 is calculated as follows:

[0078] S2.3.1 Segment the hyperspectral image X into an approximate domain coarse hyperspectral image with a coarse spatial structure. Then, based on the similarity between adjacent superpixels, an approximate domain coarse hyperspectral image is generated. Sparse unmixing, as detailed below:

[0079] The hyperspectral image X is segmented into g superpixel blocks using the SLIC algorithm to construct a coarse hyperspectral image in the approximate domain. Constructing coarse hyperspectral images based on the approximate domain The objective function is as shown in equation (4):

[0080]

[0081] Where λ2 is L 1,1 Norm sparse constraint term, λ²>0, This represents the weighted abundance matrix after demixing.

[0082] Hyperspectral images have low spatial resolution and cannot accurately represent spatial structures. Furthermore, when using superpixel segmentation, the same type of land cover may be segmented into multiple superpixel representations, resulting in spectral similarity between adjacent superpixels. Utilizing the spatial relationship characteristics between adjacent superpixels and applying them to sparse model constraints can greatly improve the accuracy of the unmixing results. Therefore, superpixel segmentation is used for hyperspectral unmixing.

[0083] Equation (4) is solved iteratively using the alternating direction multiplier method based on variable splitting to obtain the weighted abundance matrix.

[0084] S2.3.2 Using weights to guide the abundance matrix The spatial weighting factor W1 is calculated, and its calculation process can be expressed by formula (5):

[0085]

[0086] in, Represents the weighted abundance matrix The elements in the i-th row, ||·||2 represents the 2-norm of the matrix, ε1 is an adjustable parameter, and W 1,ij This represents the value in the i-th row and j-th column of W1;

[0087] Furthermore, the result of the (t+1)th iteration of the spatial weight factor W2 in step S2.3 is... Represented as formula (6):

[0088]

[0089] Where t represents the current iteration number, ε2 represents an adjustable parameter value, and N(h) represents the element s in the i-th row and j-th column of matrix S. ij Let h∈{1, 2, ..., u} be the set of neighboring elements, and u be the size of the neighborhood window. In this method, a 3×3 neighborhood window is selected to mine spatial information, i.e., u is 3. ih Let s represent the value s in the i-th row and j-th column of matrix S. ij The set of adjacent elements;

[0090] Step S3: Using the abundance matrix S as a sample, introduce spectral weighting factors and spatial weighting factors based on spatial neighborhood information to construct a dictionary spatial spectrum low-rank decomposition model;

[0091] Specifically:

[0092] S3.1 Using the columns of the abundance matrix S as samples, the abundance matrix S is expressed as formula (7):

[0093] S = DZ + E (7)

[0094] S3.2 To fully explore the correlation between the spectral and spatial information of hyperspectral images, a spectral weighting factor W is introduced based on formula (7). spe and spatial weighting factor W based on spatial neighborhood information spa Create a dictionary of empty spectrum low

[0095] The rank decomposition model is shown in formula (8):

[0096]

[0097] stS=DZ+E (8)

[0098] Where D = {d1, d2, ... d} 2k}∈R c×2k It is a dictionary, Z = {z1, z2, ... z} B}∈R 2k×B S represents the coefficients of D, the background DZ is represented as the product of the dictionary D and the coefficients Z, which is a low-rank matrix, and E is the anomaly matrix, ||·|| * The nuclear norm of a matrix is ​​denoted as . in Let ||·||1 represent the L1 norm, and λ3 > 0 be used to adjust the low-rank terms and ||(W).spe W spa The parameter W that balances sparsity between terms E||1. spe It was used to improve the row sparsity of matrix E;

[0099] Furthermore, the spectral weighting factor W in step 3... spe Result of the (t+1)th iteration Represented as formula (9):

[0100]

[0101] Where ε3 represents an adjustable parameter, E t (i,:) represents the element in the i-th row of the anomaly matrix E at the t-th iteration;

[0102] The spatial weighting factor W based on spatial neighborhood information in step 3 spa The result of the (t+1)th iteration in the i-th row and j-th column Represented as formula (10):

[0103]

[0104] Where f(·) represents the function for mining spatial correlations through the neighborhood system, as shown in formula (11):

[0105]

[0106] Where ε4 represents an adjustable parameter, and M(o) represents the element e in the i-th row and j-th column of the anomaly matrix E. ij Let o ∈ {1, 2, ..., u0} be the set of neighboring elements, and u0 be the size of the neighborhood window. In this method, a 3×3 neighborhood window is selected to mine spatial information, i.e., u0 is 3. io Let e ​​represent the value in the i-th row and j-th column of matrix E. ij The set of neighboring elements, where ε represents the weight of the set of neighboring elements. io ε represents the value in the i-th row and j-th column of matrix ε. ij The set of adjacent elements;

[0107] Specifically, Indicates with e ij The corresponding neighborhood weight values, where the function im(·) is used to measure the weights of two elements e. i and e j The importance of the relationship;

[0108] Let element e i and e jThe spatial coordinates are (a0, b0) and (c0, d0), respectively. Here, the weight ε can be measured by calculating the Euclidean distance between them. ij , ε ij The expression is: Indicates with e ij The corresponding neighborhood weight value (representing e) i element and e j The element's weight value), ε ij The calculation formula is as shown in formula (13):

[0109]

[0110] Step S4: Solve the dictionary empty spectrum low-rank decomposition model using the alternating direction multiplier method based on variable splitting to obtain the anomaly matrix;

[0111] Step S5: Obtain the reconstructed image X with the same dimensions as the hyperspectral image X using the anomaly matrix. r ;

[0112] Step S6, based on the hyperspectral image X and the reconstructed image X r The error between the two is used to extract abnormal targets and obtain an abnormal target detection image;

[0113] Specifically:

[0114] S6.1 The error is calculated using formula (12):

[0115] Error(X) = ||X - Xr||2 (12)

[0116] S6.2 Obtain a grayscale image based on the error Error(X), then select a segmentation threshold δ. Pixel values ​​in the grayscale image greater than δ are marked as 1, indicating abnormal targets; otherwise, they are marked as 0, indicating background. A binary result image with only 0 and 1 is obtained, and the abnormal target detection result is obtained.

[0117] This invention employs hyperspectral images of airports acquired using an airborne visible / infrared imaging spectrometer (AVIRIS), such as... Figure 2The AVIRIS airport hyperspectral image is a pseudo-color image, abbreviated as AVIRIS airport hyperspectral image. The AVIRIS airport hyperspectral image has a spatial resolution of 3.5 meters and a spectral resolution of 10 nm, containing a total of 224 bands. After removing low-quality and low signal-to-noise bands (1-6, 33-35, 97, 107-113, 153-166, 221-224) caused by stripe noise and water absorption, 189 bands are retained for anomalous target detection. The AVIRIS airport hyperspectral image includes buildings, grass, and concrete surfaces as the main background. Three aircraft in the AVIRIS airport hyperspectral image are considered as anomalous targets of interest. The experimental area data size of the AVIRIS airport image is 100×100 pixels, totaling 58 pixels. Figure 3 The actual ground features in the AVIRIS airport hyperspectral image are represented by hyperspectral image X. Anomaly detection was performed on the AVIRIS airport hyperspectral image of the embodiment using RXD, SegRX, LRASR, LSMAD, ADLR, LELRP-AD, and the method described in this invention. The anomaly detection accuracy is shown in Table 1.

[0118] Table 1 Comparison of Accuracy for Hyperspectral Anomaly Target Detection

[0119]

[0120] As shown in Table 1, the abnormal target detection accuracy of the present invention is as high as 99.39%, which is significantly better than other methods.

[0121] Assuming that the dictionary-based low-rank decomposition model of this invention only considers the spectral weighting factor W spe The method is Method 1, which only considers the spatial weighting factor W based on spatial neighborhood information. spa The method is Method2. Anomaly detection is performed on the hyperspectral image of AVIRIS airport using Method1 and Method2 respectively. The anomaly detection accuracy of Method1 is 99.17%, and the anomaly detection accuracy of Method2 is 99.20%. The anomaly detection accuracy of the present invention is 0.22% and 0.19% higher than that of Method1 and Method2, respectively.

[0122] from Figure 4 , Figure 5 and Figure 6 It can be seen that the abnormal target detection effect of the present invention is significantly better than that of Method1 and Method2.

[0123] The above demonstrates that, even when background and anomalous spectral distributions intersect and hyperspectral images contain mixed pixels of multiple substances (endmembers), the present invention can fully exploit the correlation between spectral and spatial information in hyperspectral images, effectively improving the accuracy of anomalous target detection. It is feasible for anomalous target detection in hyperspectral images.

[0124] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions and substitutions can be made without departing from the inventive concept, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for detecting hyperspectral anomalies, characterized in that, Includes the following steps: Step S1: Obtain hyperspectral image data X with mixed pixels, arrange the spectral vectors of the pixels in hyperspectral image data X in matrix form, and construct a linear spectral mixing model of hyperspectral image data X, expressed as formula (1): X = AS + N (1) Where X is L×B hyperspectral image data, A is L×K endmember spectral matrix, S is K×B abundance matrix composed of abundance vectors corresponding to B pixels, N is L×B noise or error matrix, and L, B and K are all positive integers. Step S2 uses the robust minimum simplex volume method to unmix the linear spectral mixing model to obtain the endmember spectral matrix A. The endmember spectral matrix A is fixed, and two spatial weighting factors are introduced to construct a dual spatial weighted sparse unmixing model to unmix the linear spectral mixing model. The abundance matrix S of each endmember spectral matrix A in the mixed pixel is calculated. Step S3: Using the abundance matrix S as a sample, introduce spectral weighting factors and spatial weighting factors based on spatial neighborhood information to construct a dictionary spatial spectrum low-rank decomposition model; Step S4: Solve the dictionary empty spectrum low-rank decomposition model using the alternating direction multiplier method based on variable splitting to obtain the anomaly matrix; Step S5: Obtain the reconstructed image X with the same dimension as the hyperspectral image data X using the anomaly matrix. r ; Step S6, based on the hyperspectral image data X and the reconstructed image X r The error between the two is used to extract abnormal targets and obtain an abnormal target detection image; Step S3 specifically involves: S3.1 Using the columns of the abundance matrix S as samples, the abundance matrix S is expressed as formula (7): S = DZ + E (7) S3.2 Based on formula (7), a spectral weighting factor is introduced. Spatial weighting factors based on spatial neighborhood information Create a dictionary empty spectrum low-rank decomposition model, as shown in formula (8): （8） Where D = {d1, d2, ... d...} 2k }∈R c×2k It is a dictionary, Z = {z1, z2, ... z} B }∈R 2k×B S is the coefficient of D, and E is the anomaly matrix. The nuclear norm of a matrix is ​​represented by its nucleus. ,in Let Z be the singular values. Describing the L1 norm, It is used to adjust low-rank terms and The parameter W that balances sparsity between terms spe It was used to promote row sparsity of the anomaly matrix E.

2. The hyperspectral anomaly detection method as described in claim 1, characterized in that, Step S2 specifically involves: S2.1 The robust minimum simplex volume method is used to unmix the linear spectral mixing model to obtain the endmember spectral matrix A; S2.2 Fix the endmember spectral matrix A, and establish the initial objective function of the linear spectral mixing model, as shown in formula (2): （2） S2.3 In formula (2), spatial weighting factors W1 and W2 are introduced to construct a dual-spatial-weighted sparse unmixing model, as shown in formula (3): （3） S2.4 The abundance matrix S is obtained by iteratively optimizing the dual-space weighted sparse unmixing model using the alternating direction multiplier method based on variable splitting. Where λ>0, λ1>0, λ and λ1 are regularization parameters, min denotes the minimization function, and ||·|| F Denotes the F-norm of a matrix, ||·|| 1,1 L represents 1,1 Norm; This represents the Hadamard product. s represents the sum of matrix elements. n The nth row represents S.

3. The hyperspectral anomaly detection method as described in claim 2, characterized in that, The spatial weighting factor W1 in step S2.3 is calculated as follows: S2.3.1 Segment the hyperspectral image data X into an approximate domain coarse hyperspectral image with a coarse spatial structure. Then, based on the similarity between adjacent superpixels, an approximate domain coarse hyperspectral image is generated. Sparse unmixing, as detailed below: The SLIC algorithm is used to segment the hyperspectral image data X into g superpixel blocks to construct a coarse hyperspectral image in the approximate domain. ∈R L×B Constructing coarse hyperspectral images based on the approximate domain The objective function is as shown in equation (4): （4） Where λ2 is L 1,1 Norm sparse constraint term, λ²>0, ∈R L×B This represents the weighted abundance matrix after demixing. Equation (4) is solved iteratively using the alternating direction multiplier method based on variable splitting to obtain the weighted abundance matrix. ; S2.3.2 Using weights to guide the abundance matrix The spatial weighting factor W1 is calculated, and the calculation process can be expressed by formula (5): （5） in, Represents the weighted abundance matrix The element in the i-th row, ||·||2 represents the 2-norm of the matrix. W is an adjustable parameter. 1,ij This represents the value in the i-th row and j-th column of W1.

4. The hyperspectral anomaly detection method as described in claim 3, characterized in that, The result of the (t+1)th iteration of the spatial weighting factor W2 in step S2.

3. Represented as formula (6): （6） Where t represents the current iteration number, This is represented as an adjustable parameter value. The element s in the i-th row and j-th column of the abundance matrix S represents... ij Let h∈{1,2,...,u} be the set of neighboring elements, u be the size of the neighborhood window, and S be the size of the neighboring window. ih s represents the value s in the i-th row and j-th column of the abundance matrix S. ij The set of adjacent elements.

5. The hyperspectral anomaly detection method as described in claim 4, characterized in that, The spectral weighting factor in step S3 Result of the (t+1)th iteration Represented as formula (9): （9） in, This is represented as an adjustable parameter. Let represent the element in the i-th row of the anomaly matrix E during the t-th iteration.

6. The hyperspectral anomaly detection method as described in claim 5, characterized in that, The spatial weighting factor based on spatial neighborhood information in step S3 The result of the (t+1)th iteration in the i-th row and j-th column Represented as formula (10): （10） Where f(·) represents a function for mining spatial correlations through the neighborhood system, as shown in formula (11): (11) in, Let M(o) be an adjustable parameter, representing the neighborhood set of the element eij in the i-th row and j-th column of the anomaly matrix E, where o∈{1,2,...,u0} is the number of neighboring element sets, u0 is the neighborhood window size, and eio represents the neighborhood set of the value eij in the i-th row and j-th column of matrix E. Represents the weight of adjacent element sets. Representation matrix The value in the i-th row and j-th column The set of adjacent elements.

7. The hyperspectral anomaly detection method as described in claim 6, characterized in that, Step S6 is as follows: S6.1 The error is calculated using formula (12): Error(X)=||X-X r ||2 (12) S6.2 Obtain a grayscale image based on the error Error(X), then select a segmentation threshold δ. Pixel values ​​in the grayscale image greater than δ are marked as 1, indicating abnormal targets; otherwise, they are marked as 0, indicating background. A binary result image with only 0 and 1 is obtained, and the abnormal target detection result is obtained.

Images