A hyperspectral anomaly detection method based on multivariate probability distribution autoencoder

Abstract

The application discloses a hyperspectral anomaly detection method based on a multivariate probability distribution self-encoder, first, a grid structure is designed to divide the rows and columns of hyperspectral data, realizing the mapping of the hyperspectral data from disorder to order, laying a foundation for the effective separation of background information and abnormal targets, and effectively calculating the difference between the abnormal and the background by quantifying the deviation value between the test points and the high-density and high-number background interval; second, a multilayer automatic encoder network based on energy weight jump connection is proposed to adapt to the hyperspectral anomaly detection task without any prior information constraint, and the inherent characteristics of the data can be effectively learned without explicitly indicating the data labels; third, the self-encoder system is combined with a multivariate probability distribution model to find hidden spatial intrinsic characteristics. It has strong generalization and detection ability and is suitable for anomaly detection in complex scenes.

Description

Technical Field

[0001] This invention belongs to the field of hyperspectral remote sensing image processing, and in particular relates to a hyperspectral anomaly detection method based on a multivariate probability distribution autoencoder that fully mines hyperspectral image data and can effectively enhance the sensitivity of detecting anomalous targets. Background Technology

[0002] In recent years, hyperspectral target detection (HTD) based on hyperspectral imagery has emerged. This technique utilizes the narrow and nearly continuous spectral and two-dimensional geometric information of ground features reflected in hyperspectral imagery to confirm the existence of a specified target on a hyperspectral data cube. HTD can be divided into spectral matching detection and hyperspectral anomaly detection (HAD). The former is target detection in the conventional sense, a "reconnaissance" technique for finding known targets, requiring prior knowledge of the target's spectral signal. The latter requires no prior knowledge of the target; it is a method for detecting unwanted targets with unknown background and target information, a "surveillance" technique for finding unknown targets of interest, detecting anomalous targets that differ from the background area. Due to the complexity of the detection scene and the sparsity and uncertainty of the detected targets in practical applications, it is impossible to obtain prior knowledge such as the spectral information of real ground features. This makes HAD, which requires no prior knowledge, more valuable for practical applications, such as agricultural disease detection, rare mineral exploration, and the discovery of military anomalies. However, the demanding detection environment with no prior knowledge and small targets, coupled with the large data volume and high redundancy of hyperspectral images, makes HAD research extremely challenging.

[0003] Statistical modeling theory forms the foundation for the development of traditional hyperspectral anomaly detection. For example, the RX algorithm proposed by Reed and Xiaoli assumes that background pixels in high-dimensional space conform to a multivariate Gaussian distribution, while anomalous pixels deviate from this distribution. It uses the covariance matrix to estimate background features, calculates the Mahalanobis distance between a single pixel and the background model, and uses this metric to quantify the spectral difference between each pixel and its corresponding neighboring background point. Therefore, it accomplishes anomaly detection without prior knowledge of specific target characteristics. Researchers have made various improvements to the RX algorithm. Based on the local RX algorithm, which addresses the complexity of the overall background of hyperspectral images, it assumes that the local background conforms to a Gaussian distribution and uses a local dual-window pattern based on a local normal model to detect anomalies, achieving good results in sub-pixel anomaly detection in low-complexity scenes. A nonlinear RX detection algorithm based on kernel methods serves as a nonlinear iteration of the RX algorithm. This method projects the original data into a high-dimensional feature space through a nonlinear mapping function, thereby achieving the separation of background and anomalous targets in the high-dimensional feature space. The HAD method based on fractional Fourier entropy innovatively utilizes frequency domain Fourier transform for signal representation extraction in an intermediate domain containing reflectance spectra and their Fourier domain information.

[0004] The aforementioned statistical modeling-based hyperspectral anomaly detection methods all suffer from overly simplistic assumptions about data distribution. In reality, data distribution is often complex and cannot be represented by a simple probability distribution. Therefore, when dealing with complex data, high false positive and false negative rates may occur. Furthermore, in hyperspectral images, anomalous pixels are typically far fewer than normal pixels, leading to severe sample imbalance in the dataset. How to suppress backgrounds and highlight anomalous targets in complex application scenarios remains a significant challenge. Fully exploring the inherent correlation characteristics of hyperspectral images and applying them to anomaly detection in hyperspectral images warrants further research. Summary of the Invention

[0005] The present invention aims to solve the above-mentioned technical problems of the prior art by providing a hyperspectral anomaly detection method based on a multivariate probability distribution autoencoder that fully mines hyperspectral image data and can effectively enhance the sensitivity of detecting anomalous targets.

[0006] The technical solution of this invention is: a hyperspectral anomaly detection method based on a multivariate probability distribution autoencoder, which is carried out according to the following steps:

[0007] Step 1. Input hyperspectral image Where M×N is the size of the band image and B is the number of bands in the band group;

[0008] Step 2. Transform the three-dimensional hyperspectral data H into two-dimensional hyperspectral data. Where L is the total number of pixels in a single-band image, calculated according to formula (1);

[0009] L=M×N (1)

[0010] Step 3. Using a mesh-based partitioning method, for The column frequency matrix F is obtained by partitioning the columns. c The inter-column center position matrix ICP c ;

[0011] Step 3.1 Calculate column according to formula (2), where column represents the number of columns in the grid distribution;

[0012] column=p×M×N (2)

[0013] Where p is the empirical probability value;

[0014] Step 3.2 will The unordered data points are arranged in an ordered manner, and the ordered set of points is divided into columns according to a grid structure of n intervals, b∈{1,2,…,B}. The frequency and center position of each interval are statistically analyzed using a probability density histogram, and this is repeated B times to obtain the column frequency matrix F after column division. c and the interval column center position matrix ICP c ;

[0015] Step 4. Using a mesh-based partitioning method, for The row frequency matrix F is obtained by row partitioning. r And the row center position matrix ICP r ;

[0016] Step 4.1 Calculate row according to formula (3), where row represents the number of rows in the grid distribution;

[0017] row = num(CC ≥ q) (3)

[0018]

[0019] Where CC is H b and H b+1 The correlation coefficient between the two bands, b∈{1,2,…,B-1}, For H b The average pixel value of the band. For H b+1 The pixel mean of the band, where q is an empirical probability value;

[0020] Step 4.2 will The unordered data points are arranged in an ordered manner, and the ordered point set is divided into rows of a grid structure according to row intervals, l∈{1,2,…,L}; By using probability density histograms to statistically analyze the frequency and center position of each interval in the distribution, the row frequency matrix F after row partitioning is obtained. r And the row center position matrix ICP r ;

[0021] Step 5. Obtain the column frequency set F by dividing the grid into columns. c _Set;

[0022] Step 5.1 For hyperspectral data from different locations, H represents the spectral dimension information. For testing pixels;

[0023]

[0024] Step 5.2 Based on tracking y b In gridded ICP c Find the corresponding center position matrix y_ICP;

[0025] Step 5.3 Calculate the column index position c_index with the smallest numerical error according to formula (6);

[0026] [~,c_index]=min|y_ICP(:)-y b | (6)

[0027] Step 5.4 Through y in each band b The grid position c_index is then given as the corresponding F. c column frequency value y b _F c ;

[0028] Step 5.5 Under the statistical analysis of B cycles of band-by-band detection, construct the column frequency set F according to formula (7). c _Set;

[0029]

[0030] Step 6. Calculate Y by dividing the grid into rows and columns. l The abnormal score (anomaly_score) is used to obtain the guide image.

[0031] Step 6.1 Traverse the grid row structure from 1 to row to determine the row index. In n iterations, n∈{1, 2, ..., row}, based on the position of n, find the row index in F. r and ICP r Find the corresponding frequency n_Fr and the corresponding center position n_ICP r ;

[0032] Step 6.2 Calculate the row index matrix row_index of the elements in the original matrix after numerical error ascending order according to formula (8), sort(·) is the function to sort the elements in ascending order in a given interval;

[0033] [~, row_index]sort(|Y l -n_ICP r |) (8) Step 6.3 Based on row_index and n_F r Determine the optimal separable band index position, band_index;

[0034] Step 6.4 Calculate the minimum column frequency min_F corresponding to the separable band according to formula (9). c and the corresponding index position min_p;

[0035] [min_F c ,min_p]=min(F c _Set(band_index)) (9)

[0036] Step 6.5 Find the minimum separation band position min_band using min_p, and obtain the corresponding F band. c The largest frequency value in the middle, max_F c ;

[0037] Step 6.6 Calculate the abnormal ratio value (score) of the pixel according to formula (10);

[0038] score = max_F c / min_F c (10)

[0039] Step 6.7 Iterate through each row, calculate the score, and sum the results to obtain the Y values ​​at different positions. l The abnormal score anomaly_score is obtained after traversal, and the guiding image G is obtained after the traversal is completed;

[0040] Step 7. Reconstruct the hyperspectral data H based on the energy weighted skip connection-based multilayer autoencoder network to obtain the reconstructed background information.

[0041] Step 7.1 After transforming the hyperspectral data H T is the total number of pixels in HSI, calculated according to formula (11);

[0042] T = L × B (11)

[0043] Step 7.2 The t-th pixel h t For each layer t∈{1,2,…,T}, the output of each layer after the fully connected layer and activation function is shown in the following equation;

[0044]

[0045]

[0046] in, It is the output data of each layer, W u and a u These correspond to the weights and biases of each layer in the autoencoder, where u∈{1,2,…,7} represents the layer number.

[0047] Step 7.3 Embed the guiding image G obtained in step 6 into the hidden layer in the middle of the network for reverse guidance. The embedding process is shown in formula (14).

[0048]

[0049] Where β is the penalty coefficient. To guide the image G after inverse subtraction transformation The size of the pixel located at position (ii, jj). For the hidden layer after reverse guidance, the horizontal coordinate ii ranges from 1 to the length S of the network layer, and the vertical coordinate jj ranges from 1 to the width D of the network layer.

[0050] Step 7.4 The output of the fifth layer of the multilayer autoencoder network based on energy weight jump connection is shown in Equation (20);

[0051]

[0052]

[0053]

[0054]

[0055]

[0056]

[0057] in, and They are based on and Energy value weight, and They are based on and Energy value;

[0058] Step 7.5 Output of the sixth layer As shown in formula (26), Two-dimensional data is transformed into three-dimensional data to reconstruct background information.

[0059]

[0060]

[0061]

[0062]

[0063]

[0064]

[0065] in, and They are based on and Energy value weight, and They are based on and Energy value;

[0066] Step 8. Calculate the reconstructed spectral vector for each pixel. Error data compared to the original spectral vector H The i-th pixel k i , where i∈{1,2,…,V} are pixel indices arranged lexicographically;

[0067] Step 9. For the difference data k i Perform local standard deviation filtering, and set the abnormal prominence error data obtained after filtering as follows:

[0068] Step 10. Model the data using a multivariate skewed t-distribution for a_k i Modeling yields formula (27);

[0069]

[0070] in, It is a Gaussian random vector. Let b_v be a generalized inverse Gaussian random variable, and b_v be a skewness vector with parameters. Obtained using the variational Bayesian method, a joint prior of the standard Wishart distribution is defined as follows: μ is the average vector, TT is the precision matrix, and m0, λ, v0 and ψ0 are hyperparameters;

[0071] Step 11. Use formula (27) to analyze the latent variables. Integrate to obtain a_k i The hyperbolic distribution is shown in formula (28);

[0072]

[0073] in, K α (·) represents the modified Bessel function of the second kind;

[0074] Step 12. If γ reaches infinity when α < 0 in the hyperbolic distribution defined in (28), then the multivariate skewed t-distribution is obtained as shown in formula (29);

[0075]

[0076] Step 13. Anomaly detection score based on multivariate skewed t-distribution It can be determined by formula (30);

[0077]

[0078] The final anomaly detection image is obtained by further transformation.

[0079] Compared with existing technologies, this invention has three improvements: First, a grid structure is designed to divide the hyperspectral data into rows and columns, realizing the mapping of hyperspectral data from disordered to ordered forms, laying the foundation for the effective separation of background information and anomalous targets. By quantifying the deviation between test points and high-density, high-quantity background intervals, the difference between anomalies and background is effectively calculated. Second, a multilayer autoencoder network based on energy weighted skip connections is proposed to be applicable to hyperspectral anomaly detection tasks without any prior information constraints. It can effectively learn the intrinsic features of the data without explicit data labels. Third, the autoencoder system is combined with a multivariate probability distribution model to discover hidden spatial intrinsic features. This invention can effectively enhance the sensitivity to detect anomalous targets without any prior information. By coupling the autoencoder system with a multivariate probability distribution model, it achieves effective learning of the intrinsic features of the data without explicit data labels, discovering hidden spatial intrinsic features. It has strong generalization and detection capabilities and is suitable for anomaly detection in complex scenarios. Attached Figure Description

[0080] Figure 1 These are sample images and ground condition maps used in embodiments of the present invention.

[0081] Figure 2 This is a comparison chart of the detection results of the present invention and other methods. Detailed Implementation

[0082] The hyperspectral anomaly detection method based on a multivariate probability distribution autoencoder of the present invention is performed according to the following steps:

[0083] Step 1. Input hyperspectral image Where M×N is the size of the band image and B is the number of bands in the band group;

[0084] Step 2. Transform the three-dimensional hyperspectral data H into two-dimensional hyperspectral data. Where L is the total number of pixels in a single-band image, calculated according to formula (1);

[0085] L=M×N (1)

[0086] Step 3. Using a mesh-based partitioning method, the mesh is partitioned... The column frequency matrix F is obtained by partitioning the columns. c and the interval column center position matrix ICP c ;

[0087] Step 3.1 Calculate column according to formula (2), where column represents the number of columns in the grid distribution;

[0088] column=p×M×N (2)

[0089] Where p is the empirical probability value set to 0.9;

[0090] Step 3.2 will The unordered data points are arranged in an ordered manner. The ordered set of points is divided into columns according to a grid structure. The frequency and center position of each interval are statistically analyzed using a probability density histogram. This process is repeated B times to obtain the column frequency matrix F after column division. c and the interval column center position matrix ICP c ;

[0091] Step 4. Using a mesh-based partitioning method, the mesh is partitioned... The row frequency matrix F is obtained by row partitioning. r And the row center position matrix ICP r ;

[0092] Step 4.1 Calculate row according to formula (3), where row represents the number of rows in the grid distribution;

[0093] row = num(CC ≥ q) (3)

[0094]

[0095] Where CC is H b and H b+1 (b∈{1, 2, ..., B-1}) Correlation coefficient between two bands For H b The average pixel value of the band. For H b+1 The pixel mean of the band, q is a probability empirical value set to 0.98;

[0096] Step 4.2 will The unordered data points are arranged in an ordered manner, and the ordered point set is divided into rows of a grid structure according to row intervals. By using probability density histograms to statistically analyze the frequency and center position of each interval in the distribution, the row frequency matrix F after row partitioning is obtained. r And the row center position matrix ICP r ;

[0097] Step 5. Obtain the column frequency set F by dividing the grid into columns. c _Set;

[0098] Step 5.1 For hyperspectral data from different locations, H represents the spectral dimension information. For testing pixels;

[0099]

[0100] Step 5.2 Based on tracking y b In gridded ICP c Find the corresponding center position matrix y_ICP;

[0101] Step 5.3 Calculate the column index position c_index with the smallest numerical error according to formula (6);

[0102] [~,c_index]=min|y_ICP(:)-y b | (6)

[0103] Step 5.4 Through y in each band b The grid position c_index then gives the corresponding F c column frequency value y b _F c ;

[0104] Step 5.5 Under the statistical analysis of B cycles of band-by-band detection, construct the column frequency set F according to formula (7). c _Set;

[0105]

[0106] Step 6. Calculate Y by dividing the grid into rows and columns. l The anomaly score is used to obtain the guide image.

[0107] Step 6.1 Traverse the grid row structure from 1 to row to determine the row index. In n (n∈{1, 2, ..., row}) iterations, based on the position of n, find the row index in F. r and ICP r Find the corresponding frequency n_F r and the corresponding center position n_ICP r ;

[0108] Step 6.2 Calculate the row index matrix row_index of the elements in the original matrix after numerical error ascending order according to formula (8), sort(·) is the function to sort the elements in ascending order in a given interval;

[0109] [~, row_indexsort(|Y l -n_ICP r |) (8)

[0110] Step 6.3 Based on row_index and n_F r Determine the optimal separable band index position, band_index;

[0111] Step 6.4 Calculate the minimum column frequency min_F corresponding to the separable band according to formula (9). c and the corresponding index position min_p;

[0112] [min_F c ,min_p]min(F c _Set(band_index)) (9)

[0113] Step 6.5 Find the minimum separation band position min_band using min_p, and obtain the corresponding F band. c The largest frequency value in the middle, max_F c ;

[0114] Step 6.6 Calculate the abnormal ratio value (score) of the pixel according to formula (10);

[0115] score = max_F c / min_F c (10)

[0116] Step 6.7 Iterate through each row, calculate the score, and sum the results to obtain the Y values ​​at different positions. lThe anomaly score (anomaly_score) is obtained after the traversal. The guiding image G is then obtained.

[0117] Step 7. Reconstruct the hyperspectral data H based on the energy weighted skip connection-based multilayer autoencoder network to obtain the reconstructed background information.

[0118] Step 7.1 After transforming the hyperspectral data H T is the total number of pixels in HSI, calculated according to formula (11);

[0119] T = L × B (11)

[0120] Step 7.2 The t-th pixel h t (t∈{1,2,…,T}), the output of each layer after the fully connected layer and activation function is shown in the following equation;

[0121]

[0122]

[0123] in, It is the output data of each layer, W u and a u These correspond to the weights and biases of each layer in the autoencoder, where u∈{1,2,…,7} represents the layer number.

[0124] Step 7.3 The guiding image G calculated in step 6 is embedded into the hidden layer in the middle of the network for reverse guidance. The embedding process is shown in formula (14).

[0125]

[0126] Where β is the penalty coefficient. To guide the image G after inverse subtraction transformation The size of the pixel located at position (ii, jj). This is the hidden layer after reverse guidance. The horizontal coordinate ii ranges from 1 to the length S of the network layer, and the vertical coordinate jj ranges from 1 to the width D of the network layer.

[0127] Step 7.4 Multilayer autoencoder network based on energy weight skip connection. Because this deep learning network is a skip connection method, the outputs of the fifth and sixth layers of the network are different from the first four layers. The energy weight method is used for connection. The output of the fifth layer is shown in formula (20).

[0128]

[0129]

[0130]

[0131]

[0132]

[0133]

[0134] in, and They are based on and Energy value weight, and They are based on and Energy value;

[0135] Step 7.5 Output of the sixth layer Calculated according to formula (26), Two-dimensional data is transformed into three-dimensional data to reconstruct background information.

[0136]

[0137]

[0138]

[0139]

[0140]

[0141]

[0142] in, and They are based on and Energy value weight, and They are based on and Energy value;

[0143] Step 8. Calculate the reconstructed spectral vector for each pixel. Error data compared to the original spectral vector H The i-th pixel k i , where i∈{1,2,…,V} are pixel indices arranged lexicographically;

[0144] Step 9. For the difference data k iPerform local standard deviation filtering, and set the abnormal prominence error data obtained after filtering as follows:

[0145] Step 10. Model the data using a multivariate skewed t-distribution for a_k i Modeling yields formula (27);

[0146]

[0147] in, It is a Gaussian random vector. Let be a generalized inverse Gaussian random variable, and b_v be the skewness vector. Parameters Obtained using the variational Bayesian method, a joint prior of the standard Wishart distribution is defined as follows: Let be the average vector, TT be the precision matrix, and m0, λ, v0, and ψ0 be hyperparameters;

[0148] Step 11. Use formula (27) to analyze the latent variables. Integrate to obtain a_k i The hyperbolic distribution is shown in formula (28);

[0149]

[0150] in, K α (·) represents the modified Bessel function of the second kind;

[0151] Step 12. If γ reaches infinity when α < 0 in the hyperbolic distribution defined in (28), then the multivariate skewed t-distribution is obtained as shown in formula (29);

[0152]

[0153] Step 13. Anomaly detection score based on multivariate skewed t-distribution It can be determined by formula (30);

[0154]

[0155] The final anomaly detection image is obtained by further transformation. Comparison of the embodiments of the present invention with other methods Figure 1 The detection results of the five datasets (a)-(e) were compared, and the results are as follows: Figure 2 As shown, Figure 2 The CCP compared six hyperspectral anomaly detection algorithms: (a) GRX; (b) CRD; (c) TTAD; (d) GAED; (e) MVSkt; and (g) an embodiment of the present invention.

[0156] from Figure 2It can be seen that the CRD method and GAED detected relatively few outliers; the visually apparent outliers of GRX and TTAD were less obvious compared to MVSkt and MPDA; TTAD and MVSkt detected outliers while the background was also relatively clear, failing to separate the target from the background; MVSkt's background suppression effect was not ideal. From a qualitative analysis perspective, the embodiments of the present invention achieved good detection results on various datasets.

Claims

1. A hyperspectral anomaly detection method based on a multivariate probability distribution autoencoder, characterized in that... Follow these steps: Step 1. Input hyperspectral image Where M×N is the size of the band image and B is the number of bands in the band group; Step 2. Transform the three-dimensional hyperspectral data H into two-dimensional hyperspectral data. Where L is the total number of pixels in a single-band image, calculated according to formula (1); L=M×N (1) Step 3. Using a mesh-based generation method, for The column frequency matrix F is obtained by partitioning the columns. c and the column center position matrix ICp c ; Step 3.1 Calculate column according to formula (2), where column represents the number of columns in the grid distribution; column=p×M×N (2) Where p is the empirical probability value; Step 3.2 will The unordered data points are arranged in an ordered manner, and the ordered set of points is divided into columns according to a grid structure of n intervals, b∈{1,2,…,B}. The frequency and center position of each interval are statistically analyzed using a probability density histogram, and this is repeated B times to obtain the column frequency matrix F after column division. c and the interval column center position matrix ICP c ; Step 4. Using a mesh-based partitioning method, for The row frequency matrix F is obtained by row partitioning. r And the row center position matrix ICP r ; Step 4.1 Calculate row according to formula (3), where row represents the number of rows in the grid distribution; row = num(CC ≥ q) (3) Where CC is H b and H b+1 The correlation coefficient between the two bands, b∈{1,2,…,B-1}, For H b The average pixel value of the band. For H b+1 The pixel mean of the band, where q is an empirical probability value; Step 4.2 will The unordered data points are arranged in an ordered manner, and the ordered point set is divided into rows of a grid structure according to row intervals, l∈{1,2,…,L}; By using probability density histograms to statistically analyze the frequency and center position of each interval in the distribution, the row frequency matrix F after row partitioning is obtained. r And the row center position matrix ICP r ; Step 5. Obtain the column frequency set F by dividing the grid into columns. c _Set; Step 5.1 For hyperspectral data from different locations, H represents the spectral dimension information. For testing pixels; Step 5.2 Based on tracking y b In gridded ICP c Find the corresponding center position matrix y_ICP; Step 5.3 Calculate the column index position c_index with the smallest numerical error according to formula (6); [~,c_index]=min|y_ICP(:)-y b | (6) Step 5.4 Through y in each band b The grid position c_index is then given as the corresponding F. c column frequency value y b _F c ; Step 5.5 Under the statistical analysis of B cycles of band-by-band detection, construct the column frequency set F according to formula (7). c _Set; Step 6. Calculate Y by dividing the grid into rows and columns. l The abnormal score (anomaly_score) is used to obtain the guide image. Step 6.1 Traverse the grid row structure from 1 to row to determine the row index. In n iterations, n∈{1, 2, ..., row}, based on the position of n, find the row index in F. r and ICP r Find the corresponding frequency n_F r and the corresponding center position n_ICP r ; Step 6.2 Calculate the row index matrix row_index of the elements in the original matrix after numerical error ascending order according to formula (8), sort(·) is the function to sort the elements in ascending order in a given interval; [~,row_index]=sort(|Y l -n_ICP r |) (8) Step 6.3 Based on row_index and n_F r Determine the optimal separable band index position, band_index; Step 6.4 Calculate the minimum column frequency min_F corresponding to the separable band according to formula (9). c and the corresponding index position min_p; [min_F c ,min_p]=min(F c _Set(band_index)) (9) Step 6.5 Find the minimum separation band position min_band using min_p, and obtain the corresponding F band. c The largest frequency value in the middle, max_F c ; Step 6.6 Calculate the abnormal ratio value (score) of the pixel according to formula (10); score=max_F c / min_F c (10) Step 6.7 Iterate through each row, calculate the score, and sum the results to obtain the Y values ​​at different positions. l The abnormal score anomaly_score is obtained after traversal, and the guiding image G is obtained after the traversal is completed; Step 7. Reconstruct the hyperspectral data H based on the energy weighted skip connection-based multilayer autoencoder network to obtain the reconstructed background information. Step 7.1 After transforming the hyperspectral data H T is the total number of pixels in HSI, calculated according to formula (11); T = L × B (11) Step 7.2 The t-th pixel h t , t∈{1,2,…,T}, the output of each layer after the fully connected layer and activation function is shown in the following equation; in, It is the output data of each layer, W u and a u These correspond to the weights and biases of each layer in the autoencoder, where u∈{1,2,…,7} represents the layer number. Step 7.3 Embed the guiding image G obtained in step 6 into the hidden layer in the middle of the network for reverse guidance. The embedding process is shown in formula (14). Where β is the penalty coefficient. To guide the image G after inverse subtraction transformation The size of the pixel located at position (ii, jj). For the hidden layer after reverse guidance, the horizontal coordinate ii ranges from 1 to the length S of the network layer, and the vertical coordinate jj ranges from 1 to the width D of the network layer. Step 7.4 The output of the fifth layer of the multilayer autoencoder network based on energy weight jump connection is shown in Equation (20); in, and They are based on and Energy value weight, and They are based on and Energy value; Step 7.5 Output of the sixth layer As shown in formula (26), Two-dimensional data is transformed into three-dimensional data to reconstruct background information. in, and They are based on and Energy value weight, and They are based on and Energy value; Step 8. Calculate the reconstructed spectral vector for each pixel. Error data compared to the original spectral vector H The i-th pixel k i , where i∈{1,2,…,V} are pixel indices arranged lexicographically; Step 9. For the difference data k i Perform local standard deviation filtering, and set the abnormal prominence error data obtained after filtering as follows: Step 10. Model the data using a multivariate skewed t-distribution for a_k i Modeling yields formula (27); in, It is a Gaussian random vector. Let b_v be a generalized inverse Gaussian random variable, and b_v be a skewness vector with parameters. Obtained using the variational Bayesian method, a joint prior of the standard Wishart distribution is defined as follows: μ is the average vector, TT is the precision matrix, and m0, λ, v0 and ψ0 are hyperparameters; Step 11. Integrate the latent variable z using formula (27) to obtain a_k. i The hyperbolic distribution is shown in formula (28); in, K α (·) represents the modified Bessel function of the second kind; Step 12. If γ reaches infinity when α < 0 in the hyperbolic distribution defined in (28), then the multivariate skewed t-distribution is obtained as shown in formula (29); Step 13. Anomaly detection score based on multivariate skewed t-distribution It can be determined by formula (30); The final anomaly detection image is obtained by further transformation.

Images