Hyperspectral image anomaly detection method using dual denoisers to replace artificial priors

Abstract

This paper proposes a method for detecting anomalies in hyperspectral images using a dual denoiser to replace artificial priors. The dual denoisers are used to perform low-rank smoothing on the dictionary coefficient tensor and denoise the anomaly tensor, respectively, to replace the artificial priors. A noise assessment module is constructed to evaluate the noise variance of each channel of the three-dimensional tensor, allowing the denoiser to adaptively set the denoising variance parameters. This method primarily addresses the complexities of the artificial prior parameter calculation and optimization process, as well as the significant discrepancy between the denoising variance parameters manually set by the denoiser and the actual noise variance of the three-dimensional tensor input to the denoiser. This method improves the robustness of detecting anomalies in different hyperspectral images and the efficiency of computational optimization during the detection process. The dual denoiser removes noise detected along with the anomaly, highlighting the anomalous target, resulting in a more effective denoising effect and improved anomaly detection accuracy.

Description

Technical Field

[0001] This invention belongs to the field of image processing technology, and more specifically, to a method for detecting anomalies in hyperspectral images using a dual denoiser to replace artificial priors. This invention can be applied to anomaly detection in hyperspectral images, such as those used in deep space exploration and Earth observation. Background Art

[0002] Hyperspectral images have been increasingly used in various fields in recent years because their high spectral resolution is well-suited for measurements in many remote sensing applications. Anomaly detection, a fundamental task in these applications, aims to locate spectral instances that deviate from the background. Anomaly pixels are defined as samples that differ significantly from the surrounding background samples, either spatially or spectrally. Anomaly detection is achieved by separating background and anomaly pixels. This principle is based on two discriminative characteristics of anomaly pixels in hyperspectral images: anomaly pixels typically occur with a lower probability than background pixels, and their spectral signatures typically deviate from those of their surrounding background pixels. Currently, many anomaly detection methods for hyperspectral images are primarily representation-based approaches. These methods model the hyperspectral image as a representation of background and anomaly pixels. Specifically, they use a subset of hyperspectral image spectral vectors as dictionary atoms to represent the remaining hyperspectral background vectors, and then isolate the anomaly pixels. These methods often require handcrafted regularizers on the dictionary coefficients of the representation, imposing artificial priors on the dictionary coefficients. However, crafting effective and meaningful regularizers is not easy, and complex regularizers can complicate the optimization problem.

[0003] In its patent application, "A Hyperspectral Image Anomaly Detection Algorithm Based on Low-Rank Representation and Learned Dictionary" (patent application number: CN201510780676.1, publication number: CN105427300A), Fudan University proposed a method for anomaly detection in hyperspectral images. The method involves the following steps: First, a learned dictionary is obtained through random selection and gradient descent. Because background probability is high and anomalies are low, this learned dictionary represents only the background. Then, a low-rank representation algorithm is used to decompose the hyperspectral image into a low-rank matrix representing the background and a sparse matrix representing the anomalies. Finally, a basic anomaly detection algorithm is applied to the sparse matrix to obtain detection results. This method learns a dictionary representing only the background, effectively separating anomaly information from the image data and reducing the computational overhead of the dictionary coefficients during the optimization process. However, this method still has some shortcomings: it only obtains a dictionary representing the background spectrum through random selection and gradient descent method, and uses this dictionary to obtain the detection results of the basic anomaly detection algorithm. There are still defects in that the parameters set for artificial low-rank prior and sparse prior are only applicable to the detection of a single image and the prior parameter calculation and optimization process is too complicated.

[0004] Xiyou Fu et al. published a method for anomaly detection in hyperspectral images in their paper "Hyperspectral Anomaly Detection via DeepPlug-and-Play Denoising CNN Regularization" (IEEE Transactions on Geoscience and Remote Sensing, 2021, PP(99):1-16). The steps of this method are as follows: first, the hyperspectral image is modeled as background pixels and anomaly pixels, and then the background pixel components are obtained by using a denoiser based on the FFDNet convolutional neural network framework as a deep prior for the background dictionary coefficients; then, the anomaly pixels are separated based on an artificially applied sparse prior; the above process is repeated until the alternating optimization process converges, and the anomaly pixels obtained at the end of the convergence are the results of anomaly detection. This method avoids imposing an artificial prior on the dictionary coefficients representing the background pixels, and plug-and-play uses a denoiser based on the FFDNet convolutional neural network framework as a deep prior to replace the artificial low-rank prior of the dictionary representation coefficients. The shortcomings of this method are that it only uses a denoising convolutional neural network as a denoiser to replace the artificial low-rank background prior for background pixel components. The constraint method for obtaining anomalous pixels still uses an artificially imposed sparse prior, which involves tedious optimization parameter adjustment and low anomalous pixel detection accuracy. During the detection process, the iterative optimization process of the dictionary coefficient denoiser manually sets a fixed denoising variance parameter, which has a significant error from the actual noise variance of the dictionary coefficient tensor input to the denoiser. Summary of the Invention

[0005] The purpose of the present invention is to address the defects of the above-mentioned existing technologies and propose a hyperspectral image anomaly detection method that uses a dual denoiser to replace artificial priors, so as to solve the technical problems in the existing technologies that the parameter calculation and optimization process for artificial low-rank priors and artificial sparse priors is too complicated and there is a large error between the manually set denoising variance parameters and the noise variance of the actual noise tensor.

[0006] The idea of ​​achieving the purpose of the present invention is to take into account the superior reconstruction generation ability of the denoiser for images and the characteristics of the denoiser end-to-end image processing, as well as the defect that there is a large error between the denoising variance parameter of the manually set denoiser and the noise variance of the tensor actually input to the denoiser. Therefore, a dual denoiser with FFDNet convolutional neural network and Gaussian filter as the basic framework is adopted to replace the low-rank prior applied to the dictionary coefficient and the sparse prior applied to the abnormal pixels respectively. First, the discriminant feature matrix of the hyperspectral image after dimensionality reduction is obtained, and the discriminant feature matrix is ​​used to generate the dictionary atomic matrix. The intermediate estimate tensor of the dictionary coefficient and the abnormal intermediate estimate tensor are obtained and then input into the denoiser. The denoiser adaptively adjusts the denoising variance parameter according to its internal noise evaluation module, outputs the intermediate estimate tensor of the dictionary coefficient and the abnormal intermediate estimate tensor after denoising, repeatedly updates the values ​​of each tensor, and outputs the abnormal image after the termination condition is met. The dual denoiser framework constructed by the present invention can directly perform end-to-end processing on different hyperspectral images, avoiding the frequent manual formulation and modification of the structure and parameters of the regularization term when processing hyperspectral images.

[0007] To achieve the above object, the technical solution adopted by the present invention includes the following steps:

[0008] Step 1. Obtain the discriminant feature matrix of dimensionality reduction:

[0009] The values ​​from the first row to the last row of the two-dimensional image of each channel in a hyperspectral image to be detected are arranged row by row into the values ​​of each column in the spectral matrix. The spectral matrix is ​​normalized and input into an encoder composed of a fully connected layer. The discriminant feature matrix of the hyperspectral image after dimensionality reduction is output, and the values ​​of each row in the matrix are arranged into a discriminant feature vector.

[0010] Step 2. Obtain the dictionary atom matrix representing the background from the discriminant feature matrix:

[0011] Step 2.1, calculate the probability that each discriminant eigenvector in the discriminant feature matrix belongs to a Gaussian component category, classify this discriminant eigenvector into the Gaussian component category corresponding to the maximum probability value among all probabilities, use the discriminant eigenvector corresponding to the maximum probability value among all probabilities that all discriminant eigenvectors belonging to each category of Gaussian components belong to the category of Gaussian components as the central discriminant eigenvector of all discriminant eigenvectors belonging to the category of Gaussian components, and use the discriminant eigenvector corresponding to the minimum probability value among all probabilities that all discriminant eigenvectors belonging to each category of Gaussian components belong to the category of Gaussian components as the boundary discriminant eigenvector of all discriminant eigenvectors belonging to the category of Gaussian components;

[0012] Step 2.2, in the order from the first category of Gaussian component category to the last category of Gaussian component category, the center discriminant feature vector of all discriminant feature vectors belonging to any category of Gaussian component and the boundary discriminant feature vectors of all discriminant feature vectors belonging to this category of Gaussian component are combined into a dictionary atomic matrix by row;

[0013] Step 3. Build the noise evaluation module:

[0014] Step 3.1: Crop a 2D noise image in an unselected channel from a 3D noise image of shape [m1, n1, c1] into 2D image blocks of length d and width d, with the number of blocks being (m-d+1)(n-d+1). Arrange the pixel values ​​from the first row to the last row of each 2D image block into a block of dimension d. 2 ×1 vector, all vector values ​​are combined into a numerical matrix by row; where m1 represents the number of row pixels of the 3D noise image, n1 represents the number of column pixels of the 3D noise image, c1 represents the number of channels of the 3D noise image, and d represents the cropping size;

[0015] Step 3.2, calculate the mean vector of all vectors;

[0016] Step 3.3, calculate the covariance matrix of the numerical matrix;

[0017] Step 3.4, calculate the eigenvalues ​​of the covariance matrix and sort the eigenvalues ​​from small to large to obtain an eigenvalue list;

[0018] Step 3.5, calculate the mean of all eigenvalues ​​in the eigenvalue list;

[0019] Step 3.6: Determine whether the mean of all eigenvalues ​​in the eigenvalue list is equal to the median of the eigenvalue list. If so, the noise variance of the selected channel is equal to the square root of the mean and then execute step 3.7. Otherwise, delete the last eigenvalue in the eigenvalue list and then execute step 3.5.

[0020] Step 3.7, determine whether all channels in the 3D noise image have been selected. If so, execute step 4 after completing the construction of the noise assessment module. Otherwise, execute step 3.1.

[0021] Step 4. Design a denoiser based on the FFDNet convolutional neural network framework:

[0022] Step 4.1: Input a 3D noise image of shape [m2, n2, c2] into the noise estimation module and output the noise variance of the 2D noise image for each channel in the 3D noise image; where m2 represents the number of row pixels in the 3D noise image, n2 represents the number of column pixels in the 3D noise image, and c2 represents the number of channels in the 3D noise image.

[0023] In step 4.2, a 2D noise image and its noise variance from an unselected channel of the 3D noise image are input to the trained FFDNet convolutional neural network, and a denoised 2D image is output. The denoising variance parameter of the network is adaptively set to the noise variance of the 2D image in the selected channel of the 3D noise image.

[0024] Step 4.3: Determine whether all channels in the 3D noisy image have been selected. If so, arrange the 2D images after all channels have been denoised into a denoised 3D image in the order of the channels in the 3D noisy image. After the denoiser design is complete, proceed to step 5. Otherwise, proceed to step 4.2.

[0025] Step 5. Design a denoiser based on the Gaussian filter framework:

[0026] Step 5.1: Input a 3D noise image of shape [m3, n3, c3] into the noise estimation module and output the noise variance of the 2D noise image for each channel in the 3D noise image; where m3 represents the number of row pixels, n3 represents the number of column pixels, and c3 represents the number of channels in the 3D noise image.

[0027] Step 5.2: Input a 2D noise image and its noise variance from an unselected channel selected from the 3D noise image into a Gaussian filter with a sliding window size of 3×3, and output a denoised 2D image; wherein the variance parameter of the filter coefficient of the sliding window convolution kernel of the Gaussian filter is adaptively set to the noise variance of the 2D noise image in the selected channel of the 3D noise image;

[0028] Step 5.3: Determine whether all channels in the 3D noisy image have been selected. If so, arrange the 2D images after all channels have been denoised into a denoised 3D image in the order of the channels in the 3D noisy image. After the denoiser design is complete, proceed to step 6. Otherwise, proceed to step 5.2.

[0029] Step 6. Detect anomalies using dual denoisers:

[0030] Step 6.1: Construct a dictionary coefficient matrix with all zero initial values. The number of rows of this matrix is ​​the same as the number of rows of the dictionary atom matrix in step 2.2, and the number of columns is the same as the number of rows of the discriminant feature matrix in step 1. Construct an anomaly matrix with all zero initial values. The number of rows of this matrix is ​​the same as the number of columns of the discriminant feature matrix in step 1, and the number of columns is the same as the number of rows of the discriminant feature matrix in step 1.

[0031] Step 6.2, calculate the gradient descent intermediate estimate matrix of the dictionary coefficient matrix according to the following formula:

[0032]

[0033] Among them, V S represents the intermediate estimation matrix of the gradient descent of the dictionary coefficient matrix, S represents the dictionary coefficient matrix, λ S Represents a parameter whose value is a real number randomly selected in the range [0.0001, 0.1]. It represents the partial derivative operation of (·) with respect to S, represents the Frobenius norm, X represents the transposed matrix of the discriminative feature matrix, D represents the transposed matrix of the dictionary atom matrix, and E represents the anomaly matrix;

[0034] Step 6.3, arrange the gradient descent intermediate estimate matrix of the dictionary coefficient matrix into a three-dimensional tensor as the dictionary coefficient intermediate estimate tensor, where the matrix of each channel in the three-dimensional tensor is composed of the arrangement of the values ​​of each column in the gradient descent intermediate estimate matrix;

[0035] In step 6.4, the intermediate estimated tensor of the dictionary coefficients is input into the denoiser based on the FFDNet convolutional neural network framework, and the three-dimensional tensor of the dictionary coefficients is output;

[0036] Step 6.5, arrange the values ​​from the first row to the last row in the two-dimensional matrix of each channel in the three-dimensional tensor of the dictionary coefficient into the values ​​of each column in the updated dictionary coefficient matrix;

[0037] Step 6.6, calculate the gradient descent intermediate estimation matrix of the anomaly matrix according to the following formula:

[0038]

[0039] Among them, V E represents the gradient descent intermediate estimation moment of the anomaly matrix, λ E Represents a parameter whose value is a real number randomly selected in the range [0.0001, 0.1]. represents the partial derivative operation of (·) with respect to E, S new Represents the updated dictionary coefficient matrix;

[0040] Step 6.7: Arrange the gradient descent intermediate estimate matrix of the anomaly matrix into a three-dimensional tensor as the anomaly intermediate estimate tensor, where the matrix of each channel in the three-dimensional tensor is composed of the values ​​of each column in the gradient descent intermediate estimate matrix;

[0041] In step 6.8, the abnormal intermediate estimation tensor is input into a denoiser based on a Gaussian filter framework, and an abnormal three-dimensional tensor is output;

[0042] Step 6.9, arrange the values ​​from the first row to the last row in the two-dimensional matrix of each channel in the anomaly three-dimensional tensor into the values ​​of each column in the updated anomaly matrix;

[0043] Step 6.10, determine whether the updated dictionary coefficient matrix and the updated anomaly matrix meet the termination condition. If so, execute step 7; otherwise, execute step 6.2;

[0044] Step 7, save the abnormal image:

[0045] Calculate the bi-norm value of each column in the updated anomaly matrix, arrange all bi-norm values ​​into a bi-norm value matrix by row, plot the bi-norm value matrix and save the anomaly image.

[0046] Compared with the existing technology, the present invention has the following advantages:

[0047] First, the present invention constructs a dual denoiser framework network and adopts a dual denoiser with FFDNet convolutional neural network and Gaussian filter as the basic framework to replace the low-rank prior applied to the dictionary coefficient tensor and the sparse prior applied to the anomaly tensor, respectively. This overcomes the defect of the overly complex calculation and optimization process of manual prior parameters in the existing technology, so that the present invention improves the robustness of detecting anomalies in different hyperspectral images while also improving the efficiency of calculation optimization during the detection process.

[0048] Second, the noise evaluator module in the dual denoiser constructed by the present invention can perform noise level evaluation on each channel before the three-dimensional tensor is input into the denoiser. The denoiser adaptively adjusts the denoising variance parameters, overcoming the defect in the prior art that there is a large error between the denoising variance parameters manually set in the iterative optimization process of the denoiser based on the FFDNet convolutional neural network framework and the noise variance of the tensor actually input into the denoiser. This makes the denoising effect of the dual denoiser designed by the present invention more significant. The dual denoiser removes the noise detected together with the anomaly, highlights the abnormal target, and improves the detection accuracy of the degree of anomaly. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is an implementation flow chart of the present invention;

[0050] Figure 2 It is a comparison diagram of simulation experiment 1 in the present invention;

[0051] Figure 3 It is a comparison diagram of simulation experiment 2 in the present invention. DETAILED DESCRIPTION

[0052] The present invention is further described in detail below with reference to the accompanying drawings and examples.

[0053] Reference Figure 1The implementation steps of the present invention are further described in detail in the following embodiments.

[0054] Step 1. Obtain the discriminant feature matrix of reduced dimension.

[0055] A hyperspectral image The values ​​from the first row to the last row of the two-dimensional image of each channel are arranged row by row into a spectral matrix The value of each column in the spectral matrix is ​​normalized and input into an encoder composed of a fully connected layer to output the discriminant feature matrix of the hyperspectral image after dimensionality reduction Arrange the values ​​of each row in the matrix into a discriminant feature vector; where M, N, and B represent the number of row pixels, column pixels, and channels of Z, respectively. represents a set of real numbers, i=1,2,...,L, L=M×N represents the number of pixels, z i represents the i-th pixel, Qi Represents a spectral vector composed of the values ​​of the ith row of the spectral matrix, F i Represents a discriminant feature vector formed by arranging the values ​​of the i-th row of the discriminant feature matrix, and P represents the discriminant feature vector F in the discriminant feature matrix F. i The fully connected layer of the encoder is composed of two tf.layers.dense functions. The input channel parameter of the first tf.layers.dense function is set to the number of channels of the hyperspectral image to be detected, the output channel parameter is 400, and the activation layer is implemented using the ReLU function. The input channel parameter of the second tf.layers.dense function is set to 400, the output channel parameter is 9, and no activation layer is set.

[0056] The fully connected layer in the encoder is composed of two tf.layers.dense functions. The input channel parameter of the first tf.layers.dense function is set to the number of channels of the hyperspectral image to be detected, the output channel parameter is 400, and the activation layer is implemented using the ReLU function. The input channel parameter of the second tf.layers.dense function is set to 400, the output channel parameter is 9, and no activation layer is set.

[0057] Step 2. Obtain the dictionary atom matrix representing the background from the discriminative feature matrix.

[0058] Step 2.1, the discriminant feature matrix Input into a feature mapping network composed of fully connected layers and output a feature matrix The values ​​of each row in this feature matrix are arranged into a feature vector; wherein, the fully connected layer of the feature mapping network is composed of a tf.layers.dense function, the input channel parameter of the tf.layers.dense function is set to the number of columns of the discriminative feature matrix, the output channel parameter is 60, and the activation layer is implemented using the ReLU function, U i Represents the feature matrix The values ​​of the i-th row are arranged into an eigenvector, and the characteristic matrix The i-th eigenvector U in i and the discriminant feature matrix The i-th discriminant feature vector F i Correspondingly, G represents the feature matrix The i-th eigenvector U in i The number of dimensions.

[0059] Step 2.2, use the softmax function to calculate the feature matrix The eigenvector U in i K initial probabilities belonging to K types of Gaussian components, the K initial probabilities of L eigenvectors form an initial probability matrix Among them, W ik Indicates that the softmax function is used to calculate the i-th eigenvector U in the feature matrix i The initial probability of belonging to the k-th Gaussian component.

[0060] Step 2.3, use Formula, respectively calculate the weighted probability of all discriminant feature vectors in the discriminant feature matrix belonging to the k-th Gaussian component weighted by the number of pixels L, the mean vector weighted by the probability of all discriminant feature vectors and their belonging to the k-th Gaussian component, and the variance matrix of the discriminant feature vector and its corresponding k-th Gaussian component weighted by probability; where, It represents the weighted probability obtained by weighting the probability that all discriminant feature vectors in the discriminant feature matrix belong to the k-th Gaussian component by the number of pixels. Represents the mean vector obtained by weighting all the discriminative feature vectors in the discriminative feature matrix with the probability of belonging to the k-th Gaussian component, It represents the variance matrix obtained by weighting the discriminant feature vector in the discriminant feature matrix with the mean vector of the k-th Gaussian component corresponding to it by probability, W ik Indicates the use of the softmax function to calculate the initial probability that the i-th eigenvector in the feature matrix belongs to the k-th Gaussian component, L represents the number of pixels, F i represents the i-th discriminant eigenvector in the discriminant feature matrix, ∑ represents the summation operation, and T represents the transposition of the matrix.

[0061] Step 2.4, use Formula, calculate the probability density value of each discriminant feature vector in the discriminant feature matrix; where, represents p(F i )The probability density of the i-th discriminant feature vector in the discriminant feature matrix, It represents the weighted probability obtained by weighting the probability that all discriminative feature vectors belong to the k-th Gaussian component by the number of pixels. It represents the variance matrix obtained by weighting the discriminant feature vector in the discriminant feature matrix with the mean vector of its corresponding k-th Gaussian component by probability. express The inverse matrix, F i represents the i-th discriminant eigenvector in the discriminant feature matrix, Represents the mean vector obtained by weighting all the discriminative feature vectors in the discriminative feature matrix with the probability of belonging to the k-th Gaussian component, represents the square root, |·| represents the absolute value operation, log represents the natural logarithm, ∑ represents the summation operation, T represents the transpose of the matrix, and K represents the total number of categories of the Gaussian component.

[0062] Step 2.5, the discriminant feature matrix Input into a decoder composed of fully connected layers and output a reconstructed spectrum vector matrix The values ​​of each row in the reconstructed spectral vector matrix are arranged into a reconstructed spectral vector; wherein, the fully connected layer of the decoder is composed of two tf.layers.dense functions. The input channel parameter of the first tf.layers.dense function is set to the number of columns of the discriminative feature matrix, the output channel parameter is 400, and the activation layer is implemented using a function. The input channel parameter of the second tf.layers.dense function is set to 400, the output channel parameter is the number of channels of the hyperspectral image in step 1, and the activation layer is not set. i It represents an i-vector formed by arranging the values ​​of the i-th row of the reconstructed spectrum matrix, and the i-th reconstructed spectrum vector in the reconstructed spectrum matrix corresponds to the i-th discriminant feature vector in the discriminant feature matrix.

[0063] Step 2.6, using the joint objective function of the encoder network in step 1, the feature mapping network in step 2.1, and the decoder network in step 2.5 The objective function is minimized by training the network. Each time the network is back-propagated, the probability of the L discriminant feature vectors in the discriminant feature matrix belonging to the K-type Gaussian components is updated. The training is iterated for 1000 cycles, and the final probability of the L discriminant feature vectors in the discriminant feature matrix belonging to the K-type Gaussian components is output. All the final probabilities are combined into a probability matrix Among them, F i Represents a discriminant feature vector composed of the values ​​of the i-th row of the discriminant feature matrix, H i Represents the i-th reconstructed spectrum vector in the reconstructed spectrum vector matrix, p(F i ) represents the probability density value of the i-th discriminant feature vector in the discriminant feature matrix, γ ikn represents the nth diagonal element value in the variance matrix obtained by weighting the i-th discriminant feature vector in the discriminant feature matrix with the mean vector of the k-th Gaussian component corresponding to it by probability, min(·) represents the value of minimization (·), represents the Frobenius norm, λ1 and λ2 represent hyperparameters, λ1 = 0.1, λ2 = 0.0001, L represents the number of pixels in the hyperspectral image in step 1.1, K represents the total number of categories of Gaussian components, ∑ represents the summation operation, and W * ik It represents the final probability that the i-th eigenvector in the feature matrix belongs to the k-th Gaussian component.

[0064] Step 2.7, for the i-th discriminant feature vector F in the discriminant feature matrix i A probability set consisting of K probabilities belonging to K types of Gaussian components like The maximum probability value is W * ij , then the i-th discriminant feature vector F in the discriminant feature matrix i Classified into the jth Gaussian component category, each discriminant feature vector in the discriminant feature matrix is ​​uniquely determined by a Gaussian component category; where 1≤i≤L, j is a constant and 1≤j≤K; for example: the third discriminant feature vector in the discriminant feature matrix belongs to the probability set composed of 7 probabilities of 7 categories of Gaussian components The maximum probability value is 0.3, and the third discriminant feature vector in the discriminant feature matrix is ​​classified into the fourth Gaussian component category.

[0065] Step 2.8, for all the discriminant feature vectors belonging to the k-th Gaussian component in the discriminant feature matrix, take the final probability that these discriminant feature vectors belong to the k-th Gaussian component, and form these final probabilities into the final probability set The discriminant feature vector corresponding to the maximum probability value in the final probability set is taken as the central discriminant feature vector of all discriminant feature vectors belonging to the k-th Gaussian component, and the final probability set is The discriminant feature vector corresponding to the minimum probability value in is used as the boundary discriminant feature vector of all discriminant feature vectors belonging to the k-th Gaussian component; kiRepresents the i-th probability value in the final probability set of the k-th Gaussian component, c represents the number of probabilities in the final probability set of the k-th Gaussian component, 1≤i≤c; for example: for all 5 discriminant feature vectors belonging to the 4th category Gaussian component in the discriminant feature matrix, take the 5 final probabilities that these 5 discriminant feature vectors belong to the 4th category Gaussian component, and form the final probability set with these 5 final probabilities The fifth discriminant feature vector corresponding to the maximum probability value of 0.95 in the final probability set is used as the central discriminant feature vector of the five discriminant feature vectors belonging to the fourth category of Gaussian components, and the fourth discriminant feature vector corresponding to the minimum probability value of 0.2 in the final probability set is used as the boundary discriminant feature vector of the five discriminant feature vectors belonging to the fourth category of Gaussian components.

[0066] Step 2.9, the center discriminant eigenvector of all discriminant eigenvectors belonging to each class of Gaussian components and the boundary discriminant eigenvectors of all discriminant eigenvectors belonging to this class of Gaussian components are combined into a dictionary atomic matrix in the order of Gaussian component categories. Among them, y jc Represents the central discriminant feature vector of the j-th cluster, y jb represents the boundary discriminant feature vector of the j-th cluster, j is a constant and 1≤j≤K, P represents the i-th discriminant feature vector F in the discriminant feature matrix F i The number of dimensions, the eigenvector y jc 、y jb The number of dimensions is equal to the value of P.

[0067] Step 3. Build the noise assessment module.

[0068] Step 3.1: Crop a 2D noise image in an unselected channel from a 3D noise image of shape [m, n, c] into 2D image blocks of length d and width d, with the number of blocks being s = (m-d+1)(n-d+1). Arrange the pixel values ​​from the first row to the last row of each 2D image block into a block of dimension d. 2 ×1 vector, all vector values ​​are organized into a numerical matrix by row Where m represents the number of row pixels of the 3D noise image, n represents the number of column pixels of the 3D noise image, c represents the number of channels of the 3D noise image, d represents the cropping size, s represents the number of 2D image blocks, s = (m-d+1)(n-d+1), v t Represents the t-th vector among all vectors, 1≤t≤s.

[0069] Step 3.2, calculate the mean vector of all vectors Where s represents the number of two-dimensional image blocks in step 3.1, vt represents the t-th vector among all vectors, 1≤t≤s, and ∑ represents the summation operation.

[0070] Step 3.3, calculate the numerical matrix The covariance matrix of Where s represents the number of two-dimensional image blocks in step 3.1, v t represents the t-th vector among all vectors, μ represents the mean vector of all vectors obtained in step 3.1, ∑ represents the summation operation, and T represents the transposition of the matrix.

[0071] Step 3.4, calculate the covariance matrix , and sort the eigenvalues ​​from small to large to get a list of eigenvalues.

[0072] Step 3.5, calculate the mean of all eigenvalues ​​in the eigenvalue list.

[0073] In step 3.6, determine whether the mean of all eigenvalues ​​in the eigenvalue list is equal to the median of the eigenvalue list. If so, the noise variance of the selected channel is equal to the square root of the mean and then execute step 3.7; otherwise, delete the last eigenvalue in the eigenvalue list and then execute step 3.5.

[0074] In step 3.7, it is determined whether all channels in the three-dimensional noise image have been selected. If so, step 4 is executed after the noise assessment module is constructed. Otherwise, step 3.1 is executed.

[0075] Step 4. Design a denoiser based on the FFDNet convolutional neural network framework.

[0076] Step 4.1: Input a 3D noise image of shape [m2, n2, c2] into the noise estimation module and output the noise variance of the 2D noise image of each channel in the 3D noise image. Among them, m2 represents the number of row pixels of the three-dimensional noise image, n2 represents the number of column pixels of the three-dimensional noise image, c2 represents the number of channels of the three-dimensional noise image, σ i Represents the noise variance of the i-th channel of the 3D noise image; for example, a 3D noise image of shape [100, 100, 3] is input into the noise assessment module, and the noise variance of the 2D noise image of each channel in the output 3D noise image is 0.1, 0.2, and 0.3 respectively.

[0077] In step 4.2, a two-dimensional noise image in an unselected channel selected from the three-dimensional noise image and its noise variance are input into the trained FFDNet convolutional neural network, and a denoised two-dimensional image is output; wherein the denoising variance parameter of the network is adaptively set to the noise variance of the two-dimensional noise image in the selected channel in the three-dimensional noise image; for example: a two-dimensional noise image in the second channel of a three-dimensional noise image with a shape of [100, 100, 3] and a noise variance of 0.2 are input into the trained FFDNet convolutional neural network, and a denoised two-dimensional image is output. Then, only the two-dimensional noise image in the first channel or the two-dimensional noise image in the third channel of the three-dimensional noise image can be selected for the second time.

[0078] Step 4.3, determine whether all channels in the three-dimensional noisy image have been selected. If so, arrange the two-dimensional images after denoising of all channels into a denoised three-dimensional image in the order of the channels of the three-dimensional noisy image. After completing the design of the denoiser, execute step 5. Otherwise, execute step 4.2. For example: determine whether all channels in a three-dimensional noisy image with a shape of [100,100,3] have been selected. If so, arrange the three denoised two-dimensional images into a denoised three-dimensional image in the order of the first channel denoised two-dimensional image, the second channel denoised two-dimensional image, and the third channel denoised two-dimensional image. Otherwise, execute step 4.2.

[0079] Step 5. Design a denoiser based on the Gaussian filter framework.

[0080] Step 5.1: Input a 3D noise image of shape [m3, n3, c3] into the noise estimation module and output the noise variance of the 2D noise image of each channel in the 3D noise image. Among them, m3 represents the number of row pixels of the 3D noise image, n3 represents the number of column pixels of the 3D noise image, c3 represents the number of channels of the 3D noise image, σ° i Represents the noise variance of the i-th channel of the 3D noise image.

[0081] In step 5.2, a 2D noise image and its noise variance from an unselected channel selected from the 3D noise image are input to a Gaussian filter with a sliding window size of 3×3, and a denoised 2D image is output. The variance parameter of the filter coefficients of the sliding window convolution kernel of the Gaussian filter is adaptively set to the noise variance of the 2D noise image from the selected channel in the 3D noise image. The nine filter coefficients of the Gaussian filter with a sliding window size of 3×3 are obtained according to the following formula:

[0082]

[0083] Among them, H i,jrepresents the filter coefficient of the i-th row and j-th column in the 3×3 Gaussian filter sliding window, (x, y) is the coordinate of any point in the 3×3 two-dimensional noise image block in the sliding window, (ux, uy) is the coordinate of the center point of the 3×3 two-dimensional noise image block in the sliding window, σ g ° is the noise variance of the selected two-dimensional noise image, 1≤g≤c3.

[0084] Step 5.3, determine whether all channels in the three-dimensional noisy image have been selected. If so, arrange the two-dimensional images after denoising all channels into a denoised three-dimensional image according to the channel order of the three-dimensional noisy image. After completing the design of the denoiser, execute step 6; otherwise, execute step 5.2.

[0085] Step 6. Detect anomalies using dual denoisers.

[0086] Step 6.1, construct a dictionary coefficient matrix with an initial value of all zeros. The number of rows of this matrix is ​​the same as the number of rows of the dictionary atomic matrix in step 2.2, and the number of columns is the same as the number of rows of the discriminant feature matrix in step 1. Construct an anomaly matrix with an initial value of all zeros. The number of rows of this matrix is ​​the same as the number of columns of the discriminant feature matrix in step 1, and the number of columns is the same as the number of rows of the discriminant feature matrix in step 1.

[0087] In step 6.2, calculate the intermediate estimation matrix of the dictionary coefficient matrix by gradient descent according to the following formula.

[0088]

[0089] Among them, V S represents the intermediate estimation matrix of the gradient descent of the dictionary coefficient matrix, S represents the dictionary coefficient matrix, λ S Represents a parameter whose value is a real number randomly selected in the range [0.0001, 0.1]. It represents the partial derivative operation of (·) with respect to S, represents the Frobenius norm, X represents the transposed matrix of the discriminative feature matrix, D represents the transposed matrix of the dictionary atom matrix, and E represents the anomaly matrix.

[0090] In step 6.3, the gradient descent intermediate estimation matrix of the dictionary coefficient matrix with a shape of [2K, L] is arranged into a three-dimensional tensor with a shape of [M, N, 2K] as the dictionary coefficient intermediate estimation tensor, and the matrix of each channel in the three-dimensional tensor is composed of the arrangement of the values ​​of each column in the gradient descent intermediate estimation matrix; wherein K represents the number of Gaussian component categories in step 2.2, L represents the number of pixels of the hyperspectral image in step 1, M represents the number of row pixels of the hyperspectral image in step 1, and N represents the number of row pixels of the hyperspectral image in step 1.

[0091] In step 6.4, the intermediate estimate tensor of the dictionary coefficient is input into the denoiser based on the FFDNet convolutional neural network framework, and a three-dimensional tensor of the dictionary coefficient with a shape of [M, N, 2K] is output.

[0092] In step 6.5, the three-dimensional tensor of dictionary coefficients with a shape of [M, N, 2K] is arranged into a two-dimensional matrix with a shape of [2K, L] as the updated dictionary coefficient matrix; wherein each column in the updated dictionary coefficient matrix is ​​composed of the values ​​from the first row to the last row in the two-dimensional matrix in each channel of the three-dimensional tensor of dictionary coefficients, arranged in rows.

[0093] Step 6.6, calculate the gradient descent intermediate estimation matrix of the anomaly matrix according to the following formula:

[0094]

[0095] Among them, V E represents the gradient descent intermediate estimation matrix of the abnormality matrix, E represents the abnormality matrix, λ E Represents a parameter whose value is a real number randomly selected in the range [0.0001, 0.1]. represents the partial derivative operation of (·) with respect to E, X represents the transposed matrix of the discriminant feature matrix, D represents the transposed matrix of the dictionary atomic matrix, S new Represents the updated dictionary coefficient matrix.

[0096] In step 6.7, the gradient descent intermediate estimation matrix of the anomaly matrix of shape [P, L] is arranged into a three-dimensional tensor of shape [M, N, P] as the anomaly intermediate estimation tensor, where the matrix of each channel in the three-dimensional tensor is composed of the values ​​of each column in the gradient descent intermediate estimation matrix; where P represents the number of dimensions of the discriminative feature vector in step 1.

[0097] In step 6.8, the abnormal intermediate estimation tensor is input into the denoiser based on the Gaussian filter framework, and an abnormal three-dimensional tensor with a shape of [M, N, P] is output.

[0098] In step 6.9, the anomaly three-dimensional tensor of shape [M, N, P] is arranged into a two-dimensional matrix of shape [P, L] as the updated anomaly matrix; wherein each column in the updated anomaly matrix is ​​composed of the values ​​from the first row to the last row of the two-dimensional matrix in each channel of the anomaly three-dimensional tensor, arranged in rows.

[0099] Step 6.10: Determine whether the updated dictionary coefficient matrix and the updated anomaly matrix meet the termination condition. If so, execute step 7; otherwise, execute step 6.2. The termination condition is as follows:

[0100]

[0101] Among them, S t Represents the dictionary coefficient matrix after the tth iteration update, R t represents the abnormal matrix updated in the tth iteration, S t+1 Represents the dictionary coefficient matrix after the tth iteration update, R t+1 represents the updated anomaly matrix for the tth iteration.

[0102] The termination conditions are as follows:

[0103]

[0104] Among them, S t Represents the dictionary coefficient matrix after the tth iteration update, R t represents the abnormal matrix updated in the tth iteration, S t+1 Represents the dictionary coefficient matrix after the tth iteration update, R t+1 represents the updated abnormality matrix at the tth iteration.

[0105] Step 7: Save the abnormal image.

[0106] Calculate the bi-norm value of each column in the updated anomaly matrix, arrange the L bi-norm values ​​by row into a bi-norm value matrix with a shape of [M, N], use the plt.imshow function to plot this bi-norm value matrix into an anomaly image with a shape of [M, N], and save the anomaly image with plt.savefig.

[0107] The effects of the present invention will be further described below in conjunction with simulation experiments:

[0108] 1. Simulation experiment conditions:

[0109] The hardware platform of the simulation experiment of the present invention is: the processor is Intel i7 10700 CPU, the main frequency is 2.9 GHz, and the memory is 16 GB.

[0110] The software platform for the simulation experiment of the present invention is: Windows 10 operating system and python 3.9.

[0111] The input images used in the simulation experiment of the present invention are Coast hyperspectral images and Hydice hyperspectral images. The Coast hyperspectral image is collected from the airborne visible / infrared imaging spectrometer AVIRIS, with an image size of 100×100×198 pixels, a total of 198 bands, and an image format of mat; the Hydice hyperspectral image is collected from the airborne sensor of the hyperspectral digital image collection experiment over the urban area of ​​California, USA, with an image size of 80×100×162 pixels, a total of 162 bands, and an image format of mat.

[0112] 2. Simulation content and result analysis:

[0113] In the simulation experiment 1 of the present invention, the present invention and an existing technology (DeCNN-AD) are used to perform anomaly detection on the input Coast hyperspectral image to obtain an abnormal image.

[0114] Simulation experiment 2 of the present invention uses the present invention and an existing technology (DeCNN-AD) to perform anomaly detection on the input Hydice hyperspectral image to obtain an abnormal image.

[0115] In the simulation experiment, an existing technology used is:

[0116] DeCNN-AD refers to the hyperspectral image anomaly detection method disclosed by Xiyou Fu et al. in their paper "Hyperspectral Anomaly Detection via Deep Plug-and-Play Denoising CNN Regularization" (IEEE Transactions on Geoscience and Remote Sensing, 2021, PP(99):1-16), abbreviated as DeCNN-AD.

[0117] The following combination Figure 2 and Figure 3 The effects of the present invention are further described.

[0118] Figure (2a) is the abnormal target label image of the Coast hyperspectral image, Figure (2b) is the result image of abnormality detection of the Coast hyperspectral image using the existing technology DeCNN-AD, and Figure (2c) is the result image of abnormality detection of the Coast hyperspectral image using the method of the present invention.

[0119] Figure (3a) is the abnormal target label image of the Hydice hyperspectral image, Figure (3b) is the result image of anomaly detection on the Hydice hyperspectral image using the existing technology DeCNN-AD, and Figure (3c) is the result image of anomaly detection on the Hydice hyperspectral image using the method of the present invention.

[0120] As can be seen from Figure (2b) and Figure (3b), the existing technology DeCNN-AD has a low degree of anomaly detection for most pixels of the abnormal target label image. The main reason is that the artificial sparse prior weakens the abnormality degree of most target abnormal pixel positions.

[0121] As can be seen from Figures (2c) and (3c), compared with the prior art DeCNN-AD, the method of the present invention has a relatively high degree of anomaly detection in most pixels of the abnormal target label image. The detected abnormal image has a more obvious spatial structure visually and is closer to the label image, which proves that the anomaly detection effect of the present invention is better than that of the prior art DeCNN-AD and the anomaly detection effect is more ideal.

[0122] The evaluation index AUC is used to evaluate the anomaly detection results of the present invention and the prior art DeCNN-AD. The calculation formula of the AUC value is as follows:

[0123]

[0124] Where f(x) is the receiver operating characteristic (ROC) curve equation of the detection results of the semantic segmentation deep convolutional network on the test set, and the AUC indicator means calculating the area under the entire ROC curve.

[0125] Table 1. Comparison of AUC of the present invention and the prior art DeCNN-AD in simulation experiments

[0126] Hyperspectral imagery Method of the present invention DeCNN-AD Coast 0.9932 0.9570 Hydice 0.9997 0.9983 Average precision 0.9965 0.9777

[0127] From the data in Table 1, it can be seen that the overall average accuracy of the hyperspectral image target detection method of the present invention is 0.9965, which is higher than that of the prior art DeCNN-AD, proving that the present invention can achieve higher hyperspectral image target detection accuracy.

[0128] The above simulation experiments show that the present invention can effectively replace the artificial prior dual denoiser, construct a noise evaluation module to evaluate the noise variance of each channel of the three-dimensional tensor, enable the denoiser to adaptively set the denoising variance parameters, effectively remove noise, and highlight abnormal targets. It solves the problems in the existing technology that the calculation and optimization process of the artificial low-rank prior and sparse prior prior items is too complicated, and there is a large error between the denoising variance parameters manually set by the denoiser and the actual three-dimensional tensor noise variance of the input denoiser. It has important practical significance in the field of hyperspectral image target detection.

Claims

1. A method for anomaly detection in hyperspectral images using a dual denoiser to replace artificial priors, characterized in that: A noise assessment module is constructed to adaptively assess the noise variance of each channel of the noise tensor, and a dual denoiser is designed to replace the artificial prior and adaptively adjust the denoising variance parameters. The steps of the anomaly detection method include the following: Step 1. Obtain the discriminant feature matrix of dimensionality reduction: Arrange the values ​​from the first row to the last row of the two-dimensional image of each channel in a hyperspectral image to be detected into the values ​​of each column in the spectral matrix. After normalizing the spectral matrix, input it into an encoder composed of a fully connected layer. Output the discriminant feature matrix of the hyperspectral image after dimensionality reduction. Arrange the values ​​of each row in the matrix into a discriminant feature vector. Step 2. Obtain the dictionary atom matrix representing the background from the discriminant feature matrix: Step 2.1, calculate the probability that each discriminant eigenvector in the discriminant feature matrix belongs to a Gaussian component category, classify this discriminant eigenvector into the Gaussian component category corresponding to the maximum probability value among all probabilities, use the discriminant eigenvector corresponding to the maximum probability value among all probabilities that all discriminant eigenvectors belonging to each category of Gaussian components belong to the category of Gaussian components as the central discriminant eigenvector of all discriminant eigenvectors belonging to the category of Gaussian components, and use the discriminant eigenvector corresponding to the minimum probability value among all probabilities that all discriminant eigenvectors belonging to each category of Gaussian components belong to the category of Gaussian components as the boundary discriminant eigenvector of all discriminant eigenvectors belonging to the category of Gaussian components; Step 2.2, in the order from the first category of Gaussian component category to the last category of Gaussian component category, the center discriminant feature vector of all discriminant feature vectors belonging to any category of Gaussian component and the boundary discriminant feature vectors of all discriminant feature vectors belonging to this category of Gaussian component are combined into a dictionary atomic matrix by row; Step 3. Build the noise evaluation module: Step 3.1: Crop a 2D noise image in an unselected channel from a 3D noise image of shape [m1, n1, c1] into 2D image blocks of length d and width d, with the number of blocks being (m-d+1)(n-d+1). Arrange the pixel values ​​from the first row to the last row of each 2D image block into a block of dimension d. 2 ×1 vector, all vector values ​​are combined into a numerical matrix by row; where m1 represents the number of row pixels of the 3D noise image, n1 represents the number of column pixels of the 3D noise image, c1 represents the number of channels of the 3D noise image, and d represents the cropping size; Step 3.2, calculate the mean vector of all vectors; Step 3.3, calculate the covariance matrix of the numerical matrix; Step 3.4, calculate the eigenvalues ​​of the covariance matrix and sort the eigenvalues ​​from small to large to obtain an eigenvalue list; Step 3.5, calculate the mean of all eigenvalues ​​in the eigenvalue list; Step 3.6: Determine whether the mean of all eigenvalues ​​in the eigenvalue list is equal to the median of the eigenvalue list. If so, the noise variance of the selected channel is equal to the square root of the mean and then execute step 3.

7. Otherwise, delete the last eigenvalue in the eigenvalue list and then execute step 3.

5. Step 3.7, determine whether all channels in the 3D noise image have been selected. If so, execute step 4 after completing the construction of the noise assessment module. Otherwise, execute step 3.

1. Step 4. Design a denoiser based on the FFDNet convolutional neural network framework: Step 4.1: Input a 3D noise image of shape [m2, n2, c2] into the noise estimation module and output the noise variance of the 2D noise image for each channel in the 3D noise image; where m2 represents the number of row pixels in the 3D noise image, n2 represents the number of column pixels in the 3D noise image, and c2 represents the number of channels in the 3D noise image. In step 4.2, a 2D noise image and its noise variance from an unselected channel of the 3D noise image are input to the trained FFDNet convolutional neural network, and a denoised 2D image is output. The denoising variance parameter of the network is adaptively set to the noise variance of the 2D image in the selected channel of the 3D noise image. Step 4.3: Determine whether all channels in the 3D noisy image have been selected. If so, arrange the 2D images after all channels have been denoised into a denoised 3D image in the order of the channels in the 3D noisy image. After the denoiser design is complete, proceed to step 5. Otherwise, proceed to step 4.

2. Step 5. Design a denoiser based on the Gaussian filter framework: Step 5.1: Input a 3D noise image of shape [m3, n3, c3] into the noise estimation module and output the noise variance of the 2D noise image for each channel in the 3D noise image; where m3 represents the number of row pixels, n3 represents the number of column pixels, and c3 represents the number of channels in the 3D noise image. Step 5.2: Input a 2D noise image and its noise variance from an unselected channel selected from the 3D noise image into a Gaussian filter with a sliding window size of 3×3, and output a denoised 2D image; wherein the variance parameter of the filter coefficient of the sliding window convolution kernel of the Gaussian filter is adaptively set to the noise variance of the 2D noise image in the selected channel of the 3D noise image; Step 5.3: Determine whether all channels in the 3D noisy image have been selected. If so, arrange the 2D images after all channels have been denoised into a denoised 3D image in the order of the channels in the 3D noisy image. After the denoiser design is complete, proceed to step 6. Otherwise, proceed to step 5.

2. Step 6. Detect anomalies using dual denoisers: Step 6.1: Construct a dictionary coefficient matrix with all zero initial values. The number of rows of this matrix is ​​the same as the number of rows of the dictionary atom matrix in step 2.2, and the number of columns is the same as the number of rows of the discriminant feature matrix in step 1. Construct an anomaly matrix with all zero initial values. The number of rows of this matrix is ​​the same as the number of columns of the discriminant feature matrix in step 1, and the number of columns is the same as the number of rows of the discriminant feature matrix in step 1. Step 6.2, calculate the gradient descent intermediate estimate matrix of the dictionary coefficient matrix according to the following formula: Among them, V S represents the intermediate estimation matrix of the gradient descent of the dictionary coefficient matrix, S represents the dictionary coefficient matrix, λ S Represents a parameter whose value is a real number randomly selected in the range [0.0001, 0.1]. It represents the partial derivative operation of (·) with respect to S, represents the Frobenius norm, X represents the transposed matrix of the discriminative feature matrix, D represents the transposed matrix of the dictionary atom matrix, and E represents the anomaly matrix; Step 6.3, arrange the gradient descent intermediate estimate matrix of the dictionary coefficient matrix into a three-dimensional tensor as the dictionary coefficient intermediate estimate tensor, where the matrix of each channel in the three-dimensional tensor is composed of the arrangement of the values ​​of each column in the gradient descent intermediate estimate matrix; In step 6.4, the intermediate estimated tensor of the dictionary coefficients is input into the denoiser based on the FFDNet convolutional neural network framework, and the three-dimensional tensor of the dictionary coefficients is output; Step 6.5, arrange the values ​​from the first row to the last row in the two-dimensional matrix of each channel in the three-dimensional tensor of the dictionary coefficient into the values ​​of each column in the updated dictionary coefficient matrix; Step 6.6, calculate the gradient descent intermediate estimation matrix of the anomaly matrix according to the following formula: Among them, V E represents the gradient descent intermediate estimation moment of the anomaly matrix, λ E Represents a parameter whose value is a real number randomly selected in the range [0.0001, 0.1]. represents the partial derivative operation of (·) with respect to E, S new Represents the updated dictionary coefficient matrix; Step 6.7: Arrange the gradient descent intermediate estimate matrix of the anomaly matrix into a three-dimensional tensor as the anomaly intermediate estimate tensor, where the matrix of each channel in the three-dimensional tensor is composed of the values ​​of each column in the gradient descent intermediate estimate matrix; In step 6.8, the abnormal intermediate estimation tensor is input into a denoiser based on a Gaussian filter framework, and an abnormal three-dimensional tensor is output; Step 6.9, arrange the values ​​from the first row to the last row in the two-dimensional matrix of each channel in the anomaly three-dimensional tensor into the values ​​of each column in the updated anomaly matrix; Step 6.10, determine whether the updated dictionary coefficient matrix and the updated anomaly matrix meet the termination condition. If so, execute step 7; otherwise, execute step 6.2; Step 7, save the abnormal image: Calculate the bi-norm value of each column in the updated anomaly matrix, arrange all bi-norm values ​​into a bi-norm value matrix by row, plot the bi-norm value matrix and save the anomaly image.

2. The method for detecting anomalies in hyperspectral images using a dual denoiser to combat Gaussian noise according to claim 1, characterized in that: The fully connected layer in the encoder described in step 1 is composed of two tf.layers.dense functions. The input channel parameter of the first tf.layers.dense function is set to the number of channels of the hyperspectral image to be detected, the output channel parameter is 400, and the activation layer is implemented using the ReLU function. The input channel parameter of the second tf.layers.dense function is set to 400 and the output channel parameter is 9.

3. The method for detecting anomalies in hyperspectral images using a dual denoiser to combat Gaussian noise according to claim 1, characterized in that: The termination conditions described in step 6.10 are as follows: Among them, S t Represents the dictionary coefficient matrix after the tth iteration update, R t represents the abnormal matrix updated in the tth iteration, S t+1 Represents the dictionary coefficient matrix after the tth iteration update, R t+1 represents the updated abnormality matrix at the tth iteration.

Images