A hyperspectral anomaly detection method based on wavelet transform quaternion matrix

Abstract

The application provides a hyperspectral anomaly detection method based on a wavelet transform quaternion matrix, and relates to a hyperspectral image target detection method.The method is as follows: first, an optimal clustering framework is used to process a hyperspectral image, the dimension of the hyperspectral image is reduced, and redundancy is eliminated; then, the hyperspectral image is subjected to one layer of three-dimensional wavelet transform to form an image X WT , and is decomposed and converted into eight sub-images; four sub-images with high frequency in the spectral dimension are replaced by a quaternion matrix to obtain a new overall image X Q ; then, the overall image X Q data is subjected to 3-D wavelet inverse transform, image data obtained by the wavelet inverse transform is reconstructed by using a stacked auto-encoder, finally, a tensor RX is used to detect SAE reconstruction error, and a final detection result is obtained.The application has the advantages that original hyperspectral image characteristics can be better preserved, high-frequency and low-frequency information can be more favorably analyzed, and original information can be better preserved.

Description

Technical Field

[0001] This invention relates to a hyperspectral image target detection method, specifically a hyperspectral image abnormal target detection method based on wavelet transform quaternion matrix. Background Technology

[0002] As a three-dimensional dataset, hyperspectral images possess two spatial dimensions and one spectral dimension, with hundreds of spectral bands. The rich spectral information provided by these hundreds of bands and the increasingly higher spatial resolution have led to the widespread application of hyperspectral images in identifying ground objects. Anomaly detection is the most common application of hyperspectral images, with the most classic algorithms being RX and Local RX, both based on test point vectors. However, anomalies typically contain multiple pixels, so using only pixel vectors negatively impacts detection accuracy. Based on the Generalized Likelihood Ratio Test (GLRT) design criterion and its modified version, one-step GLRT and two-step GLRT are proposed for detecting multi-pixel anomalies without prior information. Tensor RX (TRX), as a tensor version of Local RX, is based on test point tensors instead of test point vectors, better utilizing the spatial information of anomalies. KRX and Fractional Fourier Entropy-Based RX (FrFE-RX) do not use the original reflectance spectrum. KRX maps the original data to a nonlinear Gaussian domain in a high-dimensional feature space, while FrFE-RX performs the RX algorithm in the fractional Fourier domain.

[0003] The algorithms described above fully utilize the spectral information of hyperspectral images. However, while hyperspectral images possess rich spectral information, they also contain a significant amount of redundant information. Removing this redundant information can reduce interference and improve detection accuracy and efficiency. Dimensionality reduction, as a standard preprocessing method, is used to eliminate spectral redundancy. Principal Component Analysis (PCA), the most classic dimensionality reduction method, is a linear mapping and cannot accurately extract hyperspectral images with inherent nonlinear characteristics. Band selection is also a major dimensionality reduction method; it selects a representative set of bands from the hyperspectral image without modifying the original data, making the reduced data more interpretable. Optimal Clustering Framework (OCF), as a band selection method, develops the optimal clustering structure in hyperspectral images and selects representative bands based on a clustering ranking strategy. Furthermore, the application of deep learning (DL) theory in hyperspectral image processing has received widespread attention. Deep learning can extract deep features from hyperspectral images and achieve dimensionality reduction. Deep Belief Networks (DBNs) and Stacked Autoencoders (SAEs) are unsupervised learning models commonly used for feature extraction, dimensionality reduction, and reconstruction. However, deep learning models involve a large number of parameters, requiring extensive tuning. In addition, a large amount of computation also requires high-end hardware configurations.

[0004] In recent years, anomaly detection in hyperspectral images based on joint spatial-spectral features has become a research hotspot. Compared with the rich spectral information in hyperspectral images, the spatial and geometric information is relatively weak. Wavelet transform (WT), as a signal analysis tool, provides a method for analyzing multi-scale or multi-resolution signals and is a classic algorithm in the field of image processing. Wavelet transform can decompose an image into high-frequency and low-frequency sub-images. The background of a hyperspectral image corresponds to low-frequency information, while anomalies correspond to high-frequency information. Therefore, wavelet transform can be applied to anomaly detection in hyperspectral images. However, research on this topic has been scarce in recent years. In addition to the aforementioned joint spatial-spectral features, fusing multiple features to improve detection accuracy and algorithm versatility has also attracted widespread attention. Besides traditional weighted methods, fusion methods using quaternion matrices can perform multi-scale and multi-feature processing in parallel and have recently been applied to hyperspectral image processing. Summary of the Invention

[0005] The purpose of this invention is to provide a hyperspectral anomaly detection method based on wavelet transform quaternion matrix that can more effectively detect abnormal targets in hyperspectral images.

[0006] The present invention provides a hyperspectral anomaly detection method based on wavelet transform quaternion matrices, characterized by comprising the following steps:

[0007] (1) The acquired hyperspectral images are processed using the optimal clustering framework (OCF) to reduce the dimensionality of the original hyperspectral images and eliminate redundancy;

[0008] (2) The hyperspectral image processed by the optimal clustering framework (OCF) is transformed into image X by a single three-dimensional wavelet transform. WT It is then decomposed into eight sub-images, of which four high-frequency sub-images are HLL, HLH, HHL and HHH; and four low-frequency sub-images are LLL, LLH, LHL and LHH.

[0009] (3) Replace the four sub-images HLL, HLH, HHL and HHH with quaternion matrices respectively to obtain a new overall image X. Q ;

[0010] (4) The overall image X obtained through the quaternion matrix Q Perform 3D wavelet inverse transform on the data;

[0011] (5) Reconstruct the image data obtained by wavelet inverse transform using stacked autoencoder (SAE);

[0012] (6) Use tensor RX (TRX) to detect SAE reconstruction error and obtain the final detection result.

[0013] As a further improvement of the present invention, the replacement of the four sub-images with higher frequencies in the spectral dimension by a quaternion matrix in step (3) is achieved through the following steps:

[0014] For the four high-frequency sub-images HLL, HLH, HHL, and HHH in the spectral dimension, a quaternion matrix is ​​formed for each frequency band using the low-frequency sub-images in the spectral dimension. At least one component of the quaternion matrix is ​​a frequency band of the original high-frequency spectral sub-image, and simultaneously, at least one component of the quaternion matrix is ​​a frequency band of the corresponding low-frequency spectral sub-image. In X... WT The four sub-images with high frequencies in the spectral dimension are used to form a quaternion matrix sub-image using formula (1):

[0015] S M =a1S1+a2S2×i+a3S3×j+a4S4×k (1)

[0016] Among them, S M This is the quaternion matrix corresponding to the frequency band; a1, a2, a3, and a4 are weighting coefficients, each 0.25, and their sum is 1; i 2 =j 2 =k 2 =ijk=-1, i⊥j, i⊥k, j⊥k, k=ij, S1, S2, S3, S4 refer to the frequency band.

[0017] As a further improvement of the present invention, the high-frequency sub-image HLL, in image X Q The frequency bands of the high-frequency sub-image in the spectral dimension are formed into a quaternion matrix in any of the following ways:

[0018] Method 1: S Q-HLL =a1S WT-HLL +a2S WT-LLL ×i+a3S WT-LLL ×j+a4S WT-LLL ×k

[0019] or

[0020] Method 2: S Q-HLL =a1S WT-HLL +a2S WT-HLL ×i+a3S WT-LLL ×j+a4S WT-LLL ×k

[0021] or

[0022] Method 3: S Q-HLL =a1S WT-HLL +a2S WT-HLL ×i+a3S WT-HLL ×j+a4SWT-LLL ×k

[0023] Where S WT-LLL It is X WT The frequency bands of the low-frequency sub-image in the spectral dimension, S WT-HLL It is X WT The frequency band of the high-frequency sub-image in the spectral dimension.

[0024] As a further improvement of the present invention, the high-frequency sub-image HHL, in image X Q The frequency bands of the high-frequency sub-image in the spectral dimension are formed into a quaternion matrix in any of the following ways:

[0025] Method 1: S Q-HHL =a1S WT-HHL +a2S WT-LHL ×i+a3S WT-LHL ×j+a4S WT-LHL ×k

[0026] or

[0027] Method 2: S Q-HHL =a1S WT-HHL +a2S WT-HHL ×i+a3S WT-LHL ×j+a4S WT-LHL ×k

[0028] or

[0029] Method 3: S Q-HHL =a1S WT-HHL +a2S WT-HHL ×i+a3S WT-HHL ×j+a4S WT-LHL ×k

[0030] Where S WT-LHL It is X WT The frequency bands of the low-frequency sub-image in the spectral dimension, S WT-HHL It is X WT The frequency band of the high-frequency sub-image in the spectral dimension.

[0031] As a further improvement of the present invention, the high-frequency sub-image HLH, in image X Q The frequency bands of the high-frequency sub-image in the spectral dimension are formed into a quaternion matrix in any of the following ways:

[0032] Method 1: S Q-HLH =a1S WT-HLH +a2S WT-LLH ×i+a3S WT-LLH ×j+a4S WT-LLH ×k

[0033] or

[0034] Method 2: S Q-HLH =a1S WT-HLH +a2S WT-HLH ×i+a3S WT-LLH ×j+a4S WT-LLH ×k

[0035] or

[0036] Method 3: S Q-HLH =a1S WT-HLH +a2S WT-HLH ×i+a3S WT-HLH ×j+a4S WT-LLH ×k

[0037] Where S WT-LLH It is X WT The frequency bands of the low-frequency sub-image in the spectral dimension, S WT-HLH It is X WT The frequency band of the high-frequency sub-image in the spectral dimension.

[0038] As a further improvement of the present invention, the high-frequency sub-image HHH, in image X Q The frequency bands of the high-frequency sub-image in the spectral dimension are formed into a quaternion matrix in any of the following ways:

[0039] Method 1: S Q-HHH =a1S WT-HHH +a2S WT-LHH ×i+a3S WT-LHH ×j+a4S WT-LHH ×k

[0040] or

[0041] Method 2: S Q-HHH =a1S WT-HHH +a2S WT-HHH ×i+a3S WT-LHH ×j+a4S WT-LHH ×k

[0042] or

[0043] Method 3: S Q-HHH =a1S WT-HHH +a2S WT-HHH ×i+a3S WT-HHH ×j+a4S WT-LHH ×k

[0044] Where S WT-LHH It is X WT The frequency bands of the low-frequency sub-image in the spectral dimension, S WT-HHH It is X WT The frequency band of the high-frequency sub-image in the spectral dimension.

[0045] The advantages of this invention are:

[0046] 1. In order to remove redundant spectral information without modifying the original hyperspectral image, OCF is used to reduce the dimensionality, which better preserves the characteristics of the original hyperspectral image;

[0047] 2. In the wavelet transform quaternion matrix (QMWT) model, a single-layer 3-D wavelet transform is used to obtain eight different high-frequency and low-frequency sub-images, which is more conducive to the analysis of high-frequency and low-frequency information;

[0048] 3. For wavelet transform in the spectral dimension, low-frequency information contains the main information, while redundant information is located in the high-frequency part. To further remove noise and spectral redundancy, the four sub-images with higher frequencies in the spectral dimension are replaced with quaternion matrices. The quaternion matrix consists of high-frequency sub-images in the spectral dimension and corresponding low-frequency sub-images in the spectral dimension, thus better preserving the original information;

[0049] 4. In order to better utilize spatial characteristics, TRX replaces the traditional RX and other methods to complete the final abnormal target detection. Attached Figure Description

[0050] Figure 1 This is a schematic diagram of the first-level three-dimensional wavelet decomposition.

[0051] Figure 2 The flowchart shows the proposed wavelet transform quaternion matrix (QMWT) algorithm.

[0052] Figure 3 The image shows binary plots of Los Angeles data and the results of eight detection methods. Figure 3 (a) is the 100th band plot of the LosAngeles data. Figure 3 (b) is a schematic diagram of the actual ground feature distribution in the LosAngeles data. Figure 3 (c) is the binary image of the detection result of the RX algorithm. Figure 3 (d) is the binary image of the detection result of the local RX algorithm. Figure 3 (e) is the binary image of the detection result of the KRX algorithm. Figure 3 (f) is the binary image of the detection result of the FrFE-RX algorithm. Figure 3 (g) is the binary image of the detection result of the FrFE-LRX algorithm. Figure 3 (h) is the binary image of the detection result of the PCA-TRX algorithm. Figure 3 (i) is the binary image of the detection result of the FrFT-TRX algorithm. Figure 3 (j) is the binary image of the detection result of the QMWT algorithm;

[0053] Figure 43D-ROC curves for eight detection methods in the LosAngeles data;

[0054] Figure 5 This is a graph showing the separability of eight detection methods for the LosAngeles dataset.

[0055] Figure 6 The image shows binary plots of Pavia data and the detection results of eight detection methods. Figure 6 (a) is the 100th band plot of Pavia data. Figure 6 (b) is a schematic diagram of the actual ground cover distribution in Pavia data. Figure 6 (c) is the binary image of the detection result of the RX algorithm. Figure 6 (d) is the binary image of the detection result of the local RX algorithm. Figure 6 (e) is the binary image of the detection result of the KRX algorithm. Figure 6 (f) is the binary image of the detection result of the FrFE-RX algorithm. Figure 6 (g) is the binary image of the detection result of the FrFE-LRX algorithm. Figure 6 (h) is the binary image of the detection result of the PCA-TRX algorithm. Figure 6 (i) is the binary image of the detection result of the FrFT-TRX algorithm. Figure 6 (j) is the binary image of the detection result of the QMWT algorithm;

[0056] Figure 7 3D-ROC curves for eight detection methods in Pavia data;

[0057] Figure 8 This is a graph showing the separability of eight detection methods for Pavia data. Detailed Implementation

[0058] The present invention provides a hyperspectral anomaly detection method based on wavelet transform quaternion matrices, which is implemented through the following steps:

[0059] Step 1: To avoid modifying the original data, the acquired hyperspectral images are processed using the Optimal Clustering Framework (OCF) to reduce the dimensionality of the original hyperspectral images and eliminate redundancy.

[0060] Step 2: To better process the high-frequency and low-frequency information of the hyperspectral image and further remove noise and spectral redundancy, the hyperspectral image after OCF is transformed into image X by a single three-dimensional wavelet transform. WT The image is decomposed into eight sub-images, namely LLL, LLH, LHL, LHH, HLL, HLH, HHL and HHH;

[0061] Step 3: In the high-frequency sub-images, besides anomalous information, there will also be noise and redundant information. The four sub-images with higher frequencies in the spectral dimension are replaced with quaternion matrices. The details of quaternion matrix formation are as follows: For the four high-frequency sub-images HLL, HLH, HHL, and HHH in the spectral dimension, to further reduce spectral redundancy, quaternion matrices are formed for each frequency band using the sub-images with lower frequencies in the spectral dimension. To avoid losing too much high-frequency information, at least one component of the quaternion matrix is ​​a band from the original high-frequency sub-image. Simultaneously, to further eliminate redundancy, at least one component of the quaternion matrix is ​​a band from the corresponding low-frequency sub-image. For the four low-frequency sub-images in the spectral dimension, LLL, LLH, LHL, and LHH contain the main information from the hyperspectral image and remain unchanged.

[0062] Step 4: Perform 3-D wavelet inverse transform on the hyperspectral data obtained through the quaternion matrix;

[0063] Step 5: To better distinguish between background and unusual targets, the image data obtained by wavelet inverse transform is reconstructed using a stacked autoencoder (SAE).

[0064] Step 6: Use tensor RX (TRX) to detect SAE reconstruction errors and obtain the final detection results.

[0065] The invention will now be described in more detail with reference to the accompanying drawings, using real hyperspectral images of LosAngeles data and Pavia data respectively:

[0066] Reference Figure 1 This is a schematic diagram of the first-level three-dimensional wavelet decomposition. L and H represent the low-frequency and high-frequency components obtained by filtering the hyperspectral image through low-frequency and high-frequency filters, respectively, and the subscript "1" indicates the first-level decomposition. Similar to 2-D wavelet transform, the hyperspectral image is decomposed into a low-resolution approximation (low-frequency 3-D sub-image LLL) and a series of high-frequency 3-D sub-images (LLH, LHL, LHH, HLL, HLH, HHL, and HHH) with details of the image sequence at different resolutions.

[0067] Reference Figure 2 The flowchart of the proposed QMWT algorithm is shown. First, the hyperspectral image X = {x} is tested. i ∈R D The hyperspectral image X is denoted as {i = 1, ..., N} (where N is the number of test points in the hyperspectral image and D is the spectral dimension) and its dimensionality is reduced using OCF. Next, the resulting low-dimensional hyperspectral image X is... OCF ={x i ∈R B, i=1,…,N}(B<D) is decomposed by one-layer 3-D wavelet transform to obtain 8 sub-images. Then, for four sub-images HLL, HLH, HHL and HHH with high frequency in the spectral dimension, in order to further reduce spectral redundant information, the sub-images with low frequency in the spectral dimension are used to form a quaternion matrix for each frequency band. In order to avoid losing too much high-frequency information, at least one component of the quaternion matrix is the original high-frequency sub-image band in the spectrum. Meanwhile, in order to further eliminate redundancy, at least one component of the quaternion matrix is the frequency band of the low-frequency sub-image in the spectrum corresponding to the high-frequency sub-image in the spectrum. In X WT the four sub-images with high frequency in the spectral dimension form quaternion matrix sub-images by using formula (1), and obtain a new overall image X Q ;

[0068] S M =a1S1+a2S2×i+a3S3×j+a4S4×k (1)

[0069] wherein, S M is the quaternion matrix of the corresponding frequency band; a1, a2, a3 and a4 are weight coefficients, the sum of which is 1, and they are all set to 0.25 in the present application; i 2 =j 2 =k 2 =ijk=-1, i⊥j, i⊥k, j⊥k, k=ij, S1, S2, S3, S4 refer to frequency bands.

[0070] Taking the frequency band of HLL as an example below, by using formula (1), according to the characteristics of the test hyperspectral image, S1 is set as the frequency band of HLL, S4 is set as the frequency band of LLL, and S2 and S3 correspond to the frequency bands of HLL or LLL. For four sub-images with low and medium frequency in the spectral dimension, LLL, LLH, LHL and LHH contain the main information of the hyperspectral image and remain unchanged, and the quaternion matrix S of the corresponding frequency band Q-HLL , that is, in the frequency band of the high-frequency sub-image on the spectral dimension of image X Q , forming a quaternion matrix has the following three methods, and one can be selected according to the characteristics of image data when in use:

[0071] Method 1: S Q-HLL =a1S WT-HLL +a2S WT-LLL ×i+a3S WT-LLL ×j+a4S WT-LLL ×k

[0072] Method 2: S Q-HLL =a1S WT-HLL +a2S WT-HLL ×i+a3S WT-LLL ×j+a4S WT-LLL ×k

[0073] Method 3: S Q-HLL =a1S WT-HLL +a2S WT-HLL ×i+a3S WT-HLL ×j+a4S WT-LLL ×k

[0074] Where S WT-LLL It is X WT The frequency bands of the low-frequency sub-image in the spectral dimension, S WT-HLL It is X WT The frequency band of the high-frequency sub-image in the spectral dimension.

[0075] Similarly, for the HHL band, its quaternion matrix S Q-HHL That is, in image X Q There are three ways to form a quaternion matrix from the frequency bands of high-frequency sub-images in the spectral dimension. When using this method, choose one according to the characteristics of the image data:

[0076] Method 1: S Q-HHL =a1S WT-HHL +a2S WT-LHL ×i+a3S WT-LHL ×j+a4S WT-LHL ×k

[0077] Method 2: S Q-HHL =a1S WT-HHL +a2S WT-HHL ×i+a3S WT-LHL ×j+a4S WT-LHL ×k

[0078] Method 3: S Q-HHL =a1S WT-HHL +a2S WT-HHL ×i+a3S WT-HHL ×j+a4S WT-LHL ×k

[0079] Where S WT-LHL It is X WT The frequency bands of the low-frequency sub-image in the spectral dimension, S WT-HHL It is X WT The frequency band of the high-frequency sub-image in the spectral dimension.

[0080] Similarly, for the HLH band, its quaternion matrix S Q-HLH That is, in image X Q There are three ways to form a quaternion matrix from the frequency bands of high-frequency sub-images in the spectral dimension. When using this method, choose one according to the characteristics of the image data:

[0081] Method 1: S Q-HLH =a1S WT-HLH +a2S WT-LLH×i+a3S WT-LLH ×j+a4S WT-LLH ×k

[0082] Method 2: S Q-HLH =a1S WT-HLH +a2S WT-HLH ×i+a3S WT-LLH ×j+a4S WT-LLH ×k

[0083] Method 3: S Q-HLH =a1S WT-HLH +a2S WT-HLH ×i+a3S WT-HLH ×j+a4S WT-LLH ×k

[0084] Where S WT-LLH It is X WT The frequency bands of the low-frequency sub-image in the spectral dimension, S WT-HLH It is X WT The frequency band of the high-frequency sub-image in the spectral dimension.

[0085] Similarly, for the HHH frequency band, its quaternion matrix S Q-HHH That is, in image X Q There are three ways to form a quaternion matrix from the frequency bands of high-frequency sub-images in the spectral dimension. When using this method, choose one according to the characteristics of the image data:

[0086] Method 1: S Q-HHH =a1S WT-HHH +a2S WT-LHH ×i+a3S WT-LHH ×j+a4S WT-LHH ×k

[0087] Method 2: S Q-HHH =a1S WT-HHH +a2S WT-HHH ×i+a3S WT-LHH ×j+a4S WT-LHH ×k

[0088] Method 3: S Q-HHH =a1S WT-HHH +a2S WT-HHH ×i+a3S WT-HHH ×j+a4S WT-LHH ×k

[0089] Where S WT-LHH It is X WT The frequency bands of the low-frequency sub-image in the spectral dimension, S WT-HHH It is X WT The frequency band of the high-frequency sub-image in the spectral dimension.

[0090] For the four low-frequency sub-images in the spectral dimension, LLL, LLH, LHL, and LHH contain the main information of the hyperspectral image and remain unchanged. Then, the new image X obtained through the quaternion matrix... Q Perform a three-dimensional wavelet inverse transform to obtain X. IW Next, to better distinguish between background and anomalous targets, SAE performs X... IW Reconstruct to obtain X SR Finally, in X R Apply TRX, X R That is, X IW and X SR The difference between them is used to obtain the final abnormal target detection result.

[0091] Reference Figure 3 This is a binary image of Los Angeles data and the detection results of eight detection methods. The Los Angeles data is Los Angeles airport data obtained by the AVIRIS sensor, with a spatial resolution of 7.1m, a spatial size of 100×100 pixels, and 205 bands. Figure 3 (a) is the 100th band plot of the Los Angeles data; Figure 3 (b) is a schematic diagram of the actual ground feature distribution in LosAngeles data; Figure 3 (c) is a binary image of the global RX detection results; Figure 3 (d) is a binary image of the local RX detection result, with inner and outer window sizes of 7×7 and 9×9; Figure 3 (e) is the binary image of the KRX detection result, with a kernel parameter of 10. -5 The inner and outer window dimensions are 5×5 and 9×9 respectively; Figure 3 (f) is the binary image of the FrFE-RX detection result, with a fractional order of 0.2; Figure 3 (g) is a binary image of the FrFE-LRX detection result, with a fractional order of 0.2 and inner and outer window sizes of 7×7 and 9×9; Figure 3 (h) is a binary image of the PCA-TRX detection result. The dimension after PCA dimensionality reduction is 10, and the inner and outer window sizes are 7×7 and 9×9, respectively. Figure 3 (i) is a binary image of the FrFT-TRX detection result, with a fractional order of 0.2 and inner and outer window sizes of 7×7 and 9×9; Figure 3 (j) is the binary image of the QMWT detection result. The dimension of the OCF-reduced image is 19, and the inner and outer window sizes are 3×3 and 25×25, respectively. Sub-image S Q-HLL The frequency band is generated through method 3, sub-image S Q-HHL Frequency band usage method 3 generates sub-image S Q-HLH The frequency band was generated using method 2, while the sub-image S Q-HHHThe frequency band is generated using method 1. (Based on reference...) Figure 3 It is evident that the proposed QMWT method achieves higher resolution binary images than the standard QMWT method. Figure 3 (b)-3(i) Seven comparison methods.

[0092] Reference Figure 4 These are the 3D-ROC curves and their corresponding 2D ROC curves for eight detection methods in Los Angeles data. The 2D(P) curve for QMWT... D P F The ROC curve of QMWT is consistently higher than that of the comparison algorithm, except for KRX. D The ROC curves for τ are all higher than those of the comparison algorithm. For 2-D(P) F The lower the ROC curve, the stronger the background compression capability; the OMWT curve has a moderate height.

[0093] Reference Figure 5 This is a separability graph of eight detection methods from the Los Angeles dataset, based on a reference... Figure 5 It is evident that the proposed QMWT algorithm demonstrates superior separability between the target and the background compared to the other seven tested algorithms.

[0094] Depend on Figure 3 , 4 As shown in Figure 5, for Los Angeles data, the QMWT method of this invention outperforms the seven comparative algorithms GRX, LRX, KRX, FrFE-RX, FrFE-LRX, PCA-TRX, and FrFT-TRX in overall detection performance.

[0095] The superiority of the invention was further verified using Pavia data. (Refer to...) Figure 6 This is a binary image of the Pavia data and the detection results of eight detection methods. The Pavia data was obtained from the ROSIS-03 sensor, with a spatial resolution of 1.3m, a spatial size of 150×150 pixels, and 102 bands. Figure 6 (a) is the 100th band plot of Pavia data; Figure 6 (b) is a schematic diagram of the actual ground feature distribution in Pavia data; Figure 6 (c) is a binary image of the global RX detection results; Figure 6 (d) is a binary image of the local RX detection result, with inner and outer window sizes of 25×25 and 81×81; Figure 6 (e) is the binary image of the KRX detection result, with a kernel parameter of 10. -1 The inner and outer window dimensions are 25×25 and 29×29 respectively; Figure 6 (f) is the binary image of the FrFE-RX detection result, with a fractional order of 1; Figure 6 (g) is a binary image of the FrFE-LRX detection result, with a fractional order of 1 and inner and outer window sizes of 25×25 and 77×77; Figure 6 (h) is a binary image of the PCA-TRX detection result. The dimension of the PCA-TRX reduced dimension is 20, and the inner and outer window sizes are 3×3 and 37×37, respectively. Figure 6 (i) is a binary image of the FrFT-TRX detection result, with a fractional order of 1 and inner and outer window sizes of 3×3 and 37×37; Figure 6 (j) is the binary image of the QMWT detection result. The dimension of the OCF-reduced image is 16, and the inner and outer window sizes are 3×3 and 31×31, respectively. Sub-image S Q-HLL The frequency band is generated through method 3, sub-image S Q-HHL Frequency band usage method 3 generates sub-image S Q-HLH The frequency band was generated using method 1, while the sub-image S Q-HHH The frequency band is generated using method 3. (Based on reference...) Figure 6 It is evident that anomalous targets in GRX, LRX, KRX, FrFE-RX, and FrFE-LRX are not as clear as those in OMWT, and the background compression capabilities of PCA-TRX and FrFT-TRX are not as good as those in QMWT.

[0096] Reference Figure 7 These are the 3D-ROC curves and their corresponding 2D ROC curves for eight detection methods in the Pavia dataset. The 2D(P) curve for QMWT... D P F The ROC curve was consistently higher than that of the comparison algorithm, 2-D(P) F The ROC curve is the lowest among all curves, indicating the strongest background compression capability.

[0097] Reference Figure 8 This is a separability plot of the eight detection methods in the Pavia dataset, derived from the reference... Figure 8 It is evident that the proposed QMWT is less separable than LRX, PCA-TRX, and FrFT-TRX, but its background compression capability is superior to the comparative algorithms.

[0098] Depend on Figure 6 , 7 As shown in Figure 8, for Pavia data, the QMWT method of this invention outperforms the seven comparative algorithms GRX, LRX, KRX, FrFE-RX, FrFE-LRX, PCA-TRX, and FrFT-TRX in overall detection performance.

[0099] The above are specific embodiments of the present invention and are not intended to limit the invention. The hyperspectral anomaly detection method based on wavelet transform quaternion matrices provided by the present invention is also applicable to the detection of other hyperspectral image anomalies. Some adjustments and optimizations may be made without departing from the spirit and scope of the present invention, and the scope of protection of the present invention shall be determined by the claims.

Claims

1. A hyperspectral anomaly detection method based on wavelet transform quaternion matrix, characterized in that: Includes the following steps: (1) The acquired hyperspectral images are processed using the optimal clustering framework to reduce the dimensionality of the original hyperspectral images and eliminate redundancy; (2) The hyperspectral image processed by the optimal clustering framework is transformed into an image by a three-dimensional wavelet transform. X WT It is then decomposed into eight sub-images, of which four high-frequency sub-images are HLL, HLH, HHL and HHH; and four low-frequency sub-images are LLL, LLH, LHL and LHH. (3) Replace the four sub-images HLL, HLH, HHL and HHH with quaternion matrices respectively to obtain a new overall image. X Q ; (4) The overall image obtained through the quaternion matrix X Q Perform 3D wavelet inverse transform on the data; (5) Reconstruct the image data obtained by wavelet inverse transform using a stacked autoencoder; (6) Use tensor RX to detect SAE reconstruction error and obtain the final detection result.

2. The hyperspectral anomaly detection method based on wavelet transform quaternion matrix according to claim 1, characterized in that... In step (3), replacing the four sub-images with higher frequencies in the spectral dimension using a quaternion matrix is ​​achieved through the following steps: For the four high-frequency sub-images HLL, HLH, HHL, and HHH in the spectral dimension, a quaternion matrix is ​​formed for each frequency band using the low-frequency sub-images in the spectral dimension. At least one component of the quaternion matrix is ​​the frequency band of the original high-frequency sub-image, and at the same time, at least one component of the quaternion matrix is ​​the frequency band of the corresponding low-frequency sub-image. X WT The four sub-images with high frequencies in the spectral dimension are used to form a quaternion matrix sub-image using formula (1): ； in, S M This is the quaternion matrix corresponding to the frequency band; a 1. a 2. a 3 and a 4 represents the weighting coefficient, each of which is 0.25, and their sum is 1; It refers to the frequency band.

3. The hyperspectral anomaly detection method based on wavelet transform quaternion matrix according to claim 2, characterized in that... High-frequency sub-image HLL, in the image X Q The frequency bands of the high-frequency sub-image in the spectral dimension are formed into a quaternion matrix in any of the following ways: Method 1: ; or Method 2: ; or Method 3: ; in S WT-LLL yes X WT The frequency bands of the low-frequency sub-image in the spectral dimension. S WT-HLL yes X WT The frequency band of the high-frequency sub-image in the spectral dimension.

4. The hyperspectral anomaly detection method based on wavelet transform quaternion matrix according to claim 2, characterized in that... High-frequency sub-image HHL, in the image X Q The frequency bands of the high-frequency sub-image in the spectral dimension are formed into a quaternion matrix in any of the following ways: Method 1: ; or Method 2: ; or Method 3: ; in S WT-LHL yes X WT The frequency bands of the low-frequency sub-image in the spectral dimension. S WT-HHL yes X WT The frequency band of the high-frequency sub-image in the spectral dimension.

5. The hyperspectral anomaly detection method based on wavelet transform quaternion matrix according to claim 2, characterized in that... High-frequency sub-image HLH, in the image X Q The frequency bands of the high-frequency sub-image in the spectral dimension are formed into a quaternion matrix in any of the following ways: Method 1: ; or Method 2: ; or Method 3: ; in S WT-LLH yes X WT The frequency bands of the low-frequency sub-image in the spectral dimension. S WT-HLH yes X WT The frequency band of the high-frequency sub-image in the spectral dimension.

6. The hyperspectral anomaly detection method based on wavelet transform quaternion matrix according to claim 2, characterized in that... High-frequency sub-image HHH, in the image X Q The frequency bands of the high-frequency sub-image in the spectral dimension are formed into a quaternion matrix in any of the following ways: Method 1: ; or Method 2: ; or Method 3: ; in S WT-LHH yes X WT The frequency bands of the low-frequency sub-image in the spectral dimension. S WT-HHH yes X WT The frequency band of the high-frequency sub-image in the spectral dimension.

Images