Hyperspectral anomaly detection method based on wavelet transform quaternion matrix

Abstract

The invention provides a hyperspectral anomaly detection method based on a wavelet transform quaternion matrix, and relates to a hyperspectral image target detection method. The method comprises the following steps of: firstly, processing a hyperspectral image by using an optimal clustering framework, reducing the dimension of the hyperspectral image and eliminating redundancy, then carrying out one-layer three-dimensional wavelet transform on the hyperspectral image to form an image XWT, and decomposing and converting the image XWT into eight sub-images; the method comprises the steps that firstly, a quaternion matrix is used for replacing four subimages with the high frequency in the spectral dimension to obtain a new overall image XQ, then, 3-D wavelet inverse transformation is conducted on data of the overall image XQ, image data obtained through wavelet inverse transformation is reconstructed through a stacked auto-encoder, finally, SAE reconstruction errors are detected through tensor RX, and a final detection result is obtained. The method has the advantages that original hyperspectral image characteristics can be better reserved, high-frequency and low-frequency information can be better analyzed, and original information can be better reserved.

Description

Technical Field

[0001] The present invention relates to a hyperspectral image target detection method, and in particular to a hyperspectral image abnormal target detection method based on wavelet transform quaternion matrix. Background Art

[0002] As a three-dimensional dataset, hyperspectral images have two spatial dimensions and one spectral dimension, with hundreds of spectral bands in the spectral dimension. The rich spectral information provided by hundreds of spectral bands and the increasingly high spatial resolution make hyperspectral images widely used in identifying ground objects. Anomaly detection is the most widely used application of hyperspectral images. The most classic algorithms are RX and local RX, both of which are based on test point vectors. However, anomalies usually contain multiple pixels. Therefore, using only pixel point vectors has a negative impact on 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 to detect multi-pixel anomaly targets without prior information. Tensor RX (TRX), as a tensor version of local RX, is based on test point tensors instead of test point vectors, which can better utilize the spatial information of anomaly targets. 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, and FrFE-RX performs the RX algorithm in the fractional Fourier domain.

[0003] The above algorithms make full use of the spectral information of hyperspectral images. However, hyperspectral images have rich spectral information and also have a lot of redundant information. Removing redundant information can reduce interference and improve detection accuracy and efficiency. Dimensionality reduction is a standard preprocessing method used to eliminate spectral redundancy. Principal component analysis (PCA), as the most classic dimensionality reduction method, is a linear mapping and cannot accurately extract hyperspectral images with inherent nonlinear characteristics. Band selection is also one of the main methods of dimensionality reduction. It selects a set of representative bands in hyperspectral images without modifying the original data, which makes the reduced data more interpretable. The optimal clustering framework (OCF), as a band selection method, develops the optimal clustering structure in hyperspectral images and selects representative bands based on the cluster ranking strategy. In addition, the application of deep learning (DL) theory in hyperspectral image processing has also received widespread attention. Deep learning can extract deep features of hyperspectral images and achieve dimensionality reduction. Deep belief network (DBN) and stacked autoencoder (SAE) models are unsupervised learning models that are commonly used for feature extraction, dimensionality reduction, and reconstruction. However, deep learning models involve a large number of parameters and require a lot of tuning work. In addition, a large amount of calculations also requires high hardware device configuration.

[0004] In recent years, abnormal target detection in hyperspectral images based on spatial-spectral joint features has become one of the research hotspots. Compared with the rich spectral information of hyperspectral images, the expression of spatial and geometric information is weak. As a signal analysis tool, wavelet transform (WT) provides a method to analyze 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 sub-images and low-frequency sub-images. The background of a hyperspectral image corresponds to low-frequency information, while the abnormal target corresponds to high-frequency information. Therefore, wavelet transform can be applied to abnormal target detection in hyperspectral images. However, in recent years, there have been few studies on this topic. In addition to the above-mentioned spatial-spectral joint features, the fusion of multiple features to improve detection accuracy and algorithm versatility has also attracted widespread attention. In addition to the traditional weighted method, the fusion method using quaternion matrix can also perform multi-scale and multi-feature processing in parallel, and has recently been applied to hyperspectral image processing. Summary of the invention

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

[0006] A hyperspectral anomaly detection method based on wavelet transform quaternion matrix of the present invention is characterized by comprising the following steps:

[0007] (1) The acquired hyperspectral images are processed using the optimal clustering framework (OCF) to reduce the dimension 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 through a layer of three-dimensional wavelet transformation WT , and decomposed and converted into eight sub-images, of which the four high-frequency sub-images are HLL, HLH, HHL and HHH; the four low-frequency sub-images are LLL, LLH, LHL and LHH;

[0009] (3) Use quaternion matrices to replace the four sub-images HLL, HLH, HHL and HHH with higher frequencies in the spectral dimension, and obtain a new overall image X Q ;

[0010] (4) The overall image X obtained by the quaternion matrix Q The data were subjected to 3-D inverse wavelet transform;

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

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

[0013] As a further improvement of the present invention, the step (3) of replacing the four sub-images with higher frequencies in the spectral dimension with the quaternion matrix is ​​achieved by 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-image in the spectral dimension, at least one component of the quaternion matrix is ​​the frequency band of the original spectral high-frequency sub-image, and at least one component of the quaternion matrix is ​​the frequency band of the spectral low-frequency sub-image corresponding to the spectral high-frequency sub-image; in X WT The four sub-images with high frequencies in the spectral dimension of are formed into quaternion matrix sub-images using formula (1):

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

[0016] Among them, S M is the quaternion matrix of the corresponding frequency band; a1, a2, a3 and a4 are weight coefficients, all of which are 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 frequency bands.

[0017] As a further improvement of the present invention, the 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 by any of the following methods:

[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 Yes X WT The frequency band of the low-frequency sub-image in the spectral dimension, S WT-HLL Yes X WT Frequency bands 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 is Q The frequency bands of the high-frequency sub-image in the spectral dimension are formed into a quaternion matrix by any of the following methods:

[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 Yes X WT The frequency band 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.

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

[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 Yes X WT The frequency band of the low-frequency sub-image in the spectral dimension, S WT-HLH Yes X WT Frequency bands 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 the image X Q The frequency bands of the high-frequency sub-image in the spectral dimension are formed into a quaternion matrix by any of the following methods:

[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 Yes X WT The frequency band of the low-frequency sub-image in the spectral dimension, S WT-HHH Yes X WT Frequency bands of the high-frequency sub-image in the spectral dimension.

[0045] The advantages of the present invention are:

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

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

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

[0049] 4. In order to better utilize spatial characteristics, TRX replaces traditional RX and other methods to complete the final abnormal target detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is a schematic diagram of the first layer of three-dimensional wavelet decomposition;

[0051] Figure 2 It is the flowchart of the proposed quaternion matrix wavelet transform (QMWT) algorithm;

[0052] Figure 3 This is a binary image of the Los Angeles data and the detection results of 8 detection methods, where Figure 3 (a) is the 100th band map of Los Angeles data. Figure 3 (b) is a schematic diagram of the actual distribution of objects in Los Angeles 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 local RX algorithm detection result. Figure 3 (e) is the binary image of the detection result of KRX algorithm. Figure 3 (f) is the binary image of the detection result of FrFE-RX algorithm. Figure 3 (g) is the binary image of the detection result of FrFE-LRX algorithm. Figure 3 (h) is the binary image of the detection result of PCA-TRX algorithm. Figure 3 (i) is the binary image of the detection result of FrFT-TRX algorithm, Figure 3 (j) is the binary image of the detection result of QMWT algorithm;

[0053] Figure 43D-ROC curves of 8 detection methods for Los Angeles data;

[0054] Figure 5 This is the separability graph of 8 detection methods for Los Angeles data;

[0055] Figure 6 is the binary image of the Pavia data and the detection results of 8 detection methods, where Figure 6 (a) is the 100th band diagram of Pavia data. Figure 6 (b) is a schematic diagram of the actual distribution of objects in the 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 local RX algorithm detection result. Figure 6 (e) is the binary image of the detection result of KRX algorithm. Figure 6 (f) is the binary image of the detection result of FrFE-RX algorithm. Figure 6 (g) is the binary image of the detection result of FrFE-LRX algorithm. Figure 6 (h) is the binary image of the detection result of PCA-TRX algorithm. Figure 6 (i) is the binary image of the detection result of FrFT-TRX algorithm, Figure 6 (j) is the binary image of the detection result of QMWT algorithm;

[0056] Figure 7 3D-ROC curves of 8 detection methods for Pavia data;

[0057] Figure 8 Separability diagram of 8 detection methods for Pavia data. DETAILED DESCRIPTION

[0058] The hyperspectral anomaly detection method based on wavelet transform quaternion matrix of the present invention is implemented by the following steps:

[0059] Step 1: To avoid modifying the original data, the acquired hyperspectral image is processed using the optimal clustering framework (OCF) to reduce the dimension of the original hyperspectral image and eliminate redundancy;

[0060] Step 2: In order to better process the high-frequency and low-frequency information of the hyperspectral image and further remove noise and spectral redundant information, the hyperspectral image after OCF is transformed through a layer of three-dimensional wavelet transform to form image X WT , decomposition is transformed into eight sub-images, namely LLL, LLH, LHL, LHH, HLL, HLH, HHL and HHH;

[0061] Step 3: In the high-frequency sub-image, in addition to abnormal information, there will be noise and redundant information. The four sub-images with higher frequencies in the spectral dimension are replaced by quaternion matrices respectively; the details of the quaternion matrix formation are as follows: for the four sub-images HLL, HLH, HHL and HHH with high frequencies in the spectral dimension, in order to further reduce the spectral redundant information, the sub-images with lower frequencies 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 spectral high-frequency sub-image band; at the same time, in order to further eliminate redundancy, at least one component of the quaternion matrix is ​​the frequency band of the spectral low-frequency sub-image corresponding to the spectral high-frequency sub-image. For the four sub-images with low frequencies in the spectral dimension, LLL, LLH, LHL and LHH contain the main information of 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: In order to better distinguish the background and abnormal targets, the image data obtained by inverse wavelet transform is reconstructed using stacked autoencoders (SAE);

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

[0065] The present invention is described in more detail below with reference to the accompanying drawings, using real hyperspectral image Los Angeles data and Pavia data as examples:

[0066] Reference Figure 1 , is a schematic diagram of the first layer of 3D 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 number "1" represents the first layer of decomposition. Similar to the 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) of the image sequence details at different resolutions.

[0067] Reference Figure 2 , Flowchart of the proposed QMWT algorithm. First, the test hyperspectral image X = {x i ∈R D , i=1,…,N} (N is the number of test points in the hyperspectral image, D is the spectral dimension) through OCF dimensionality reduction. Secondly, the obtained low-dimensional hyperspectral image X OCF ={x i ∈R B, for \(i = 1,\ldots,N\) (\(B < D\)) are decomposed into 8 sub-images through a 3-D wavelet transform. Subsequently, for the four high-frequency sub-images HLL, HLH, HHL, and HHH in the spectral dimension, in order to further reduce spectral redundant information, the low-frequency sub-image in the spectral dimension is used to form a quaternion matrix for each frequency band. To avoid losing too much high-frequency information, at least one component of the quaternion matrix is the original spectral high-frequency sub-image band. At the same time, to further eliminate redundancy, at least one component of the quaternion matrix is the frequency band of the spectral low-frequency sub-image corresponding to the spectral high-frequency sub-image. In X WT The four sub-images with high frequency in the spectral dimension of X Q ;

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

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

[0070] Taking the frequency band of HLL as an example below, using formula (1), according to the characteristics of the test hyperspectral image, let S1 be the frequency band of HLL, S4 be the frequency band of LLL, and S2 and S3 correspond to the frequency bands of HLL or LLL. 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. The quaternion matrix S Q-HLL , that is, in the image X Q For the frequency bands of the high-frequency sub-images in the spectral dimension, there are the following three ways to form a quaternion matrix. When using, choose any one according to the characteristics of the image data:

[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 Yes X WT The frequency band of the low-frequency sub-image in the spectral dimension, S WT-HLL Yes X WT Frequency bands 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 for the frequency band of the high-frequency sub-image in the spectral dimension. When using it, 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 Yes X WT The frequency band 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.

[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 for the frequency band of the high-frequency sub-image in the spectral dimension. When using it, 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 Yes X WT The frequency band of the low-frequency sub-image in the spectral dimension, S WT-HLH Yes X WT Frequency bands of the high-frequency sub-image in the spectral dimension.

[0085] Similarly, for the HHH band, its quaternion matrix S Q-HHH , that is, in image X Q There are three ways to form a quaternion matrix for the frequency band of the high-frequency sub-image in the spectral dimension. When using it, 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 Yes X WT The frequency band of the low-frequency sub-image in the spectral dimension, S WT-HHH Yes X WT Frequency bands 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 by the quaternion matrix Q Perform three-dimensional wavelet inverse transform to obtain X IW Next, in order to better distinguish the background from the abnormal targets, SAE IW Rebuild to get 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 , which is a binary map of Los Angeles data and the detection results of 8 detection methods. Los Angeles data is Los Angeles airport data obtained by 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 map of Los Angeles data; Figure 3 (b) is a schematic diagram of the actual distribution of objects in Los Angeles data; Figure 3 (c) is the binary image of the global RX detection result; Figure 3 (d) is the 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 KRX detection result, the kernel parameter is 10 -5 , the inner and outer window sizes are 5×5 and 9×9; Figure 3 (f) is the binary image of the FrFE-RX detection result, with a fractional order of 0.2; Figure 3 (g) is the binary image of the FrFE-LRX detection result, the fractional order is 0.2, and the inner and outer window sizes are 7×7 and 9×9; Figure 3 (h) is a binary image of the PCA-TRX detection result. The dimension after PCA dimension reduction is 10, and the inner and outer window sizes are 7×7 and 9×9; Figure 3 (i) is the binary image of the FrFT-TRX detection result, the fractional order is 0.2, and the inner and outer window sizes are 7×7 and 9×9; Figure 3 (j) is a binary image of the QMWT detection result. The dimension after OCF dimension reduction is 19, and the inner and outer window sizes are 3×3 and 25×25; sub-image S Q-HLL The frequency band is generated by method 3, and the sub-image S Q-HHL The frequency band is generated using method 3, and the sub-image S Q-HLH The frequency band of is generated using method 2, and the sub-image S Q-HHHThe frequency band is generated by method 1. Figure 3 It can be seen that the binary image clarity of the detection result of the proposed QMWT method is higher than Figure 3 (b)-7 comparison methods of 3(i).

[0092] Reference Figure 4 , which are the 3D-ROC curves of the 8 detection methods in Los Angeles data and their corresponding 2-D ROC curves. D , P F )ROC curves are always higher than those of the comparison algorithms. Except for KRX, QMWT’s 2-D (P D , τ)ROC lines are higher than those of the comparison algorithms. F ,τ)ROC curve, the lower the curve, the stronger the background compression ability, and the height of the OMWT curve is moderate.

[0093] Reference Figure 5 , is the separability graph of the 8 detection methods for Los Angeles data, from the reference Figure 5 It can be seen that the separability of the target and background of the proposed QMWT algorithm is better than that of the other seven tested algorithms.

[0094] Depend on Figure 3 , 4 As shown in Figure 5, for the Los Angeles data, the detection effect of the QMWT method of the present invention is better than that of the seven comparison algorithms, namely GRX, LRX, KRX, FrFE-RX, FrFE-LRX, PCA-TRX and FrFT-TRX.

[0095] The superiority of the present invention is further verified by using Pavia data. Figure 6 It is a binary image of the Pavia data and the detection results of 8 detection methods. The Pavia data is obtained by 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 map of Pavia data; Figure 6 (b) is a schematic diagram of the actual distribution of objects in the Pavia data; Figure 6 (c) is the binary image of the global RX detection result; Figure 6 (d) is the 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 KRX detection result, the kernel parameter is 10 -1 , the inner and outer window sizes are 25×25 and 29×29; Figure 6 (f) is the binary image of the FrFE-RX detection result, with a fractional order of 1; Figure 6 (g) is the binary image of the FrFE-LRX detection result, the fractional order is 1, and the inner and outer window sizes are 25×25 and 77×77; Figure 6 (h) is a binary image of the PCA-TRX detection result. The dimension after PCA dimension reduction is 20, and the inner and outer window sizes are 3×3 and 37×37; Figure 6 (i) is the binary image of the FrFT-TRX detection result, the fractional order is 1, and the inner and outer window sizes are 3×3 and 37×37; Figure 6 (j) is a binary image of the QMWT detection result. The dimension after OCF dimensionality reduction is 16, and the inner and outer window sizes are 3×3 and 31×31; sub-image S Q-HLL The frequency band is generated by method 3, and the sub-image S Q-HHL The frequency band is generated using method 3, and the sub-image S Q-HLH The frequency band of is generated using method 1, and the sub-image S Q-HHH The frequency band is generated by method 3. Figure 6 It can be seen that the abnormal 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 of QMWT.

[0096] Reference Figure 7 , are the 3D-ROC curves of the 8 detection methods of Pavia data and their corresponding 2-D ROC curves. D , P F )ROC curve is always higher than the curve of the comparison algorithm, 2-D (P F ,τ)ROC curve is the lowest among all the curves, indicating that the background compression ability is the strongest.

[0097] Reference Figure 8 , is the separability graph of the eight detection methods for Pavia data, referred to Figure 8 It can be seen that the separability of the proposed QMWT is not as good as that of LRX, PCA-TRX and FrFT-TRX, but its background compression ability is worse than the comparison algorithms.

[0098] Depend on Figure 6 , 7 As shown in Figure 8, for Pavia data, the detection effect of the QMWT method of the present invention is better than that of the seven comparison algorithms, namely GRX, LRX, KRX, FrFE-RX, FrFE-LRX, PCA-TRX and FrFT-TRX.

[0099] The above is a specific embodiment of the present invention and is not intended to limit the present invention. The hyperspectral anomaly detection method based on wavelet transform quaternion matrix provided by the present invention is also applicable to other hyperspectral image abnormal target detection. Without departing from the essence and scope of the present invention, some adjustments and optimizations can be made, and the protection scope of the present invention shall be subject to the claims.

Claims

1. A hyperspectral anomaly detection method based on wavelet transform quaternion matrix, characterized by The following steps are involved: (1) The acquired hyperspectral images are processed using an 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 image X through a layer of three-dimensional wavelet transform. WT , and decomposed and converted into eight sub-images, of which the four high-frequency sub-images are HLL, HLH, HHL and HHH; the four low-frequency sub-images are LLL, LLH, LHL and LHH; (3) Use quaternion matrices to replace the four sub-images HLL, HLH, HHL and HHH with higher frequencies in the spectral dimension, and obtain a new overall image X Q ; (4) The overall image X obtained by the quaternion matrix Q The data were subjected to 3-D inverse wavelet transform; (5) Reconstruct the image data obtained by inverse wavelet transform using stacked autoencoders; (6) Use tensor RX to detect the 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 is characterized in that In step (3), replacing the four sub-images with higher frequencies in the spectral dimension with the quaternion matrix is ​​achieved by 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-image in the spectral dimension, at least one component of the quaternion matrix is ​​the original spectral high-frequency sub-image band, and at least one component of the quaternion matrix is ​​the frequency band of the spectral low-frequency sub-image corresponding to the spectral high-frequency sub-image; in X WT The four sub-images with high frequencies in the spectral dimension of are formed into quaternion matrix sub-images using formula (1): S M =a1S1+a2S2×i+a3S3×j+a4S4×k (1) Among them, S M is the quaternion matrix of the corresponding frequency band; a1, a2, a3 and a4 are weight coefficients, all of which are 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 frequency bands.

3. The hyperspectral anomaly detection method based on wavelet transform quaternion matrix according to claim 2 is characterized in that 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 by any of the following methods: Method 1: S Q-HLL =a1S WT-HLL +a2S WT-LLL ×i+a3S WT-LLL ×j+a4S WT-LLL ×k or Method 2: S Q-HLL =a1S WT-HLL +a2S WT-HLL ×i+a3S WT-LLL ×j+a4S WT-LLL ×k or Method 3: S Q-HLL =a1S WT-HLL +a2S WT-HLL ×i+a3S WT-HLL ×j+a4S WT-LLL ×k Where S WT-LLL Yes X WT The frequency band of the low-frequency sub-image in the spectral dimension, S WT-HLL Yes X WT Frequency bands 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 is characterized in that 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 by any of the following methods: Method 1: S Q-HHL =a1S WT-HHL +a2S WT-LHL ×i+a3S WT-LHL ×j+a4S WT-LHL ×k or Method 2: S Q-HHL =a1S WT-HHL +a2S WT-HHL ×i+a3S WT-LHL ×j+a4S WT-LHL ×k or Method 3: S Q-HHL =a1S WT-HHL +a2S WT-HHL ×i+a3S WT-HHL ×j+a4S WT-LHL ×k Where S WT-LHL Yes X WT The frequency band 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 is characterized in that 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 by any of the following methods: Method 1: S Q-HLH =a1S WT-HLH +a2S WT-LLH ×i+a3S WT-LLH ×j+a4S WT-LLH ×k or Method 2: S Q-HLH =a1S WT-HLH +a2S WT-HLH ×i+a3S WT-LLH ×j+a4S WT-LLH ×k or Method 3: S Q-HLH =a1S WT-HLH +a2S WT-HLH ×i+a3S WT-HLH ×j+a4S WT-LLH ×k Where S WT-LLH Yes X WT The frequency band of the low-frequency sub-image in the spectral dimension, S WT-HLH Yes X WT Frequency bands 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 is characterized in that 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 by any of the following methods: Method 1: S Q-HHH =a1S WT-HHH +a2S WT-LHH ×i+a3S WT-LHH ×j+a4S WT-LHH ×k or Method 2: S Q-HHH =a1S WT-HHH +a2S WT-HHH ×i+a3S WT-LHH ×j+a4S WT-LHH ×k or Method 3: S Q-HHH =a1S WT-HHH +a2S WT-HHH ×i+a3S WT-HHH ×j+a4S WT-LHH ×k Where S WT-LHH Yes X WT The frequency band of the low-frequency sub-image in the spectral dimension, S WT-HHH Yes X WT Frequency bands of the high-frequency sub-image in the spectral dimension.

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