Hyperspectral anomaly detection method based on residual learning and background estimation

Abstract

The embodiment of the application discloses a hyperspectral anomaly detection method based on residual learning and background estimation, and the method comprises the following steps: obtaining a reconstructed hyperspectral background through a background estimation method; performing down-sampling on the reconstructed hyperspectral background through two different filters to obtain two down-sampled hyperspectral images; training a network based on the two down-sampled hyperspectral images through a background loss of cross approximation; inputting a hyperspectral image into the loss training network to perform anomaly component prediction, obtaining an anomaly component, and then calculating an anomaly detection result by using a Mahalanobis distance.

Description

Technical Field

[0001] This invention relates to the field of hyperspectral anomaly detection technology, and in particular to a hyperspectral anomaly detection method based on residual learning and background estimation. Background Technology

[0002] Hyperspectral images (HSI) acquired by remote sensing systems contain scene information across hundreds of continuous spectral bands, spanning the ultraviolet, visible, and infrared wavelengths. The rich spectral information in hyperspectral images facilitates the differentiation of various targets of interest through spectral features. Therefore, hyperspectral images are widely used in target detection.

[0003] The purpose of hyperspectral anomaly detection is to distinguish pixels that differ from their surrounding background in both spatial and spectral dimensions, in the absence of prior spectral information. This technology has been widely applied in fields such as resource exploration, environmental monitoring, and precision agriculture. Despite its unique advantages, hyperspectral anomaly detection still faces various challenges in practical applications, such as the lack of prior information and complex background categories.

[0004] Over the past few decades, numerous hyperspectral anomaly detection methods have emerged. Existing hyperspectral anomaly detection methods can be broadly categorized into two types: traditional methods and deep learning-based methods. Traditional methods include statistical methods and data representation-based methods. Among statistical methods, one representative approach is the well-known Reed-Xiaoli (RX) method. It assumes the background follows a multivariate Gaussian distribution and detects anomalies by calculating the Mahalanobis distance between the tested pixel and the background pixels. However, in real hyperspectral images, the mean and covariance used in the RX method are easily affected by anomalous pixels. This factor impacts the detection performance of the RX method. Therefore, based on this problem, researchers have proposed methods such as Local RX and Kernel RX. Data representation-based methods assume that the test pixel can be represented by several similar pixels. Among them, the Co-representation Detector assumes that each background pixel can be approximated by its neighboring pixels, while anomalies cannot (be approximated by neighboring pixels). Low-rank and sparse representation detectors assume the background is low-rank and the anomalies are sparse. Their goal is to construct low-rank and sparse matrices. To preserve the three-dimensional information of hyperspectral images, a vector low-rank sparse representation method is used instead of the traditional two-dimensional low-rank sparse representation to reconstruct the background. Traditional methods have been successfully applied due to their high execution efficiency. However, due to the complexity of the background in real hyperspectral images, statistical methods struggle to accurately assess background statistical features, which affects anomaly detection performance. Data representation-based methods also struggle to construct accurate background dictionaries, impacting the accuracy of background reconstruction. Summary of the Invention

[0005] Therefore, it is necessary to propose a hyperspectral anomaly detection method based on residual learning and background estimation to address the above problems.

[0006] A hyperspectral anomaly detection method based on residual learning and background estimation, the method comprising:

[0007] The reconstructed hyperspectral background was obtained using a background estimation method.

[0008] The reconstructed hyperspectral background is downsampled using two different filters to obtain two downsampled hyperspectral images;

[0009] The network is trained based on the two downsampled hyperspectral images using a cross-approximation background loss.

[0010] The input hyperspectral image is fed into a loss training network to predict anomalous components, and the Mahalanobis distance is then used to calculate the anomaly detection result.

[0011] In the above scheme, obtaining the reconstructed hyperspectral background through the background estimation method specifically includes:

[0012] Each band of the input hyperspectral image HSI Y is convolved with the j-th non-center convolution kernel c. j Perform convolution, convolution feature map pass Obtain; among them, It is the image of the o-th spectral band in the hyperspectral image;

[0013] The local spectral similarity score of the hyperspectral image is obtained through... Determine; in the formula, Let represent the j-th local spectral similarity score of HSI.

[0014] The maximum value among the local spectral similarity scores is taken as the background number.

[0015] The background data G is binarized to extract the clean background HSI.

[0016] In the above scheme, the binarization operation on the background data G to extract clean original background data specifically includes:

[0017] The values ​​in G are sorted in ascending order using the sort(.) function to obtain a ranking score vector: R = sort(G);

[0018] Binarize G Among them, E m,n G represents the background number at position (m,n) in binarization. m,nHere, G is the background number at position (m,n), T is the background ratio threshold, and [.] is the upper bound function, r [T·M·N] In R, it is the [T·M·N]th element;

[0019] Reconstructed hyperspectral background Calculated as

[0020] Where m and n represent two-dimensional spatial coordinates, m = 1, 2, ..., M, n = 1, 2, ..., N, in binary format. The hyperspectral image reconstructed from the spectral pixels at position (m, n) This represents the spectral pixels of the input hyperspectral image at position (m, n). Let represent the mean background spectrum of the neighborhood centered at (m, n).

[0021] In the above scheme, the background spectrum average vector The calculation is as follows: Where U represents the set of spectral pixels between the outer window and the inner window centered at (m, n), and W represents the number of spectral pixels in the set U.

[0022] In the above scheme, the reconstructed hyperspectral background is processed using two different filters. Downsampling was performed to obtain two downsampled hyperspectral background images. and Specifically, it includes:

[0023] For the reconstructed hyperspectral background of the input Two downsampled hyperspectral images are obtained by performing a convolution operation with a stride of 2 using two fixed downsampling filters v1 and v2.

[0024] in, This represents a convolution operation with a stride of 2.

[0025] In the above scheme, the input hyperspectral image is fed into a lightweight network based on residual learning to predict anomalous components and obtain anomalous component A, specifically including:

[0026] The anomalous components are determined according to A = f(Y; θ), where A represents the predicted anomalous result of the input HSI. A1 and A2 represent the anomalous components predicted by a lightweight network based on residual learning for the downsampled hyperspectral images Y1 and Y2, respectively.

[0027] In the above scheme, the input hyperspectral image is fed into the training network, and the input HSIY is downsampled using a pair of downsamplers to obtain HSIY1 and HSIY2, specifically including:

[0028]

[0029] in, This represents a convolution operation with a stride of 2.

[0030] In the above scheme, the input hyperspectral image is fed into a loss training network to predict anomalous components, specifically including:

[0031] Two 3×3 convolutional layers are used to extract spatial-spectral features from HSI;

[0032] A 1×1 convolutional layer is used to fine-tune the learned spectral information;

[0033] For the i-th layer feature F i The output feature F after the convolutional layer i+1 Represented as F i+1 =max(α) slope ×Z i+1 Z i+1 ), i = 1, 2, 3.; where w i and b i These represent the weights and biases of the i-th layer, respectively. Z represents the convolution operation. i+1 α represents the output of the i-th convolutional layer. slope The parameter represents the slope of the negative axis.

[0034] In the above scheme, the background loss is expressed as:

[0035]

[0036] Consistency loss can be expressed as:

[0037] Predicting Background D A1 D A2 Represented as:

[0038] D A1 =Y1-A1

[0039] D A2 =Y2-A2;

[0040] Background prediction X obtained by downsampling D1 X D2 Represented as

[0041] X D1 =D1(YA)

[0042] X D2 =D2(YA),

[0043] D1(.) and D2(.) represent downsampling operations using filters v1 and v2, respectively.

[0044] In the above scheme, the calculation of anomaly detection results using Mahalanobis distance to a lightweight network based on residual learning specifically includes:

[0045] According to D(a) j )=(a j -ξ) T Λ -1 (a j -ξ) Calculate the anomaly detection results; where, a in j This represents the pixel spectrum of the predicted outlier component A at location j. and In the equation, A represents the global mean vector and the inverse covariance matrix of the entire predicted anomaly component, and D represents the anomaly detection result.

[0046] The embodiments of the present invention have the following beneficial effects:

[0047] This invention employs a background estimation method based on non-centered convolutional kernels to calculate the pseudo-background, uses the difference between the pseudo-background and the hyperspectral image to obtain the anomalous component, reconstructs the anomalous component using the proposed lightweight convolutional neural network based on residual learning, and finally calculates the anomaly detection result based on the predicted anomalous component using Mahalanobis distance. Attached Figure Description

[0048] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0049] in:

[0050] Figure 1 This is a framework diagram of a hyperspectral anomaly detection method based on residual learning and background estimation provided by an embodiment of the present invention;

[0051] Figure 2 This invention provides a schematic diagram of a non-centered convolutional kernel in a hyperspectral anomaly detection method based on residual learning and background estimation, as provided in an embodiment of the invention.

[0052] Figure 3 This is a schematic diagram of pairwise downsampling in a hyperspectral anomaly detection method based on residual learning and background estimation, provided in an embodiment of the present invention.

[0053] Figure 4 The pseudo-color images and baseline ground truth values ​​for five datasets are: (a) WHU-Hi-River (b) Pavia (c) Texas Coast (d) San Diego I (e) San Diego II.

[0054] Figure 5 Comparison of anomaly detection results of different methods on five datasets: (a) WHU-Hi-River (b) Pavia (c) Texas Coast (d) San Diego I (e) San Diego II;

[0055] Figure 6 3D-ROC curves for different algorithms on five datasets: (a) WHU-Hi-River, (b) Pavia, (c) Texas Coast, (d) San Diego I, (e) San Diego II;

[0056] Figure 7 The 2DROC (detection rate, false alarm rate) curves for five datasets are: (a) WHU-Hi-River, (b) Pavia, (c) Texas Coast, (d) San Diego I, and (e) San Diego II.

[0057] Figure 8 2DROC (detection rate, threshold) curves for five datasets: (a) WHU-Hi-River, (b) Pavia, (c) Texas Coast, (d) San Diego I, (e) San Diego II;

[0058] Figure 9 The 2DROC (false alarm rate, threshold) curves for five datasets are: (a) WHU-Hi-River, (b) Pavia, (c) Texas Coast, (d) San Diego I, and (e) San Diego II. Detailed Implementation

[0059] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0060] This invention provides a hyperspectral anomaly detection method based on residual learning and background estimation, the method comprising:

[0061] Step 101: Obtain the reconstructed hyperspectral background using a background estimation method;

[0062] Specifically, this application proposes a three-layer lightweight CNN, such as... Figure 1 As shown, this network is used to learn anomalies rather than background.

[0063] First, the mathematical model for the hyperspectral image Y is:

[0064] Y = X + A

[0065] in, It is an input hyperspectral image. It is the background matrix. is the anomaly matrix, M and N are the spatial dimensions of the input HSI, and B is the number of spectral bands in the input hyperspectral image of the input HSI.

[0066] Compared to reconstructing complex backgrounds, directly learning anomalous features through CNNs is more efficient and requires fewer parameters. Therefore, a proposed lightweight CNN method is used to reconstruct anomalous components. The reconstruction process can be represented as follows:

[0067] A = f(Y; θ)

[0068] In the formula, f(·) is the function that the lightweight CNN needs to fit, and θ is the set of parameters that need to be optimized in the lightweight CNN.

[0069] Specifically, the proposed lightweight CNN consists of three convolutional layers. Its architecture is as follows: Figure 1 As shown, two 3×3 convolutional layers are used to extract spatial-spectral features from HSI. Then, a 1×1 convolutional layer is used to fine-tune the learned spectral information. For the i-th layer feature F... i The output feature F after the convolutional layer i+1 It can be represented as

[0070]

[0071]

[0072] Where w i and b i Let represent the weights and biases of the i-th layer, respectively. Z represents the convolution operation. i+1 This represents the output of the i-th convolutional layer. Equation 4 defines the activation function, using the LeakyReLU function, α. slope The parameter represents the slope of the negative axis. In the experiment, α slope =0.2. F1 = Y, F4 are the reconstructed hyperspectral anomaly components.

[0073] Non-central convolution kernels such as Figure 2 As shown. Edge or corner pixels of the kernel are used as test pixels. This way, information from one side of the test pixel is considered for each convolution kernel. By integrating information from all eight non-center convolution kernels, image details can be preserved to the maximum extent. To improve the efficiency of the proposed method, fixed weights are applied to the convolutions. The weights of the convolution kernels are as follows: Figure 2 As shown in (d).

[0074] Each band of the input hyperspectral image HSI Y is convolved with the j-th non-center convolution kernel c. j Perform convolution, convolution feature map pass Obtain; among them, It is the image of the o-th spectral band in the hyperspectral image;

[0075] The local spectral similarity score of the hyperspectral image is obtained through... Determine; in the formula, Let represent the j-th local spectral similarity score of HSI.

[0076] The maximum value among the local spectral similarity scores is taken as the background number.

[0077] The background data G is binarized to extract the clean background HSI.

[0078] The values ​​in G are sorted in ascending order using the sort(.) function to obtain a ranking score vector: R = sort(G);

[0079] Binarize G Among them, E m,n G represents the background number at position (m,n) in binarization. m,n Here, G is the background number at position (m,n), T is the background ratio threshold, and [.] is the upper bound function, r [T·M·N] In R, it is the [T·M·N]th element;

[0080] To obtain a clean hyperspectral image of the background, a dual-window-based background rendering method was employed. The dual-window-based background rendering method is as follows: Figure 2 As shown. In the background values, larger scores are associated with background locations, while smaller scores are associated with anomaly locations. Reconstructed hyperspectral background. Calculated as Where m and n represent two-dimensional spatial coordinates, m = 1, 2, ..., M, n = 1, 2, ..., N, in binary format. The hyperspectral image reconstructed from the spectral pixels at position (m, n) This represents the spectral pixels of the input hyperspectral image at position (m, n). Let represent the mean background spectrum of the neighborhood centered at (m, n).

[0081] A clean background HSI is obtained through background estimation methods and used to support the subsequent training process.

[0082] The background spectrum average vector The calculation is as follows: Where U represents the set of spectral pixels between the outer window and the inner window centered at (m, n), and W represents the number of spectral pixels in the set U.

[0083] Step 102: Downsample the reconstructed hyperspectral background using two different filters to obtain two downsampled hyperspectral images;

[0084] Specifically, the proposed downsampling method, such as Figure 3 As shown. For the input background hyperspectral image, make Using two fixed downsampling filters v1 and v2 Perform a convolution operation with a stride of 2 on the input. For the reconstructed hyperspectral background... Two downsampled hyperspectral images are obtained by performing a convolution operation with a stride of 2 using two fixed downsampling filters v1 and v2.

[0085] in, This represents a convolution operation with a stride of 2.

[0086] The anomalous components are determined according to A = f(Y; θ), where A represents the predicted anomalous result of the input HSI. A1 and A2 represent the anomalous components predicted by a lightweight network based on residual learning for the downsampled hyperspectral images Y1 and Y2, respectively.

[0087] The input hyperspectral image will be fed into the training network. The input HSIY will be downsampled using a pair of downsamplers to obtain HSIY1 and HSIY2, specifically including:

[0088]

[0089] in, This represents a convolution operation with a stride of 2.

[0090] The input hyperspectral image Y and the downsampled hyperspectral images Y1 and Y2 are fed into the proposed lightweight CNN for training. After forward inference, their corresponding network outputs are obtained as follows:

[0091] A = f(Y; θ)

[0092] A1 = f(Y1; θ)

[0093] A2 = f(Y2; θ)

[0094] Where A represents the prediction result of the input HSI. A1 and A2 represent the prediction results of the downsampled hyperspectral images Y1 and Y2, respectively.

[0095] To further reduce the impact of anomalies and noise on the background, a background loss based on cross-approximation is proposed. After pairwise downsampling, the edges of the two downsampled hyperspectral images mainly face orthogonal directions. When mapping one hyperspectral image obtained through two different downsampling filters to the other downsampled background hyperspectral image, low-frequency background information is preserved in the background matrix, while high-frequency details are mainly in the predicted anomaly matrix; anomalies are generally considered to be high-frequency information. Through cross-approximation, as many anomalies as possible are assigned to the anomaly matrix, which is beneficial for anomaly detection tasks.

[0096] Background Prediction HSID A1 and D A2 It can be calculated as

[0097] D A1 =Y1-A1

[0098] D A2 =Y2-A2

[0099] Desired predicted background hyperspectral image D A1 It should be compared with the downsampled background hyperspectral image. A perfect match. Similarly, the predicted background hyperspectral image D... A2 It should be compared with the downsampled background hyperspectral image. The match is very good, and the background loss can be expressed as:

[0100]

[0101] Manual downsampling introduces human bias and can lead to overfitting during training, hindering network optimization. Therefore, to mitigate the impact of downsampling on training, a consistency loss is proposed. A pair of downsampling methods is set after the prediction results to obtain the downsampled background prediction X. D1 X D2 ,

[0102] X D1 =D1(YA)

[0103] X D2 =D2(YA)

[0104] D1(.) and D2(.) represent downsampling operations using filters v1 and v2, respectively.

[0105] Expectation X D1 With D A1 Good match, X D2 With D A2 Good matching. This ensures that the positions of paired downsamplers do not affect the training process. The consistency loss can be expressed as:

[0106]

[0107] Step 103: Train the network based on the two downsampled hyperspectral images using a cross-approximation background loss;

[0108] Step 104: The input hyperspectral image will be fed into the loss training network to predict the anomalous components, obtain the anomalous components, and then use the Mahalanobis distance to calculate the anomaly detection result.

[0109] Specifically, two 3×3 convolutional layers are used to extract spatial-spectral features from HSI;

[0110] A 1×1 convolutional layer is used to fine-tune the learned spectral information;

[0111] For the i-th layer feature F i The output feature F after the convolutional layer i+1 Represented as F +1 =max(α) slope ×Z i+1 Z i+1 ), i = 1, 2, 3.; where w i and b i These represent the weights and biases of the i-th layer, respectively. Z represents the convolution operation. i+1 α represents the output of the i-th convolutional layer. slope The parameter represents the slope of the negative axis.

[0112] According to D(a) j )=(a j -ξ) T Λ -1 (a j -ξ) Calculate the anomaly detection results; where, a in j This represents the pixel spectrum of the predicted outlier component A at location j. and In the equation, A represents the global mean vector and the inverse covariance matrix of the entire predicted anomaly component, and D represents the anomaly detection result.

[0113] like Figure 1 As shown, this method consists of four steps. First, a pseudo-background is calculated using a background estimation method based on non-centered convolutional kernels. Second, the anomalous components are obtained using the difference between the pseudo-background and the hyperspectral image. Third, the anomalous components are reconstructed using the proposed lightweight convolutional neural network based on residual learning. Finally, the anomaly detection result is calculated using Mahalanobis distance based on the predicted anomalous components.

[0114] Experimental results

[0115] To verify the performance of our method, it was compared with eight existing high-performing anomaly detection algorithms. The comparison methods included RX, CRD, PCA-TLRSR, HAD-AHMID, RGAE, Auto-AD, LREN, and DeCNNAD.

[0116] Experimental Dataset

[0117] 1) WHU-Hi-River: This dataset was collected on March 21, 2018, along the banks of a long river in Honghu, Hubei Province, China. The hyperspectral image is 105×168 pixels with a spatial resolution of 6 cm. Figure 4 As shown in (a), the hyperspectral image has 135 bands. The two plastic plates and two gray plates are considered anomalous targets.

[0118] 2) Pavia: This dataset was collected in Pavia, Italy, by a reflective optical system imaging spectrometer (rossi-03) sensor. The HSI has a size of 150×150 and a spatial resolution of 1.3m. Figure 4 (b) shows that the HSI has 102 bands. Vehicles on the bridge are considered anomalous targets.

[0119] 3) Texas Coast: This dataset was acquired on August 29, 2010, off the coast of Texas, USA, using an Airborne Visible / Infrared Imaging Specification Measurement Instrument (AVIRIS) sensor. The HSI has dimensions of 100×100 pixels and a spatial resolution of 17.2 m. Figure 4As shown in (c). HSI has 204 bands. All bands were used in the experiment.

[0120] 4) San Diego I: This dataset was collected by the AVIRIS sensor in San Diego, USA. The HSI is 400×400 pixels, with 244 bands and a spectral resolution of 0.37 °Cm–2.51 °Cm. In the experiment, 189 bands were selected by removing low signal-to-noise ratio and absorption bands. Two 100×100 regions were cropped from the HSI, as shown below. Figure 4 As shown in (d) and (e), the aircraft was considered an anomalous target. These two HSIs were donated as Santiago 1 and Santiago 2, respectively.

[0121] Evaluation indicators

[0122] The experiment used three evaluation metrics—3D ROC curve (Chang (2020)), 2D ROC curve (2D ROC), and area under the 2D ROC curve (AUC)—to objectively evaluate the performance of various anomaly detection methods. In the experiment, the parameters of the eight methods were set according to the authors' suggestions and the performance of the AUC values.

[0123] Experimental results

[0124] The detection results of this method on different datasets are as follows: Figure 5As shown. For the RX method, no anomalies were detected on the San Diego II dataset (row 5). Targets were detected on other datasets, but the backgrounds were also clear, which could lead to some false alarms. For the CRD method, the targets on the WHU-Hi-River dataset (row 1) were not clearly defined, while the backgrounds on the other datasets remained relatively clear. For PCA-TLRSR, the backgrounds on all datasets were clear. However, some noise existed on the San Diego II dataset, making the detection results less than ideal. For the HAD-AHMID method, anomalies were effectively enhanced on all five datasets. However, the backgrounds on the Texas Coast, San Diego I, and San Diego II datasets remained relatively clear. The RGAE method clearly detected anomalies on all five datasets, but the backgrounds were also relatively clear. The Auto-AD method effectively detected targets on the first three datasets. On the Pavia dataset, both target and background results were satisfactory, but the backgrounds on the WHU-Hi-River and Texas Coast datasets remained relatively clear. Anomalies on the San Diego I and San Diego II datasets could not be clearly detected. For the LREN method, anomalies can be detected, but the background remains relatively clear. For DeCNNAD, targets are detected on all five datasets, but the background is clear on the Texas Coast dataset, leading to some false alarms. The results of the proposed anomaly detection algorithm show that the proposed method can effectively detect anomalies and has good background suppression. Overall, from a subjective evaluation perspective, the proposed method outperforms other methods.

[0125] From an objective evaluation perspective, 3D-ROC curves and AUC values ​​are used to evaluate the performance of the method. 3D-ROC curves on different datasets are shown below. Figure 6 As shown. Figure 6 The curves for the methods marked in red are similar to those for other methods, except for the Auto-AD method on the SanDiego I method. A relatively lower curve indicates a lower detection rate or a higher false alarm rate.

[0126] 2D-ROC (detection rate, false alarm rate) curves on different datasets are as follows: Figure 7 As shown, the corresponding variables are shown in Table 1. Figure 7As shown, the method marked with a red line is almost at the top of the curve. On the Pavia, Texas Coast, and San Diego II datasets, the proposed method's curve is not at the top of all the curves on the left, but it is close to some other state-of-the-art methods. On these datasets, the overall position remains in the upper range. Overall, the proposed method has satisfactory performance. In Table 1, the best values ​​are shown in bold. As can be seen, the proposed method achieves the best value on all datasets. On different datasets, compared with the suboptimal method, the proposed method outperforms the WHU-Hi-River, Pavia, Texas Coast, San Diego I, and San Diego II datasets by 0.0005, 0.0227, 0.0056, 0.0004, and 0.0018, respectively.

[0127] 2D-ROC curves (probe probability, threshold) on different datasets, such as Figure 8 As shown, the corresponding values ​​of the variables are shown in Table 2. Figure 8 As shown, the results of the method highlighted in red are close to those of other methods. On the Pavia, Texas Coast, and San Diego I datasets, the curve of the proposed method is at the top of all curves. In Table 2, the best values ​​are shown in bold. It can be seen that PCA-TLRSR achieves the best value on the WHU-Hi-River and Texas Coast datasets, while DeCNND achieves the best value on the San Diego I and San Diego II datasets. On the Pavia dataset, the CRD method achieves the best value. In this metric, the proposed method does not achieve the best performance. This is because the detected targets appear relatively blurry in the results of the proposed method, resulting in relatively low target pixel values ​​at the edges, making effective separation with a high threshold impossible. However, on some datasets, the variable () value is close to other state-of-the-art methods and can achieve sub-optimal or third-best performance.

[0128] 2D-ROC curves (false alarm rate, threshold) on different datasets are shown below. Figure 9 The corresponding values ​​of each variable are shown in Table 3. For example... Figure 9As shown, the results of the proposed method are highlighted in red, and its performance is relatively low compared to most other state-of-the-art methods. This indicates that the proposed method has good background suppression performance. On the WHU-Hi-River dataset, the CRD method outperforms the proposed method. On the Pavia, San Diego I, and San Diego II datasets, the Auto-AD method outperforms the proposed method. However, on these datasets, the results of the proposed method are close to the best performance. In Table 3, the best values ​​are shown in bold. It can be seen that CRD achieves the best performance on the WHU-Hi-River dataset, and Auto-AD achieves the best performance on the Pavia, San Diego I, and San Diego II datasets. On the Texas Coast dataset, the proposed method achieves the best performance. Although it does not achieve the best performance on some datasets, its values ​​still reach the second or third best performance. Overall, the proposed method achieves satisfactory background suppression results.

[0129] Table 1 shows the AUC (detection probability, false alarm rate) values ​​of the detection results for the five datasets.

[0130]

[0131] Table 2 shows the AUC (probe probability, threshold) values ​​of the detection results for the five datasets.

[0132]

[0133] Table 3 shows the AUC (false alarm rate, threshold) values ​​of the detection results for the five datasets.

[0134]

[0135] Furthermore, to evaluate the execution efficiency of these methods, the time consumption of the proposed method and comparative methods on five datasets is presented. Auto-AD, LREN, and the proposed method were implemented using Python 3. The remaining methods were implemented using Matlab 2022b. All methods were executed on a computer equipped with an Intel Core Ti9-12900H processor, 16GB of RAM, and an NVIDIA GeForce RTX 3060 laptop GPU. The speed of the methods with and without GPU acceleration was measured separately. The time consumption results are shown in Table 4, with the best values ​​shown in bold. It can be seen that the RX method is the fastest without GPU acceleration. With GPU acceleration, the method achieves the best processing time. This means that the proposed method has satisfactory execution efficiency.

[0136] Table 4 shows the results of different algorithms on five datasets.

[0137]

[0138] This invention proposes a hyperspectral anomaly detection method based on residual learning and background estimation using optical CNNs. During the training phase, residual learning is used to directly learn the anomaly components instead of the background components. This transformation reduces the complexity of learning and enables the design of lightweight CNNs. Based on residual learning, a lightweight CNN with only three layers is proposed to extract anomaly features. To constrain training, a camouflaged background is obtained through a background estimation method based on non-centered convolutional kernels. To further improve the purity of the camouflaged background, a downsampling method is introduced, along with a joint loss function combining background loss and consistency loss. In the prediction phase, the anomaly detection result is obtained using the Mahalanobis distance of the predicted anomaly components. Comparative experiments with eight state-of-the-art methods were conducted on five real-world datasets. The results show that the proposed method can enhance anomalies and suppress background. The method achieves high AUC values ​​on all five test datasets, indicating good anomaly detection performance.

[0139] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0140] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A hyperspectral anomaly detection method based on residual learning and background estimation, characterized in that, The method includes: The reconstructed hyperspectral background was obtained using a background estimation method. ; The reconstructed hyperspectral background is processed using two different filters. Downsampling was performed to obtain two downsampled hyperspectral background images. and Specifically, this includes: the reconstructed hyperspectral background image as input. Through two fixed downsampling filters v 1 and v 2. Perform a convolution operation with stride 2 to obtain two downsampled hyperspectral images. , , , ;in, This represents a convolution operation with a stride of 2; The input hyperspectral image is fed into the training network, and the input HIS Y is downsampled using a pair of downsamplers to obtain HSI. and HSI Specifically, it includes: , ;in, This represents a convolution operation with a stride of 2; The input hyperspectral image is fed into a lightweight network based on residual learning to predict anomalous components, resulting in anomalous component A. Specifically, this includes: based on... Identify the outlier components, where A represents the predicted outlier result of the input HSI; and They represent: downsampled hyperspectral images and Anomaly components predicted by a lightweight network based on residual learning; The network is trained based on the two downsampled hyperspectral images using a cross-approximation background and consistency loss; The background loss is represented as: ; Consistency loss is expressed as: , ; Prediction Background , Represented as: , ; Background prediction obtained by downsampling , Represented as , , D 1(.), D 2(.) indicates that the downsampling operation uses a filter respectively. v 1 and v 2 represents; The hyperspectral image to be detected will be fed into a network that has been trained with loss to predict anomalous components. The anomalous components will then be obtained, and the Mahalanobis distance will be used to calculate the anomaly detection result.

2. The hyperspectral anomaly detection method based on residual learning and background estimation according to claim 1, characterized in that, The reconstructed hyperspectral background is obtained through a background estimation method. Specifically, it includes: Each band of the input hyperspectral image HSI Y is compared with the first... j non-central convolution kernels c j Perform convolution, convolution feature map pass Obtain; among them, It is the image of the o-th spectral band in the hyperspectral image; The local spectral similarity score of the hyperspectral image is obtained through... Determine; in the formula, Indicates the HSI's first j Local spectral similarity scores; The maximum value among the local spectral similarity scores is taken as the background number. , ; For the background number G Perform binarization to extract the clean background HSI.

3. The hyperspectral anomaly detection method based on residual learning and background estimation according to claim 2, characterized in that, The number of backgrounds G Perform binarization to extract clean, original background data, specifically including: Use the sort(.) function to sort G Sort the values ​​in the array in ascending order to obtain a ranking score vector: ; right G Perform binarization operation ;in, E m,n This represents the number of background elements in the binarized representation at position (m, n). G m,n Background number G The value at position (m,n) T This represents the background scaling threshold, and [.] is the floor function. exist R The middle is the first Element; Reconstructed hyperspectral background Calculated as ;in, m and n Represents two-dimensional coordinates in space. m =1, 2, 3, M, n =1, 2, N, Represents the position of the spectral pixel ( m , n Reconstructed hyperspectral image, This represents the input hyperspectral image at location ( m , n ) spectral pixels, Indicates ( m , n The mean background spectrum of the neighborhood centered at ).

4. The hyperspectral anomaly detection method based on residual learning and background estimation according to claim 3, characterized in that, The background spectrum average vector The calculation is as follows: Among them, C U Indicates ( m , n The set of spectral pixels between the outer and inner windows centered on the center. W express U The number of spectral pixels in the set.

5. The hyperspectral anomaly detection method based on residual learning and background estimation according to claim 1, characterized in that, The input hyperspectral image will be fed into a loss training network for anomaly component prediction, resulting in the anomaly components, specifically including: Two 3×3 convolutional layers are used to extract spatial-spectral features from HSI; A 1×1 convolutional layer is used to fine-tune the learned spectral information; For the i Layer features F i Output features after convolutional layer F i+1 Represented as , ;in, and They represent the first i Layer weights and biases This represents the convolution operation. Z i+1 Indicates the first i The output of the convolutional layer, The parameter represents the slope of the negative axis.

6. The hyperspectral anomaly detection method based on residual learning and background estimation according to claim 5, characterized in that, The calculation of anomaly detection results using the Mahalanobis distance-based lightweight network based on residual learning specifically includes: according to Calculate the anomaly detection results; among which, In Predict the location of outlier component A. j pixel spectrum, and In and out, respectively, are the global mean vector and covariance inverse matrix of the entire predicted anomaly component. D This indicates an anomaly detection result.

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