A Hyperspectral Anomaly Detection Method and System Based on Low-Rank Constrained Autoencoder

Abstract

This application discloses a hyperspectral anomaly detection method and system based on low-rank constrained autoencoders. The method applies low-rank constraints to the hidden layer representation of an autoencoder network, mines high-order low-rank characteristics for background reconstruction, and uses reconstruction errors to identify anomalies. The method implementation steps include: Step 1: Inputting the hyperspectral data X to be detected, setting network parameters W and b, learning rate α, and initial values ​​for adjustment parameters λ1 and λ2; Step 2: Constructing a loss function for the hyperspectral data X using low-rank constraints; Step 3: Learning the network using the loss function, updating the network parameters {W, b}, and obtaining the reconstructed data of the input data X; Step 4: Constructing an error matrix E; Step 5: Detecting the reconstruction error matrix.

Description

Technical Field

[0001] This application relates to the technical field of hyperspectral anomaly detection, specifically to a hyperspectral anomaly detection method and system based on low-rank constrained autoencoders. Background Technology

[0002] Anomalous targets in hyperspectral images generally refer to targets whose spectral information differs significantly from that of surrounding pixels. Typically, anomalous targets in hyperspectral images are small and sparsely distributed. The biggest difference between hyperspectral anomaly detection and hyperspectral target detection is that hyperspectral anomaly detection does not require any prior knowledge of the target; that is, it does not need to know the spectral information of the anomalous target. It only needs to compare the target with the spectral characteristics of its surrounding environment. If there is a significant difference, it can be considered a potentially suspicious target. Hyperspectral anomaly detection can often provide regions of interest for further accurate target identification. Its most prominent feature is that it does not require any prior spectral information about the target to be detected, directly identifying suspicious potential targets in the image. Therefore, hyperspectral anomaly target detection systems have been widely used in environmental monitoring, mineral resource exploration, and national security.

[0003] Currently, deep neural networks are being applied to hyperspectral anomaly detection because they can extract both low-level and high-level abstract features. Autoencoders or deep belief networks are frequently used to extract features from hyperspectral images, and then reconstruction errors are used to detect anomalous targets. To further improve detection accuracy, stacked autoencoders are used to extract spectral features, followed by sparse low-rank matrix factorization to detect anomalous targets. Additionally, hyperspectral anomaly detection methods based on convolutional neural networks train the convolutional neural network using the spectral differences between different pixel pairs and determine anomalous targets by calculating similarity scores.

[0004] Existing deep neural network-based learning methods in anomaly detection networks do not fully exploit the essential structure of hyperspectral data. Anomalies have a lower probability of occurrence compared to the background, which is the dominant component and possesses low-rank priors. How to better mine higher-order, low-rank characteristics for background reconstruction and utilize reconstruction errors to identify anomalies is a pressing technical problem that needs to be solved.

[0005] Low-rank background properties have been widely used in traditional shallow representations but have not been incorporated into deep learning. Autoencoders (AEs) are widely used unsupervised networks designed to reconstruct input data with minimal reconstruction error. To uncover low-rank background properties during data reconstruction, low-rank constraint-based AEs are used for hyperspectral anomaly detection. Specifically, low-rank constraints are applied to the hidden layer representation of the AE to explore deep low-rank representations. Given the highly nonlinear nature of the data, the proposed deep low-rank representation method better uncovers higher-order low-rank properties for background reconstruction and utilizes reconstruction errors to identify anomalies compared to traditional shallow low-rank representation methods.

[0006] The background description is provided for the purpose of understanding the relevant technologies in this field and is not intended as an admission of prior art. Summary of the Invention

[0007] Therefore, the present invention aims to provide a hyperspectral anomaly detection method and system based on low-rank constrained autoencoders, which applies low-rank constraints to the hidden layer representation of autoencoder networks, mines high-order low-rank characteristics for background reconstruction, and uses reconstruction errors to identify anomalies.

[0008] In a first aspect, embodiments of the present invention provide a hyperspectral anomaly detection method based on low-rank constrained autoencoders, characterized by comprising the following steps:

[0009] Step 1: Input the hyperspectral data X to be detected, set the network parameters W and b, learning rate α, and adjust the initial values ​​of parameters λ1 and λ2;

[0010] Step 2: Construct the loss function for the hyperspectral data X using low-rank constraints. The loss function is as follows:

[0011] Where, x i Let i represent the i-th sample. This represents the reconstruction of the i-th sample. ||·|| * W represents a low-rank constraint. (l) and b (l) λ1 and λ2 represent the weights and biases of the l-th layer of the network, respectively, λ1 and λ2 are two adjustment parameters, and Z is the feature representation of the input data X in the deep feature space.

[0012] Step 3: Use the loss function to learn the network, update the network parameters {W, b}, and obtain the reconstructed data of the input data X. Where f represents the encoding function;

[0013] Step 4: Construct the error matrix E, where

[0014] Step 5: Detect the reconstruction error matrix;

[0015] Optionally, the encoding function f is a non-linear function;

[0016] Optionally, the initial values ​​of λ1 and λ2 can be set to 1;

[0017] In a second aspect of this invention, an embodiment of the invention provides a hyperspectral anomaly detection system based on low-rank constraint autoencoders, characterized by comprising a hyperspectral data acquisition module, a feature representation module, a low-rank constraint module, and a reconstructed data module. The hyperspectral data acquisition module encodes the acquired hyperspectral data and inputs it into the feature representation module; the feature representation module decodes the encoded data and inputs it into the reconstructed data module.

[0018] Optionally, the low-rank constraint module belongs to the feature representation module;

[0019] Optionally, the feature representation module constructs an objective function under the constraints of the low-rank constraint module:

[0020] Where l = 1, 2, ..., L (L is the number of network layers). X is the input data. To reconstruct the data, rank(·) represents the rank function, W (l) and b (l) λ1 and λ2 represent the weights and biases of the l-th layer of the network, respectively, and are two adjustment parameters.

[0021] Optionally, the loss function for a low-rank constrained autoencoder network is:

[0022]

[0023] Where, x i Let i represent the i-th sample. This represents the reconstruction of the i-th sample. ||·|| * W represents a low-rank constraint, rank(·) represents the rank function. (l) and b (l) λ1 and λ2 represent the weights and biases of the l-th layer of the network, respectively, and λ1 and λ2 are two adjustment parameters. Z is the feature representation of the input data X in the deep feature space.

[0024] Other optional features and technical effects of the embodiments of the present invention are partly described below and partly apparent from reading this document. Attached Figure Description

[0025] Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings. The elements shown are not limited to the scale shown in the drawings, and the same or similar reference numerals in the drawings denote the same or similar elements, wherein:

[0026] Figure 1 A schematic diagram of the structure of an autoencoder network in which embodiments of the present invention can be implemented is shown;

[0027] Figure 2 A schematic diagram of a hyperspectral anomaly detection system that can implement embodiments of the present invention is shown;

[0028] Figure 3 A flowchart illustrating a hyperspectral anomaly detection method that can be implemented according to embodiments of the present invention is shown.

[0029] Figure 4 A schematic diagram comparing the ROC curve (receiver operating characteristic curve) of a hyperspectral anomaly detection method that can implement embodiments of the present invention with that of existing methods is shown.

[0030] Figure 5 A schematic diagram comparing a hyperspectral anomaly detection method that can implement embodiments of the present invention with existing methods on a dataset is shown. Detailed Implementation

[0031] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings. Here, the illustrative embodiments and descriptions of this invention are used to explain the invention, but are not intended to limit the invention.

[0032] The term "comprising" and its variations as used herein signify open inclusion, i.e., "including but not limited to". Unless otherwise stated, the term "or" means "and / or". The term "based on" means "at least partially based on". The terms "one example embodiment" and "one embodiment" mean "at least one example embodiment". The term "another embodiment" means "at least one additional embodiment". The terms "first", "second", etc., may refer to different or the same objects. Other explicit and implicit definitions may also be included below.

[0033] In an embodiment of the present invention, a hyperspectral anomaly detection method and system based on low-rank constrained autoencoders are provided. The method applies low-rank constraints to the hidden layer representation of an autoencoder network, mines high-order low-rank characteristics for background reconstruction, and uses reconstruction errors to identify anomalies.

[0034] Figure 1 A schematic diagram of the structure of an autoencoder network that can implement embodiments of the present invention is shown, such as... Figure 1 The autoencoder network shown includes: input X, hidden layer Z, and output. exist Figure 1 The input x in the autoencoder network shown can be represented as follows after encoding and hidden layer Z:

[0035]

[0036] Where θ1={w1,b1}, w1 and b1 represent the weights and biases of the coding layer, respectively; f represents the coding function, which is generally a non-linear function, where f can be a sigmoid function, a tanh function or a ReLU function.

[0037] exist Figure 1 The output of the autoencoder network shown This can be expressed as formula (2):

[0038]

[0039] Where θ2 = {w2, b2}, w2 and b2 represent the weights and biases of the decoding layer, respectively.

[0040] Figure 1 The autoencoder network shown aims to reconstruct the input data as accurately as possible. Therefore, the objective function is shown in equation (3):

[0041]

[0042] Where, x, These are the input data and the decoded data, respectively.

[0043] Figure 2 A schematic diagram of a hyperspectral anomaly detection system that can implement embodiments of the present invention is shown, such as... Figure 2 The schematic diagram of the hyperspectral anomaly detection system shown includes: a hyperspectral data acquisition module, a feature representation module, a low-rank constraint module, and a data reconstruction module. The low-rank constraint module can be a standalone module or included within the feature representation module; this application does not impose specific limitations. Figure 2 In the illustrated embodiment, the hyperspectral data acquisition module encodes the acquired hyperspectral data and inputs it into the feature representation module; the feature representation module decodes the encoded data and inputs it into the reconstructed data module. Figure 1 In the illustrated embodiment, the hidden layer Z is the feature representation of the input data in the deep feature space. To mine the low-rank prior of the data within the deep autoencoder framework, a low-rank constraint module is introduced, and the objective function is constructed as shown in equation (4):

[0044]

[0045] Where l = 1, 2, ..., L (L is the number of network layers). X is the input data. To reconstruct the data, rank(·) represents the rank function, W (l) and b (l)λ1 and λ2 represent the weights and biases of the l-th layer of the network, respectively. λ1 and λ2 are two adjustment parameters. In formula (4), the first term is the reconstruction error term, the second term is the low-rank constraint term, and the third term is the constraint term on the magnitude of the network parameters.

[0046] The loss function of a low-rank constrained autoencoder network is expressed as shown in Equation (5):

[0047]

[0048] Where, x i Let i represent the i-th sample. This represents the reconstruction of the i-th sample. ||·|| * This indicates a low-rank constraint.

[0049] In hyperspectral images, the background constitutes the vast majority of the total pixels and contributes the most to network learning; therefore, the designed low-rank autoencoder network (LOC) can effectively learn the background. From a residual perspective, the LOC shows small residuals for representing background pixels but relatively large residuals for representing anomalous pixels. Therefore, the reconstruction error of the LOC can be used to identify anomalies.

[0050] The designed loss function (5) is used to learn the network, and the network parameters {W, b} are obtained to obtain the reconstructed data of the hyperspectral data X. As shown in formula (6):

[0051]

[0052] The error between the input data and the reconstructed data is The reconstruction error includes noise and anomalies. To remove the influence of Gaussian noise, the RX (Reed-Xiaoli) operator is used to detect anomalies in the error term E, and the detection results are output.

[0053] Figure 3 A flowchart illustrating a hyperspectral anomaly detection method that can implement embodiments of the present invention is shown, as follows: Figure 3 The hyperspectral anomaly detection method shown includes the following steps:

[0054] S301: Collect input data and set initial values ​​for parameters; use the collected hyperspectral data as input data X for the autoencoder network, set the number of layers L, the number of neurons per layer, the initial network parameters W and b, the learning rate α, and the initial values ​​of adjustment parameters λ1 and λ2. Set the number of network layers to 5. When λ2∈[1,10], the results obtained by the hyperspectral data anomaly detection method provided in this application embodiment are relatively stable. For convenience, the values ​​of λ1 and λ2 can be set to 1.

[0055] S302: Construct a loss function for the hyperspectral data X under low-rank constraints, and update the network parameters of each layer of the network based on the loss function. W(l) , b(l) The loss function is shown in formula (5) in the above embodiment.

[0056] S303: Obtain the reconstructed data of X in,

[0057] S304: Obtain the reconstruction error matrix, where the reconstruction error matrix E is...

[0058] S305: The reconstruction error matrix can be detected by using the RX operator to detect anomalies in the error matrix E.

[0059] S306: Outputs hyperspectral anomaly detection results.

[0060] Figure 4 A schematic diagram comparing the ROC curve (receiver operating characteristic curve) of a hyperspectral anomaly detection method that can implement embodiments of the present invention with that of existing methods is shown. Figure 4 Figure 407 shows the ROC curve of the hyperspectral anomaly detection method provided in the embodiment of this application, while 401, 402, 403, 404, 405 and 406 are the ROC curves of hyperspectral anomaly detection methods in the prior art. Figure 4 The horizontal axis represents the false alarm rate, and the vertical axis represents the detection rate. The closer the ROC curve is to the upper left of the diagram, the higher the detection accuracy of the hyperspectral anomaly detection method. For example... Figure 4 As shown, when the detection rate reaches 0.9, the false alarm rates of methods 401, 402, and 407 are low, all less than 0.05, which is superior to other methods. When the detection rate is 1, the false alarm rates of methods 401, 405, and 407 are also low. Overall, the hyperspectral anomaly detection methods provided in this application's embodiments perform well. In existing methods, although they perform well when the false alarm rate is below 0.05, it is difficult to achieve a detection rate of 1, resulting in missed detections of some anomalies.

[0061] Figure 5 A schematic diagram comparing a hyperspectral anomaly detection method that can implement embodiments of the present invention with existing methods on a dataset is shown. Figure 5Figure (a) is a reference image showing the location of the anomalous pixels. Figures (b) to (h) are the detection results obtained using different methods, with Figure (h) showing the detection result of the hyperspectral data detection method provided in this embodiment. Figure (a) shows that the anomalies in the dataset are pixel-level point anomalies. The background statistics-based methods in Figures (b) and (c) can effectively compress the background, but due to the interference of anomalies in the background statistics, Figures (b) and (c) show some missed detections of anomalous pixels. In Figure (d), the detected anomalies contain a lot of background interference, resulting in inaccurate detection results. In Figure (e) obtained using the unmixing-based method, some anomalies are missed, while some background areas are falsely detected as anomalies. The low-rank representation method can effectively detect anomalies while compressing the background. In its detection result Figure (f), the contrast between the background and anomalies is obvious, making it easy to distinguish the anomalies, indicating that the low-rank prior plays a positive role in hyperspectral anomaly detection. Comparing Figure (g) and Figure (h), it can be seen that in the detection result image obtained by using the hyperspectral data anomaly detection method provided in the embodiments of this application, anomalies are easily distinguished and are superior to the detection algorithms of the prior art, which is helpful for detecting anomalies.

[0062] This document describes several embodiments of the present invention; however, for the sake of brevity, the descriptions of the embodiments are not exhaustive, and identical or similar features or parts between the embodiments may be omitted. In this document, "one embodiment," "some embodiments," "example," "specific example," or "some examples" refers to embodiments applicable to at least one, but not all, of the present invention. The above terms do not necessarily refer to the same embodiments or examples. Without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described herein, as well as the features of the different embodiments or examples.

[0063] The exemplary systems and methods of the present invention have been specifically shown and described with reference to the above embodiments, which are merely examples of the best mode for implementing the systems and methods. Those skilled in the art will understand that various changes can be made to the embodiments of the systems and methods described herein without departing from the spirit and scope of the invention as defined in the appended claims when implementing the systems and / or methods.

Claims

1. A hyperspectral anomaly detection method based on low-rank constraint self-encoding, characterized in that, The method comprises the following steps: Step one, input the hyperspectral data X to be detected, set the initial values of network parameters W, b, learning rate α, and λ1 and λ2; Step two, construct a loss function of the hyperspectral data X by using low rank constraint, and the loss function is: where x i denotes the i-th sample, denotes the reconstruction of the i-th sample;‖·‖ * denotes the low-rank constraint, W (l) and b (l) denote the weights and biases of the l-th layer of the network, λ1and λ2are two tuning parameters, and Z is the feature representation of the input data X in the deep feature space. Construct a target function under the low-rank constraint: where l = 1, 2,..., L (L is the number of network layers); X is the input data, is the reconstructed data, rank(·) denotes the rank function, W (l) and b (l) denote the weight and bias of the l-th layer of the network, respectively, and λ1 and λ2 are two adjustment parameters. Step three, update the network parameters {W, b} by using the loss function learning network, and obtain the reconstructed data of the input data X wherein f represents an encoding function; Step four: Construct the error matrix E, where Step five: detect the reconstruction error matrix. 2.The method of claim 1, wherein, The encoding function f is a nonlinear function.

3. The low-rank constraint based self-encoding hyperspectral anomaly detection method of claim 1, wherein, The initial values of λ1 and λ2 are set to 1.

4. A hyperspectral anomaly detection system based on low-rank constrained auto-encoding, characterized in that, The hyperspectral data acquisition module, the feature representation module, the low-rank constraint module, and the reconstruction data module, the hyperspectral data acquisition module encodes the collected hyperspectral data and inputs it to the feature representation module; The feature representation module decodes the encoded data and inputs it to the reconstruction data module; The feature representation module constructs a target function under the constraint of the low-rank constraint module: where l = 1, 2, …, L (L is the number of network layers); X is the input data, is the reconstructed data, rank(·) denotes the rank function, W (l) and b (l) denote the weight and bias of the l-th layer of the network, respectively, and λ1and λ2are two adjustment parameters; The loss function of the low-rank constraint auto-encoding network is: where x i denotes the i-th sample, denotes the reconstruction of the i-th sample;‖·‖ * denotes the low-rank constraint, rank(·) denotes the rank function, W (l) and b (l) denote the weights and biases of the l-th layer of the network, λ1and λ2are two tuning parameters, and Z is the feature representation of the input data X in the deep feature space.

5. The low-rank constraint based self-encoding hyperspectral anomaly detection system of claim 4, wherein, The low-rank constraint module belongs to the feature representation module.

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