Hyperspectral image anomaly detection method based on S2 / 3 and sparse regular term

Abstract

The invention relates to the technical field of computer vision, in particular to a hyperspectral image anomaly detection method based on S2 / 3 and sparse regular terms. The method comprises the following steps: acquiring and preprocessing a hyperspectral image to obtain three-dimensional data of the hyperspectral image; carrying out dimensionality reduction on the three-dimensional data through a principal component analysis method; reconstructing the three-dimensional data subjected to dimension reduction into a two-dimensional Casorati matrix, and establishing an HSI model according to the obtained Casorati matrix; according to the obtained HSI model, establishing a low-rank sparse matrix decomposition model based on S2 / 3 and a sparse regular term, and calculating to obtain an output abnormal matrix; and extracting the anomaly metric of each pixel point according to the output anomaly matrix, and generating an anomaly detection result graph. The problem of deviation of an optimal solution is solved, the problem that inherent information of the HSI is not fully utilized due to the fact that most methods neglect spatial information of the HSI is solved, the problem that most methods do not capture an inherent sparse structure of a low-rank component is solved, the noise influence is effectively restrained, and the model robustness is improved.

Description

Technical Field

[0001] The present invention relates to the field of computer vision technology, and particularly to a hyperspectral image anomaly detection method based on S 2 / 3 and sparse regularization terms. Background Technique

[0002] With the increasing development of information technology and aerospace technology, remote sensing technology has begun to come into people's view. Under the background of increasingly refined research requirements, traditional remote sensing technology has gradually developed towards hyperspectral remote sensing technology. In hyperspectral remote sensing, hyperspectral images (HSI), as data carriers, are high-dimensional data with many related spectral bands obtained by advanced spectral imagers or satellites, and show great potential in many fields such as agriculture, visual monitoring, and urban planning. Anomaly detection is one of the important directions in hyperspectral image analysis. In some specific scenarios, such as disaster monitoring, etc., it is crucial to detect abnormal targets or regions in the image in a timely and accurate manner. However, traditional target detection often requires prior knowledge of the approximate spectral characteristics of the target, but it is extremely difficult to determine the target spectrum in real scenarios. In such a complex situation, anomaly detection does not need to rely on specific target spectral information, can more flexibly adapt to complex environments, and shows significant advantages.

[0003] In hyperspectral remote sensing, anomaly detection aims to detect abnormal pixels in hyperspectral images. This "anomaly" is reflected in that, compared with other pixels, its features are significantly different in space or spectrum. And these abnormal pixels often correspond to unusual or meaningful things. For example, rare plant species, lost adventurers in the desert, polluted coastal waters, etc. That is, anomaly detection plays an important role in discovering potential information.

[0004] Early traditional anomaly detection methods mainly obtained effective information from the background, that is, first extracted the features of the normal background from the image, and then used the difference between the background and the anomaly to distinguish the abnormal part. However, such methods are easily interfered by abnormal data points, and the complexity or instability in calculating the inverse covariance matrix will affect the final effect. Low-Rank and Sparse Matrix Decomposition (LRaSMD) technology helps to solve the above problems.

[0005] LRaSMD is a technique for processing high-dimensional data by decomposing data into a low-rank matrix and a sparse matrix. In recent years, low-rank sparse matrix decomposition models have been favored by most hyperspectral image anomaly detection researchers, especially the Robust Principal Component Analysis (RPCA) model, as shown in the following formula.

[0006] min rank(L)+λ||S||0

[0007] s.t.M=L+S (1)

[0008] Where M is a two-dimensional Casorati matrix converted by column-wise vectorization of the observed HSI band by band, and L and S represent the low-rank term and the sparse term respectively. However, solving equation (1) is NP-hard. A common method is to use the nuclear norm to approximate the rank function and relax the l0 operator to the l1 norm, thus approximately converting it into a convex optimization domain. As shown in equation (2) below.

[0009] min||L|| * +λ||S||1

[0010] s.t.M=L+S (2)

[0011] Where the nuclear norm of matrix L is defined as the sum of its singular values, i.e., ||L|| * =∑ i σ i (L),σ i represents the i-th singular value of matrix L. However, the nuclear norm minimization method treats all singular values equally and shrinks them at the same threshold. The weighted nuclear norm method proposed on this basis is more flexible. But these methods all have deviations in the optimal solution. Considering that the observed data will be contaminated by noise in the actual application scenario, the LRaSMD-based Mahalanobis Distance Method (LSMAD) models the HSI into equation (3):

[0012] M=L+S+N (3)

[0013] Where N is the noise term. LSMAD uses the LRaSMD theory for the observed Casorati matrix M to obtain the background component L and the sparse component S. The modeling strategy of equation (3) is also the modeling basis of the present invention. The above methods only utilize the spectral information of the HSI and ignore the spatial information. The Spectral-Spatial Total Variation (SSTV) regularization is widely applied to anomaly detection because it can fully utilize the spatial information of the HSI.

[0014] In summary, in the application of hyperspectral image anomaly detection, most of the methods based on LRaSMD have the following problems: First, regular methods such as nuclear norm and weighted nuclear norm used in most methods will lead to deviation of the solution. Second, the spatial information and spectral information of HSI are not considered simultaneously. Third, the inherent sparse structure of the low-rank component is ignored. Summary of the Invention

[0015] To solve the above technical problems, the present invention provides a hyperspectral image anomaly detection method based on S 2 / 3 and sparse regular terms, including the following steps:

[0016] S1. Obtain a hyperspectral image and preprocess the hyperspectral image to obtain three-dimensional data of the hyperspectral image;

[0017] S2. Reduce the dimension of the three-dimensional data by principal component analysis;

[0018] S3. Reconstruct the three-dimensional data after dimension reduction into a two-dimensional Casorati matrix, and establish an HSI model based on the obtained Casorati matrix;

[0019] S4. According to the obtained HSI model, establish a low-rank sparse matrix decomposition model based on S 2 / 3 and sparse regular terms, and calculate to obtain an output anomaly matrix;

[0020] S5. Extract the anomaly measure of each pixel point according to the output anomaly matrix, and generate an anomaly detection result map.

[0021] Further, step S3 includes the following steps:

[0022] S301. Construct an original HSI data cube including spatial and spectral dimensions, and perform one-dimensional expansion on the spatial dimension of the HSI data cube, and arrange each spectral band into a column vector respectively. The HSI data cube can be expressed as:

[0023] R×C×B

[0024] where R is the height of the image scene, C is the width of the image scene, and B is the number of spectral bands;

[0025] S302. Rearrange the HSI data cube according to the obtained column vectors to obtain a two-dimensional Casorati matrix. The size of the two-dimensional Casorati matrix can be expressed as:

[0026] H×B

[0027] where H = R×C, representing the total number of pixels in the image scene, and B is the number of spectral bands;

[0028] S303. Based on the obtained two-dimensional Casorati matrix, establish an HSI data model, which can be expressed as:

[0029] M = L + S + N

[0030] where M is the two-dimensional Casorati matrix, L is the low-rank term representing the background part, S is the sparse term representing the abnormal part, and N is the noise.

[0031] Furthermore, step S4 includes the following steps:

[0032] S401. Establish a low-rank and sparse matrix decomposition model based on S 2 / 3 and the sparse regularization term, which can be expressed as:

[0033]

[0034] s.t. ||M - L - S|| F ≤ η

[0035]

[0036] where L is the low-rank term representing the background part, σ i is the i-th singular value of matrix L, S is the sparse term representing the abnormal part, D h is the differential operator in the horizontal spatial direction, D v is the differential operator in the vertical spatial direction, D s is the finite difference operator along the spectral direction, λ1, λ2, λ3 are trade-off parameters, G is the forward transformation operator, η is a constant proportional to the standard deviation of Gaussian noise, used to control the noise tolerance of the denoising model, and j is the summation index;

[0037] S402. Based on the alternating direction multiplier method, calculate the low-rank and sparse matrix decomposition model obtained in step S401 to obtain the output abnormal matrix.

[0038] Furthermore, step S402 includes the following steps:

[0039] S402-1. According to the low-rank and sparse matrix decomposition model obtained in step S401, introduce auxiliary variables and separate the variables of the low-rank and sparse matrix decomposition model. The separated low-rank and sparse matrix decomposition model can be expressed as:

[0040]

[0041] s.t. X = L, P = D h LD s , Q = D v LD s,W = G(L), ||M - L - S|| F ≤ η

[0042]

[0043] Wherein, X, P, Q, and W are respectively introduced auxiliary variables, is the set of real numbers, ‖·‖ F represents the Frobenius norm of a matrix, which is defined as the square root of the sum of the squares of all elements of the matrix.

[0044] S402-2. Perform augmented Lagrangian transformation on the low-rank sparse matrix decomposition model after separating the variables, and its formula can be expressed as:

[0045]

[0046] Wherein, B1, B2, B3, B4, and B5 are respectively Lagrange multipliers, μ is a penalty parameter, and λ1, λ2, and λ3 are trade-off parameters;

[0047] S402-3. According to the augmented Lagrangian function obtained in step S402-2, update the variables in the augmented Lagrangian function in turn by the iterative alternating method;

[0048] S402-4. According to the calculated variables, determine whether the iteration condition is satisfied. The iteration condition can be expressed as:

[0049] ||M - L - S|| F / ||M|| F ≤ ε

[0050] Wherein, ε is the relative error threshold. When the condition is satisfied, the matrix S is output; otherwise, return to step S402-3.

[0051] Further, step S5 includes the following steps:

[0052] S501. Transpose the output abnormal matrix obtained in step S4 to obtain the transposed output abnormal matrix;

[0053] S502. Calculate the abnormal intensity of each pixel in the transposed output abnormal matrix, and its formula can be expressed as:

[0054] r i = ||S′ i ||2

[0055] Wherein, r i is the abnormal intensity, S′ is the transposed output abnormal matrix, and S′ i is the i-th column of the transposed output abnormal matrix S′, and i is the total number of all pixels in the transposed matrix.

[0056] The beneficial effects of the present invention are as follows:

[0057] By providing a hyperspectral image anomaly detection method based on S 2 / 3 and sparse regularization terms, the prior information of the HSI is fully utilized to improve the anomaly detection performance of the model. First, the Schatten 2 / 3 quasi-norm is used to better approximate the rank function, and the prior rank information is fully utilized, so that the model can obtain a clear low-rank part in the application of low-rank and sparse matrix decomposition. On the other hand, an l 2,2 / 3 constraint is imposed on the sparse term, which can solve the over-penalization that may be caused by the l1 norm and is more effective than l 2,1 . The above strategies are beneficial to better separate the background and anomaly parts. Then, the piecewise smoothness constraint is incorporated into the low-rank sparse matrix decomposition to improve the utilization rate of spatial information, thereby suppressing the influence of noise and enhancing the robustness of the model. Secondly, an additional sparse prior on the low-rank component is introduced, and a sparse regularization term is imposed on the low-rank part to capture its inherent sparse structure in the transform domain to obtain a more accurate solution to this problem. Finally, each sub-problem of the model is solved in the form of a closed solution, making the solution of the model simple and fast. Brief Description of the Drawings

[0058] Figure 1 、Flowchart of a hyperspectral image anomaly detection method based on S 2 / 3 and sparse regularization terms of the present invention.

[0059] Figure 2 、Schematic diagram of the algorithm of a hyperspectral image anomaly detection method based on S 2 / 3 and sparse regularization terms of the present invention.

[0060] Figure 3 、Schematic diagram of the pseudo-color image of the Pavia dataset in the embodiment of the present invention.

[0061] Figure 4 、Anomaly ground truth map of the Pavia dataset in the embodiment of the present invention.

[0062] Figure 5 、Pseudo-color images and anomaly ground truth maps of the 7 real datasets used in the embodiment of the present invention.

[0063] Figure 6 、Anomaly detection result map on the Texas Coast dataset in the embodiment of the present invention.

[0064] Figure 7 、Anomaly detection result map on the Los Angeles1 dataset in the embodiment of the present invention.

[0065] Figure 8, Anomaly detection result graph on the Los Angeles2 dataset of the embodiment of the present invention.

[0066] Figure 9 , Anomaly detection result graph on the Pavia dataset of the embodiment of the present invention.

[0067] Figure 10 , Anomaly detection result graph on the Airport dataset of the embodiment of the present invention.

[0068] Figure 11 , ROC curve graph on the real dataset Texas Coast of the embodiment of the present invention.

[0069] Figure 12 , ROC curve graph on the real dataset Los Angeles1 of the embodiment of the present invention.

[0070] Figure 13 , ROC curve graph on the real dataset Los Angeles2 of the embodiment of the present invention.

[0071] Figure 14 , ROC curve graph on the real dataset Pavia of the embodiment of the present invention.

[0072] Figure 15 , ROC curve graph on the real dataset Airport of the embodiment of the present invention.

[0073] Figure 16 , AUC result graph of the embodiment of the present invention. Detailed implementation manners

[0074] For those skilled in the art to better understand the content of the present invention, make the purpose, technical solutions and advantages of the present invention clearer, the following further details the present invention in conjunction with embodiments and drawings. The illustrative embodiments of the present invention and their descriptions are only used to explain the present invention and do not further limit the present invention.

[0075] As Figure 1 shown, the embodiment of the present invention provides a hyperspectral image anomaly detection method based on S 2 / 3 and sparse regularization terms. As Figure 2 shown, it is the algorithm schematic diagram of the above-mentioned hyperspectral image anomaly detection method based on S 2 / 3 and sparse regularization terms. Combining the experiment on the Pavia Center real dataset to illustrate the specific implementation manner of the present invention. The size of this dataset is 150×150×102, that is, it contains 102 bands, and the size of each band image is 128×160. This experiment needs to separate anomalies from the background and detect the anomalies as Figure 4 shown.

[0076] Step 1: Input the three-dimensional data Pavia.mat of the hyperspectral image;

[0077] Step 2: Reduce the dimension by the principal component analysis method. The size of the dataset after dimension reduction is 150×150×10, and only 10 bands are retained;

[0078] Step 3: Reconstruct the Pavia dataset of 150×150×10 after dimension reduction into a two-dimensional Casorati matrix M of size 225000×10;

[0079] Step 4: Input the matrix M into the low-rank sparse matrix decomposition model based on S 2 / 3 and the sparse regularization term, and output the anomaly matrix S of size 225000×10;

[0080] Specifically, Step 4 includes the following steps:

[0081] S401. Establish a low-rank sparse matrix decomposition model based on S 2 / 3 and the sparse regularization term, which can be expressed as:

[0082]

[0083] s.t.||M - L - S|| F ≤η

[0084]

[0085] where L is the low-rank term representing the background part, σ i is the i-th singular value of the matrix L, S is the sparse term representing the anomaly part, D h is the differential operator in the horizontal spatial direction, D v is the differential operator in the vertical spatial direction, D s is the finite difference operator along the spectral direction, λ1, λ2, λ3 are trade-off parameters, G is the forward transformation operator, and η is a constant proportional to the standard deviation of Gaussian noise, which is used to control the noise tolerance of the denoising model.

[0086] S402. Based on the alternating direction multiplier method, calculate the low-rank sparse matrix decomposition model obtained in Step S401 to obtain the output anomaly matrix.

[0087] Furthermore, Step S402 includes the following steps:

[0088] S402-1. According to the low-rank sparse matrix decomposition model obtained in Step S401, introduce auxiliary variables for variable separation. The low-rank sparse matrix decomposition model after variable separation can be expressed as:

[0089]

[0090] such that \(X = L\), \(P = D\) h LD s , \(Q = D\) v LD s , \(W = G(L)\), \(\|M - L - S\|\) F \(\leq\eta\)

[0091] S402 - 2. Augment the Lagrangian transform for the low - rank sparse matrix decomposition model after separating the variables, and its formula can be expressed as:

[0092]

[0093] where \(B1\), \(B2\), \(B3\), \(B4\), \(B5\) are Lagrange multipliers respectively, \(\mu\) is the penalty parameter, and \(\lambda1\), \(\lambda2\), \(\lambda3\) are trade - off parameters;

[0094] S402 - 3. According to the augmented Lagrangian function obtained in step S402 - 2, use the iterative alternating method to update the variables in the augmented Lagrangian function in turn;

[0095] S402 - 4. According to the calculated variables, judge whether the iteration condition is satisfied. The iteration condition can be expressed as:

[0096] \(\|M - L - S\|\) F / \(\|M\|\) F \(\leq\varepsilon\)

[0097] where \(\varepsilon\) is a preset relative error threshold. When the condition is satisfied, the matrix \(S\) is output, otherwise return to step S402 - 3.

[0098] Furthermore, in step S402 - 3, using the iterative alternating method to update the variables in the augmented Lagrangian function in turn includes the following update strategies:

[0099]

[0100] Then update the Lagrange multipliers and the penalty parameter, and its update strategy is as follows:

[0101]

[0102] Specifically, at the \((k + 1)\) - th iteration, first update \(X\) k+1 :

[0103]

[0104] Then update \(S\) k+1 :

[0105]

[0106] Next, update P k+1 :

[0107]

[0108] Then, update Q k+1 :

[0109]

[0110] Next, update W k+1 :

[0111]

[0112] Update L k+1 :

[0113]

[0114] Finally, update the Lagrange multipliers and penalty parameters:

[0115]

[0116]

[0117] Specifically, the solution method of the said X k+1 is as follows:

[0118] Given a matrix of rank r whose singular value decomposition is Y = UDiag(σ)V T , where are two orthogonal singular value matrices, σ = (σ1, σ2, …, σ r ) T represents the non-increasing order arrangement of the singular values of Y. For any λ > 0, the 2 / 3 threshold operator of the matrix is expressed as:

[0119]

[0120] where, is the 2 / 3 threshold function. For a given real number 2 / 3 threshold function is defined as:

[0121]

[0122] φ λ (t) = arccosh(27t 2 λ - 3 / 2 / 16)

[0123] Therefore, problem X can be easily derived k+1 The closed-form solution is as follows:

[0124]

[0125] Specifically, the solution method for S k+1 is as follows:

[0126] Given the matrix For the following optimization problem:

[0127]

[0128] Its closed-form solution is where and where \(T_{i}\) i represents the \(i\)-th row of \(T\) (\(i = 1,\ldots,m\)), and \(Y_{ij}\) i,j is each element of the matrix \(Y\) (\(i = 1,\ldots,m\); \(j = 1,\ldots,n\)).

[0129] Therefore, the solution to problem S k+1 is as follows:

[0130]

[0131] Specifically, the solution methods for \(P\) k+1 , \(Q\) k+1 and \(W\) k+1 are as follows:

[0132] Given the matrix For the following optimization problem:

[0133]

[0134] Its closed-form solution is and where \(z\) is each element of the matrix \(Z\), from which we can obtain:

[0135]

[0136] where \(\lambda=\lambda_{2} / 2\mu\) k ;

[0137]

[0138] where \(\lambda=\lambda_{2} / 2\mu\) k ;

[0139]

[0140] Specifically, the solution method for \(L\) k+1 is as follows:

[0141] The known Parseval's theorem states that unitary transforms (such as the Discrete Fourier Transform (DFT), Hadamard Transform (HT), and Discrete Cosine Transform (DCT)) can be energy-conserving, that is is a unitary transform. The transform method adopted in the present invention is the discrete cosine transform. Then, let F(·) be the inverse operation of the forward transform operator G(·). By applying the inverse transform to the fourth term on the right side of the equation for L k+1 and using Parseval's theorem, it can thus be rewritten as:

[0142]

[0143] According to the properties of the Kronecker product, if there are matrices N, K, L, M and N = KLM is satisfied, then N can be expressed as where the lowercase letters represent the vertical stacking of the corresponding matrix columns. Then, let A = F(W k+1 - B 4k ), then the rewritten equation for L k+1 can be rewritten as:

[0144]

[0145] After differentiating the rewritten equation for L k+1 , the following linear equation can be obtained:

[0146]

[0147] where This problem can be solved using the LSQR algorithm.

[0148] Step 5: Visualize the anomaly detection results. First, transpose S, and then calculate the l2 norm of each column of the transposed matrix S'. Since the size of the matrix S' is 10×22500, a row vector r of size 1×22500 can be obtained after calculation. Then, reconstruct r into a matrix R* of the original data size, that is, 150×150. Finally, display R* in the form of a picture, which is the anomaly detection result graph.

[0149] To evaluate the anomaly detection effect of the model, we conduct evaluations from the perspectives of 2 evaluation metrics and visual effects.

[0150] (1) ROC curve

[0151] The two-dimensional Receiver Operating Characteristic curve (ROC) represents the relationship between the detection probability \(P\) D and the False Alarm (FA) probability \(P\) F as the separation threshold \(\tau\in(0,1)\) varies. Here, \(P\) D and \(P\) F can be calculated as follows:

[0152]

[0153] where \(N\) D and \(N\) T represent the number of true anomaly pixels detected and the number of all true anomaly pixels at a specific \(\tau\), respectively, and \(N\) F and \(N\) A represent the number of false anomaly pixels detected at the threshold \(\tau\) and the number of all pixels in the image, respectively.

[0154] (2) AUC value

[0155] The AUC value is usually used as an important performance evaluation metric to estimate the algorithm performance under different parameters. Ideally, this value is 1. The closer this value is to 1, the better the algorithm performance under this parameter. The calculation formula of AUC is:

[0156]

[0157] To verify the effectiveness of the model proposed in this patent, the following seven methods are selected for comparison in this embodiment:

[0158] (1) Reed-Xiaoli (RX) algorithm: This method is a classic hyperspectral image anomaly detection method based on PCA and Mahalanobis distance, and is a benchmark for early statistical algorithms.

[0159] (2) The Low-Rank and Sparse Matrix Decomposition-Based Mahalanobis Distance Method (LSMAD): This method is based on low-rank sparse matrix decomposition. By introducing Mahalanobis distance and low-rank background attribute constraints, it can effectively avoid the instability of sparse components and ensure the accuracy and stability of background estimation in anomaly detection.

[0160] (3) The Low-Rank and Sparse Representation Method (LRASR): It uses Low-Rank Representation (LRR) to model the background part, adds a sparse-inducing regularization term to the representation coefficients to characterize the local representation of each pixel, and proposes a dictionary construction strategy to make the atoms in the dictionary more likely to belong to the background. The dictionary covers all ground material classes in the scene.

[0161] (4) The Graph and Total Variation Regularized Low-Rank Representation Method (GTVLRR): This method fully considers the valuable spatial information in hyperspectral images and the local geometric information of hyperspectral data, incorporates graph regularization and Total Variation (TV) regularization into the LRR formula to preserve the local geometric structure and spatial relationships in hyperspectral images.

[0162] (5) The Robust Hyperspectral Denoising Method (RhyDe). This is a hyperspectral image denoising and anomaly detection algorithm based on low-rank and sparse representation. This method achieves explicit low-rank representation, promotes self-similarity, and preserves rare pixels by using a collaborative sparsity. That is, it can effectively retain outlier information while denoising, providing a guarantee for the anomaly detection task.

[0163] (6) S 1 / 2 and the Graph Regularization Method (The S 1 / 2 and Total Variation Low Rank Matrix Decomposition Method, SRLRRSSTV): This method is a low-rank matrix decomposition method using the S 1 / 2 norm and having an image denoising module. It uses two-dimensional Total Variation (TV) regularization in space and one-dimensional Total Variation regularization along the spectral dimension, and combines spectral-spatial total variation (SSTV) regularization in this way to maximize the utilization of the spatial characteristics of HSI.

[0164] (7) The Tensor Low-Rank and Sparse Representation with PCA method (PCA-TLRSR): This method designates the Principal Component Analysis (PCA) method as a preprocessing step, and separates the low-rank background part represented by the tensor background dictionary and the corresponding coefficient part by extending the Three-Dimensional Tensor Low-Rank Representation (3D TLR) model.

[0165] In addition to the above-mentioned Pavia dataset, the experimental dataset also includes 4 other real datasets: Texas Coast, Los Angeles1, Los Angeles2, and Airport. Their pseudo-color images and anomaly ground truth maps are as Figure 5 shown, where the first row is the pseudo-color image and the second row is the anomaly ground truth map.

[0166] The experimental results of each method in this embodiment are as Figure 6 、 Figure 7 、 Figure 8 、 Figure 9 、 Figure 10 shown, and the differences in the anomalies detected by each method can be visually and intuitively felt in Figures 6 to 10 . For example, in Figure 6 , by comparing the result graphs of other methods, it can be seen that the method proposed in the present invention can well suppress the background while detecting most of the anomalies, and there is no background residue as shown in Figure 6 -e, Figure 6 -h, Figure 6 -i, etc. As shown in Figure 8 , the effect on the Los Angeles2 dataset is generally poor, but overall, RhyDe and the method proposed in the present invention can show better detection performance.

[0167] As shown in Figure 11 、 Figure 12 、 Figure 13 、 Figure 14 、 Figure 15 are the ROC curves of different algorithms on 5 real datasets. The closer the curve is to the upper left corner, the better the performance of the method. It can be easily seen that the red curve corresponding to the method proposed in the present invention is significantly closer to the upper left and is in the first echelon.

[0168] The AUC results of different methods on different datasets are as Figure 16As shown, the method proposed by the present invention can achieve the best AUC value on these 5 data sets.

[0169] In summary, whether it is qualitative evaluation or quantitative evaluation, the method proposed by the present invention can show good anomaly detection performance, which effectively demonstrates the effectiveness of the proposed method.

[0170] The present invention is described from the viewpoints of purpose of use, efficacy, progress and novelty. It has practical progressiveness and meets the functional enhancement and use requirements emphasized by the patent law. The above description and drawings of this application are only the preferred embodiments of this application and do not limit this application. Therefore, all those similar or identical to the structure, device, features, etc. of this application, that is, all equivalent substitutions or modifications made according to the scope of the patent application of this application, shall fall within the scope of the patent application protection of this application.

[0171] The specific embodiments described above have further elaborated on the purpose, technical solution and beneficial effects of the present invention. It should be understood that the above is only the specific embodiment of the present invention and is not used to limit the protection scope of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method based on S 2 / 3 A hyperspectral image anomaly detection method with a sparse regularization term, characterized in that: The following steps are involved: S1. Acquire a hyperspectral image and preprocess the hyperspectral image to obtain three-dimensional data of the hyperspectral image; S2. Reduce the dimensionality of three-dimensional data by principal component analysis; S3. reconstructing the reduced 3D data into a 2D Casorati matrix, and establishing an HSI model based on the obtained Casorati matrix; S4. According to the obtained HSI model, establish 2 / 3 A low-rank sparse matrix decomposition model with sparse regularization terms is constructed, and the output anomaly matrix is ​​calculated; S5. Extract the anomaly measurement of each pixel according to the output anomaly matrix and generate an anomaly detection result graph.

2. A method based on S according to claim 1. 2 / 3 A hyperspectral image anomaly detection method with a sparse regularization term, characterized in that: Step S3 includes the following steps: S301. Construct an original HSI data cube including spatial and spectral dimensions, and perform one-dimensional expansion on the spatial dimension of the HSI data cube, and arrange each spectral band into a column vector. The HSI data cube can be expressed as: R×C×b Among them, R is the image scene height, C is the image scene width, and B is the number of spectral bands; S302. According to the obtained column vector, the HSI data cube is rearranged to obtain a two-dimensional Casorati matrix. The size of the two-dimensional Casorati matrix can be expressed as: H×B Among them, H = R × C, which represents the total number of pixels in the image scene, and B is the number of spectral bands; S303. According to the obtained two-dimensional Casorati matrix, an HSI data model is established, which can be expressed as: M=L+S+N Among them, M is the two-dimensional Casorati matrix, L is the low-rank term representing the background part, S is the sparse term representing the abnormal part, and N is the noise.

3. A method based on S according to claim 1. 2 / 3 A hyperspectral image anomaly detection method with a sparse regularization term, characterized in that: Step S4 includes the following steps: S401. Establishment based on S 2 / 3 and a low-rank sparse matrix factorization model with sparse regularization terms, which can be expressed as: s.t.||M-L-S|| F ≤η Among them, σ i is the i-th singular value of matrix L, D h is the differential operator in the horizontal space direction, D v is the differential operator in the vertical space direction, D s is the finite difference operator along the spectrum, λ1, λ2, λ3 are trade-off parameters, G is the forward transformation operator, η is a constant proportional to the standard deviation of Gaussian noise, and j is the summation index; S402. Based on the alternating direction multiplier method, the low-rank sparse matrix decomposition model obtained in step S401 is calculated to obtain an output anomaly matrix.

4. A method based on S according to claim 3. 2 / 3 A hyperspectral image anomaly detection method with a sparse regularization term, characterized in that: Step S402 includes the following steps: S402-1. According to the low-rank sparse matrix decomposition model obtained in step S401, auxiliary variables are introduced and the low-rank sparse matrix decomposition model is subjected to variable separation. The low-rank sparse matrix decomposition model after variable separation can be expressed as: s.t.X=L,P=D h LD s ,Q=D v LD s ,W=G(L),||M-L-S|| F ≤η Among them, X, P, Q, and W are auxiliary variables introduced respectively. is the set of real numbers, ‖·‖ F represents the F-norm of a matrix, which is defined as the square root of the sum of the squares of all elements of the matrix; S402-2. Perform an augmented Lagrangian transform on the low-rank sparse matrix decomposition model after the variable separation, and the formula can be expressed as: Among them, B1, B2, B3, B4, B5 are Lagrange multipliers, μ is the penalty parameter, λ1, λ2, λ3 are trade-off parameters; S402-3. According to the augmented Lagrangian function obtained in step S402-2, the variables in the augmented Lagrangian function are updated sequentially by an iterative alternation method; S402-4. According to the calculated variables, determine whether the iteration condition is met, and the iteration condition can be expressed as: ||M-L-S|| F / ||M|| F ≤ε Wherein, ε is the relative error threshold. When the condition is met, the matrix S is output, otherwise, the process returns to step S402-3.

5. A method based on S according to claim 1. 2 / 3 A hyperspectral image anomaly detection method with a sparse regularization term, characterized in that: Step S5 includes the following steps: S501. Transpose the output anomaly matrix obtained in step S4 to obtain a transposed output anomaly matrix; S502. Calculate the abnormal intensity of each pixel in the transposed output abnormal matrix, which can be expressed as: r i ＝||S′ i ||2 Among them, r i is the anomaly intensity, S′ is the transposed output anomaly matrix, S′ i is the i-th column of the transposed output anomaly matrix S′, and i is the total number of all pixels in the transposed matrix.

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