Hyperspectral anomaly detection method based on low-rank representation and collaborative representation

Abstract

The application discloses a hyperspectral anomaly detection method based on low rank representation and collaborative representation, mainly solves the problems that the existing anomaly detection method is insufficient in comprehensively utilizing global and local information of a hyperspectral image and a background dictionary is unreliable. The scheme comprises the following steps: 1) constructing a progressive background dictionary based on low rank representation, establishing a low rank representation model, and obtaining a background part and an anomaly part by optimizing and solving the low rank representation model; 2) constructing a local background dictionary based on similarity on the basis of the progressive background dictionary, establishing a collaborative representation model, and obtaining a reconstruction residual of collaborative representation of each pixel by optimizing and solving the collaborative representation model; and 3) fusing the anomaly part obtained by the low rank representation and the reconstruction residual obtained by the collaborative representation in a Hadamard product mode to obtain a final anomaly detection result. By combining the low rank representation and the collaborative representation, the global-local information of the hyperspectral image can be fully considered, the hyperspectral anomaly detection performance is effectively improved, and the false alarm rate is reduced.

Description

Technical Field

[0001] This invention belongs to the field of hyperspectral remote sensing image processing technology, and further relates to hyperspectral anomaly detection, specifically a hyperspectral anomaly detection method based on low-rank representation and cooperative representation, which can be used in precision agriculture, military reconnaissance, marine monitoring, mineral exploration, etc. Background Technology

[0002] Hyperspectral anomaly detection does not require any prior knowledge of the target; it can detect pixels in a scene whose features differ from those of surrounding pixels and classify them as anomalous targets. As an unsupervised process, hyperspectral anomaly detection technology has been widely applied in fields such as precision agriculture, military reconnaissance, marine monitoring, and mineral exploration.

[0003] In recent years, methods based on low-rank and collaborative representations have developed rapidly in the field of hyperspectral anomaly detection, attracting widespread attention from researchers. For example, Xu Yang et al. proposed a low-rank and sparse representation-based hyperspectral anomaly detection method in their paper "Anomaly Detection in Hyperspectral Images Based on Low-Rank and Sparse Representation." Li Wei and Du Qian proposed a collaborative representation-based method in their paper "Collaborative Representation for Hyperspectral Anomaly Detection." In these representation-based anomaly detection methods, the construction of the background dictionary plays a decisive role in the representation effect, but it suffers from two problems: 1) insufficient coverage of ground cover types may lead to missed detections; 2) the atoms in the background dictionary are not pure enough, and when anomalous pixels are mixed in, the background dictionary becomes contaminated, causing missed detections. Furthermore, in existing hyperspectral anomaly detection tasks, low-rank representation only considers global information, while collaborative representation only considers local information; neither of them comprehensively considers the global and local information of the hyperspectral image, resulting in poor detection results. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of existing technologies by proposing a hyperspectral anomaly detection method based on low-rank representation and cooperative representation. This method constructs a corresponding background dictionary and effectively combines low-rank and cooperative representations, solving the problem that existing methods suffer from impure background dictionaries, resulting in missed detections and poor detection results. This invention adopts a progressive framework, constructing the low-rank representation dictionary step by step, effectively selecting a pure and representative background dictionary. Based on this, a similarity-based background dictionary is selected for the cooperative representation. Simultaneously, the detection results of low-rank and cooperative representations are effectively combined, further improving the hyperspectral anomaly detection performance and effectively reducing the false alarm rate.

[0005] The approach to implementing this invention is as follows: First, a progressive background dictionary based on low-rank representation is constructed, a low-rank representation model is established, and the sparse outlier part is obtained after optimizing and solving it; second, a background dictionary based on similarity is selected for each pixel to be tested, a collaborative representation model is established, the model is optimized and solved, and the reconstruction residual of the collaborative representation is calculated; finally, the outlier part obtained by the low-rank representation and the reconstruction residual obtained by the collaborative representation are fused in the form of Hadamard product to obtain the final detection result.

[0006] The specific steps for achieving the above objectives according to the present invention include the following:

[0007] (1) Construct a progressive background dictionary:

[0008] (1.1) Input the original hyperspectral image X 3D ∈R w×h×b Where w represents the width, h represents the height, and b is the number of spectral bands; a sliding window is used to process the original hyperspectral image X. 3D The hyperspectral image is divided into T sub-blocks by setting the sliding window size to m×m. For the t-th sub-block X t 3D ∈R m×m×b Two-dimensionalization yields X t ∈R (n / T)×b n = w × h represents the number of pixels;

[0009] (1.2) The original hyperspectral image is two-dimensionalized to obtain the hyperspectral image X∈R. n×b The average spectral vector of X is calculated according to the following formula. And use it as the reference vector:

[0010]

[0011] Where, x ν Let ν represent the ν-th pixel in X, where ν = 1, 2, ..., n;

[0012] (1.3) Calculate the relationship between each pixel in each hyperspectral sub-block and the [missing information]. The Rao-SID distance between the elements is used to select the pixels corresponding to the maximum and minimum Rao-SID distances in each sub-block as reference pixels, resulting in a reference dictionary of 2T pixels, i.e., G = [g1, g2, ..., g...]. 2T ]∈R 2T×b , where 2T << n;

[0013] (1.4) Cluster the reference dictionary G, dividing it into k different clusters ψ = {ψ1, ψ2, ..., ψ3} based on similarity. k};

[0014] (1.5) Calculate the approximation of each pixel in the cluster to all pixels within the cluster in turn. and the similarity to pixels outside the cluster.

[0015]

[0016]

[0017] Where, n k This represents the number of pixels in the k-th cluster. Represents the i-th pixel in the k-th cluster. This represents the j-th pixel in the k-th cluster, where i, j = 1, 2, ..., n k ; Represents the current cluster ψ k The j'th pixel outside, j' = 1, 2, ..., (nn) k ),nn k It is the current cluster ψ k All pixels outside;

[0018] For the current cluster ψ k Each pixel in Perform the following calculations and sort the results in ascending order. Sort the data and select the first p pixels as ψ. k The representative pixel in the image is:

[0019]

[0020] Each cluster is calculated sequentially to obtain k×p representative pixels, forming a representative dictionary D = [d1, d2, ..., dp]. k×p ];

[0021] (1.6) Calculate the Rao-SID distance between any two pixels in the dictionary, and use the maximum distance as the threshold d. Threshold :

[0022]

[0023] Where, d a' It represents the a'-th pixel in the dictionary, d b' Here, a' and b' represent the b'-th pixel in the dictionary, and a' and b' are the pixel indices in the dictionary, where a', b' = 1, 2, ..., k × p;

[0024] Calculate x ν With the pixel d in the dictionary D a' Rao-SID distance d between RS (x ν ,d a' The smaller the distance, the closer the two pixels are; let the minimum distance be d'. RS (x ν ), will be greater than d Threshold d' RS (x ν The corresponding pixel x) ν Defined as a potential representative pixel, i.e., pixel x is determined according to the following formula. ν Is it a potential representative pixel?

[0025]

[0026] Add all potential representative pixels to the representative dictionary to construct the final progressive background dictionary D' = [d'1, d'2, ..., d'']. l ]∈R b×l l is the number of pixels in the progressive background dictionary, l≥(k×p);

[0027] (2) Establish a low-rank representation model:

[0028] (2.1) Establish a low-rank representation model for the entire hyperspectral image based on the progressive background dictionary D':

[0029] X = D'S + E

[0030] Where S = [s1, s2, ..., s n ]∈R l×n Let E be the coefficient matrix, where E = [e1, e2, ..., e n ]∈R b×n This is an abnormal part;

[0031] (2.2) The objective function for constructing the low-rank representation model is as follows:

[0032]

[0033] st X=D'S+E

[0034] Among them, ||·|| * The nuclear norm is the sum of the singular values ​​of a matrix, ||·||. 2,1 Indicate l 2,1 Norm, which is the sum of the l2 norms of the columns of a matrix, λ LRR Represents the balance parameters of the low-rank representation;

[0035] (2.3) The objective function of the low-rank representation model is optimized using the alternating direction multiplier method to obtain the anomaly part E. * ;

[0036] (2.4) Using E * The response value determines the anomaly level of the v-th pixel:

[0037]

[0038] Where u represents the band, u = 1, 2, ..., b; T(x ν ) represents matrix E * The l2 norm of column v, when it is greater than the threshold, x ν Pixels are identified as anomalous; conversely, x ν For normal pixels; the degree of abnormality of all pixels is represented as a low-rank result R. LRR ;

[0039] (3) Based on a progressive background dictionary D' with low-rank representation, the pixels x in the hyperspectral image X are... ν As the pixel to be measured, select the pixel in D' that is the same as x. ν The local background dictionary Z = {z1, z2, ..., zn} is composed of the s most similar pixels. s}∈R b×s That is, a similarity-based collaborative representation background dictionary;

[0040] (4) Establish a collaborative representation model, the steps are as follows:

[0041] (4.1) Based on the local background dictionary Z, pixel x ν Establish a collaborative representation model:

[0042] x ν =Zα+r v

[0043] Where α represents x ν The corresponding representation vector, r v Represents the residual vector;

[0044] (4.2) The objective function for constructing the collaborative representation model is as follows:

[0045]

[0046] Where, λ CR Trade-off parameters for collaborative representation;

[0047] (4.3) The objective function of the collaborative representation model is rewritten, and the pixel to be measured is rewritten as... Rewrite the background dictionary as follows Here, 1 is a row vector with a value of 1 in 1×s, such that α satisfies the constraint that the sum is 1; at the same time, a distance weighting matrix Γ is introduced to control the size of α;

[0048] (4.4) Optimize the rewritten objective function and calculate the objective function's performance on the desired outcome. Taking the partial derivatives and setting the result to 0, we get the following result:

[0049]

[0050] In solving Then, the pixel x to be measured is calculated according to the following formula. v The residual is represented by:

[0051]

[0052] (4.5) Calculate the representation residuals for all pixels in the hyperspectral image X sequentially to obtain the cooperative representation results:

[0053] R CR =[r1 CR r2 CR ,...,r n CR ];

[0054] (5) Represent the low-rank result R LRR and the results of the cooperative representation R CR Feature fusion is performed using the Hadamard product method, i.e., R = R LRR ⊙R CR The final anomaly detection result is obtained as R = [r1, r2, ..., r]. n ].

[0055] Compared with the prior art, the present invention has the following advantages:

[0056] First, this invention proposes a progressive background dictionary construction method. Based on the spectral features of the image, a reference dictionary representing global features and a representative dictionary representing local features are selected step by step. While selecting pixels that cover all types of land features, the inclusion of anomalous pixels is avoided, making the selected global background dictionary pure and representative. On this basis, the most similar pixel is selected for collaborative representation of each pixel to be tested, which solves the problem of difficult pixel parameter setting and easy inclusion of anomalous pixels in traditional dual-window selection, thus affecting the performance of anomaly detection.

[0057] Secondly, this invention effectively combines low-rank representation and cooperative representation. By using Hadamard product to fuse the residuals of the low-rank representation and the cooperative representation to obtain the final detection result, it comprehensively considers the global and local information of the image, reduces the false alarm rate, and further improves the detection accuracy. Attached Figure Description

[0058] Figure 1 This is a schematic diagram of the application process of the method of the present invention.

[0059] Figure 2 This is a schematic diagram illustrating the progressive dictionary construction process in the method of the present invention;

[0060] Figure 3 This is a schematic diagram of the datasets used in this invention; where (I) represents the pseudo-color image and its labels of the Gulfport dataset; (II) represents the pseudo-color image and its labels of the Texas Coast-I dataset; and (III) represents the pseudo-color image and its labels of the Texas Coast-II dataset.

[0061] Figure 4 The image shows a comparison of the detection results of the method of this invention and mainstream methods on three datasets; where (Ia) represents the label of the Gulfport dataset; (Ib) to (Ij) represent the detection maps of RX, CRD, LRASR, LSMAD, GTVLRR, GAED, NJCR, AHMID and the method of this invention on the Gulfport dataset, respectively; (II-a) represents the label of the Texas Coast-I dataset; (II-b) to (II-j) represent the detection maps of RX, CRD, LRASR, LSMAD, GTVLRR, GAED, NJCR, AHMID and the method of this invention on the Texas Coast-I dataset, respectively; (III-a) represents the label of the Texas Coast-II dataset; (III-b) to (III-j) represent the detection maps of RX, CRD, LRASR, LSMAD, GTVLRR, GAED, NJCR, AHMID and the method of this invention on the Texas Coast-II dataset, respectively.

[0062] Figure 5 The method of this invention and mainstream methods are compared on three datasets. The graph shows the performance of the method of this invention and the mainstream method on the Gulfport, Texas Coast-I, and Texas Coast-II datasets, respectively. Curve, where P D P represents the true yang rate. F Indicates the false positive rate;

[0063] Figure 6 The method of this invention and mainstream methods are compared on three datasets. The graph shows the performance of the method of this invention and the mainstream method on the Gulfport, Texas Coast-I, and Texas Coast-II datasets, respectively. Curve, where P F τ represents the false positive rate, and τ represents the threshold. Detailed Implementation

[0064] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0065] Example 1: Refer to Figure 1 and Figure 2 The present invention proposes a hyperspectral anomaly detection method based on low-rank representation and cooperative representation, which is implemented according to the following steps:

[0066] Step 1. Construct a progressive background dictionary:

[0067] (1.1) Input the original hyperspectral image X 3D ∈R w×h×b Where w represents the width, h represents the height, and b is the number of spectral bands; a sliding window is used to process the original hyperspectral image X. 3D The hyperspectral image is divided into T sub-blocks by setting the sliding window size to m×m. For the t-th sub-block X t 3D ∈R m×m×b Two-dimensionalization yields X t ∈R (n / T)×b n = w × h represents the number of pixels;

[0068] (1.2) The original hyperspectral image is two-dimensionalized to obtain the hyperspectral image X∈R. n×b The average spectral vector of X is calculated according to the following formula. And use it as the reference vector:

[0069]

[0070] Where, x ν Let ν represent the ν-th pixel in X, where ν = 1, 2, ..., n;

[0071] (1.3) Calculate the relationship between each pixel in each hyperspectral sub-block and the [missing information]. The Rao-SID distance between the elements is used to select the pixels corresponding to the maximum and minimum Rao-SID distances in each sub-block as reference pixels, resulting in a reference dictionary of 2T pixels, i.e., G = [g1, g2, ..., g...]. 2T ]∈R 2T×b , where 2T << n.

[0072] The Rao-SID distance is used to characterize the dissimilarity between two pixels; that is, the larger the distance, the greater the difference between the two pixels. Its calculation formula is as follows:

[0073]

[0074]

[0075] d RS (x u' ,x v' )=tan(d Rao (x u' ,x v' ))·d SID (x u' ,x v' )

[0076] Where, d RS (x u' ,x v' ) represents pixel x u' and x v' The Rao-SID distance between them has a dimension of b×1; B is the band index.

[0077] (1.4) Cluster the reference dictionary G, dividing it into k different clusters ψ = {ψ1, ψ2, ..., ψ3} based on similarity. k In this embodiment, density peak clustering is used to cluster the reference dictionary G. The implementation steps are as follows:

[0078] (1.4.1) Input reference dictionary G = [g1, g2, ..., g 2T ]∈R 2T×b Calculate the pairwise similarity matrix F between elements based on Euclidean distance, and estimate the cutoff distance d. c This distance is in d cDraw a circle with a radius of 20%, and let the number of data points falling inside the circle account for 2% of all data points. This leads to the deduction.

[0079] The similarity matrix F above is calculated according to the following formula:

[0080] f p'q' =||g p' -g q' ||2

[0081] Among them, f p'q' The element in the p'-th row and q'-th column of the similarity matrix F is used to represent element g in the reference dictionary G. p' and g q' The similarity between them is given by p',q'=1,2,...,2T, where p',q'=1,2,...,2T are the pixel indices in the reference dictionary G.

[0082] (1.4.2) Calculate the local density ρ and center offset distance δ based on the similarity matrix and cutoff distance, and plot the decision graph of ρ and δ. The calculation formulas for the local density ρ and center offset distance δ are as follows:

[0083]

[0084]

[0085] (1.4.3) Select cluster centers based on the decision graph, and assign the remaining samples to clusters according to the principle of highest density and closest distance;

[0086] (1.4.4) Complete the clustering and obtain the clustering result ψ={ψ1,ψ2,...,ψ k}

[0087] (1.5) Calculate the approximation of each pixel in the cluster to all pixels within the cluster in turn. and the similarity to pixels outside the cluster.

[0088]

[0089]

[0090] Where, n k This represents the number of pixels in the k-th cluster. Represents the i-th pixel in the k-th cluster. This represents the j-th pixel in the k-th cluster, where i, j = 1, 2, ..., n k ; Represents the current cluster ψ k The j'th pixel outside, j' = 1, 2, ..., (nn) k ),nn kIt is the current cluster ψ k All pixels outside;

[0091] For the current cluster ψ k Each pixel in Perform the following calculations and sort the results in ascending order. Sort the data and select the first p pixels as ψ. k The representative pixel in the image is:

[0092]

[0093] Each cluster is calculated sequentially to obtain k×p representative pixels, forming a representative dictionary D = [d1, d2, ..., dp]. k×p ];

[0094] (1.6) Calculate the Rao-SID distance between any two pixels in the dictionary, and use the maximum distance as the threshold d. Threshold :

[0095]

[0096] Where, d a' It represents the a'-th pixel in the dictionary, d b' Here, a' and b' represent the b'-th pixel in the dictionary, and a' and b' are the pixel indices in the dictionary, where a', b' = 1, 2, ..., k × p;

[0097] Calculate x ν With the pixel d in the dictionary D a' Rao-SID distance d between RS (x ν ,d a' The smaller the distance, the closer the two pixels are; let the minimum distance be d'. RS (x ν ), will be greater than d Threshold d' RS (x ν The corresponding pixel x) ν Defined as a potential representative pixel, i.e., pixel x is determined according to the following formula. ν Is it a potential representative pixel?

[0098]

[0099] Add all potential representative pixels to the representative dictionary to construct the final progressive background dictionary D' = [d'1, d'2, ..., d'']. l ]∈R b×l l is the number of pixels in the progressive background dictionary, l≥(k×p);

[0100] Step 2. Establish a low-rank representation model:

[0101] (2.1) Establish a low-rank representation model for the entire hyperspectral image based on the progressive background dictionary D':

[0102] X = D'S + E

[0103] Where S = [s1, s2, ..., s n ]∈R l×n Let E be the coefficient matrix, where E = [e1, e2, ..., e n ]∈R b×n This is an abnormal part;

[0104] (2.2) The objective function for constructing the low-rank representation model is as follows:

[0105]

[0106] st X=D'S+E

[0107] Among them, ||·|| * The nuclear norm is the sum of the singular values ​​of a matrix, ||·||. 2,1 Indicate l 2,1 Norm, which is the sum of the l2 norms of the columns of a matrix, λ LRR Represents the balance parameters of the low-rank representation;

[0108] (2.3) The objective function of the low-rank representation model is optimized using the alternating direction multiplier method to obtain the anomaly part E. * ;

[0109] (2.4) Using E * The response value determines the anomaly level of the v-th pixel:

[0110]

[0111] Where u represents the band, u = 1, 2, ..., b; T(x ν ) represents matrix E * The l2 norm of column v, when it is greater than the threshold, x ν Pixels are identified as anomalous; conversely, x ν For normal pixels; the degree of abnormality of all pixels is represented as a low-rank result R. LRR ;

[0112] Step 3. Based on the progressive background dictionary D' with low-rank representation, the pixels x in the hyperspectral image X are... ν As the pixel to be measured, select the pixel in D' that is the same as x. ν The local background dictionary Z = {z1, z2, ..., zn} is composed of the s most similar pixels.s}∈R b×s This refers to a collaborative representation background dictionary based on similarity; specifically, this embodiment measures the degree of similarity based on Euclidean distance, and the calculation formula is as follows:

[0113] d(d' l' ,x ν )=||d' l' -x ν ||2,

[0114] Wherein d(d') l' ,x ν ) is the pixel d' in D' l' With x ν The Euclidean distance between them, where l' is the pixel index in D', and l' = 1, 2, ..., l.

[0115] Step 4. Establish the collaborative representation model, the steps are as follows:

[0116] (4.1) Based on the local background dictionary Z, pixel x ν Establish a collaborative representation model:

[0117] x ν =Zα+r v

[0118] Where α represents x ν The corresponding representation vector, r v Represents the residual vector;

[0119] (4.2) The objective function for constructing the collaborative representation model is as follows:

[0120]

[0121] Where, λ CR Trade-off parameters for collaborative representation;

[0122] (4.3) The objective function of the collaborative representation model is rewritten, and the pixel to be measured is rewritten as... Rewrite the background dictionary as follows Here, 1 is a row vector with a value of 1 in 1×s, such that α satisfies the constraint that the sum is 1; at the same time, a distance weighting matrix Γ is introduced to control the size of α.

[0123] The objective function of the collaborative representation model described above is rewritten as follows:

[0124]

[0125] in, This is the new representation vector.

[0126] The distance weighting matrix Γ above is represented as follows:

[0127]

[0128] (4.4) Optimize the rewritten objective function and calculate the objective function's performance on the desired outcome. Taking the partial derivatives and setting the result to 0, we get the following result:

[0129]

[0130] In solving Then, the pixel x to be measured is calculated according to the following formula. v The residual is represented by:

[0131]

[0132] (4.5) Calculate the representation residuals for all pixels in the hyperspectral image X sequentially to obtain the cooperative representation results:

[0133] R CR =[r1 CR r2 CR ,...,r n CR ];

[0134] Step 5. Represent the low-rank result R LRR and the results of the cooperative representation R CR Feature fusion is performed using the Hadamard product method, i.e., R = R LRR ⊙R CR The final anomaly detection result is obtained as R = [r1, r2, ..., r]. n ].

[0135] Example 2: The overall implementation steps of the hyperspectral anomaly detection method proposed in this example are the same as in Example 1. The construction process of the progressive background dictionary will now be described in further detail:

[0136] First, for each cluster, representative pixels are selected based on the principle of smaller pixel differences within the cluster and larger pixel differences outside the cluster, as follows:

[0137] a) To satisfy the principle of small pixel differences within a cluster, the approximation of each pixel in the cluster to all pixels within the cluster is calculated sequentially using the following formula:

[0138]

[0139] Where, n k This represents the number of pixels in the k-th cluster. Represents the i-th pixel in the k-th cluster. This represents the j-th pixel in the k-th cluster, where i, j = 1, 2, ..., n k ;

[0140] b) To satisfy the principle of large pixel differences between clusters, the approximation degree between each pixel in the cluster and the pixels outside the cluster is calculated sequentially. The calculation formula is as follows:

[0141]

[0142] in, Represents the current cluster ψ k The j'th pixel outside, j' = 1, 2, ..., (nn) k ),nn k It is the current cluster ψ k All pixels outside;

[0143] c) The representative pixel in the dictionary should have the smallest distance to the least similar pixel in the current cluster and the largest distance to the most similar pixel outside the current cluster. The selection strategy for the representative dictionary is as follows:

[0144]

[0145] Following the strategy described above, in each cluster ψ k If the p pixels with the smallest distance are selected as the representative pixels in the current cluster, then k×p representative pixels can be selected to form a representative dictionary, i.e., D=[d1,d2,...,dp]. k×p ];

[0146] Then, calculate the Rao-SID distance between any two pixels in the dictionary, and use the maximum distance as the threshold d. Threshold :

[0147]

[0148] Where, d a' It represents the a'-th pixel in the dictionary, d b' Here, a' and b' represent the b'-th pixel in the dictionary, and a' and b' are the pixel indices in the dictionary, where a', b' = 1, 2, ..., k × p;

[0149] Finally, for each pixel x in the hyperspectral image X ν Calculate the value of each pixel d in the dictionary D. a' With x ν The Rao-SID distance between the two pixels. The smaller the distance, the closer the two pixels are considered to be. The minimum distance is denoted as d'. RS (x ν If the minimum distance is found, then the pixel corresponding to x is the closest pixel in the dictionary. νThe pixels. d' RS (x ν ) and d Threshold Compare, if d' RS (x ν ) greater than d Threshold Then we consider x ν If a pixel is not in the representation dictionary, it is a potential representative pixel and needs to be added to the representation dictionary. Then, sequentially determine each pixel x in X. ν If a pixel is a potential representative pixel, determine whether it needs to be added to the representative dictionary.

[0150]

[0151] After the judgment is completed, the final progressive background dictionary D' = [d'1, d'2, ..., d'] can be constructed. l ]∈R b×l l is the number of pixels in the progressive background dictionary, l≥(k×p).

[0152] The effects of the present invention will be further explained below with reference to experiments.

[0153] 1. Experimental conditions:

[0154] The experiments of this invention were conducted in a hardware environment with a CPU clock speed of 2.00 GHz and 16 GB of memory, and a software environment with Windows 10 operating system and MATLAB R2021b.

[0155] 2. Experiment Content:

[0156] This experiment evaluates the performance of the proposed method on the Gulfport, Texas Coast-I, and Texas Coast-II datasets. On each dataset, the detection performance of the proposed method is compared with that of eight mainstream methods from both qualitative (including detection maps and two ROC curves) and quantitative (including two AUC values) perspectives.

[0157] The mainstream methods mainly include RX [paper: Adaptive multiple-band CFAR detection of an optical pattern with unknown spectral distribution], CRD [paper: Collaborative representation for hyperspectral anomaly detection], LRASR [paper: AnomalyDetection in Hyperspectral Images Based on Low-Rank and SparseRepresentation], LSMAD [paper: A low-rank and sparse matrix decomposition-based mahalanobis distance method for hyperspectral anomaly detection], GTVLRR [paper: Graph and total variation regularized low-rank representation for hyperspectral anomaly detection], GAED [paper: Hyperspectral anomaly detection with guided autoencoder], NJCR [paper: Nonnegative-constrained jointcollaborative representation with union dictionary for hyperspectral anomaly detection] and AHMID [paper: Anomaly detection of hyperspectral image with hierarchical anti-noise mutual-incoherence-induced low-rank representation].

[0158] 3. Simulation Results and Analysis:

[0159] Figure 4This is a comparison chart of the detection results of the method of this invention and mainstream methods on three datasets; where (I)-(III) correspond to the Gulfport, Texas Coast-I, and Texas Coast-II datasets, respectively; (a) represents the label; (b)-(i) correspond to eight existing methods: RX, CRD, LRASR, LSMAD, GTVLRR, GAED, NJCR, and AHMID, respectively; and (j) corresponds to the method of this invention. See details: Figure 4 In the table, (Ia) represents the label of the Gulfport dataset, and (Ib) to (Ij) represent the detection results of RX, CRD, LRASR, LSMAD, GTVLRR, GAED, NJCR, AHMID, and the method of the present invention on the Gulfport dataset, respectively; (II-a) represents the label of the Texas Coast-I dataset, and (II-b) to (II-j) represent the detection results of RX, CRD, LRASR, LSMAD, GTVLRR, GAED, NJCR, AHMID, and the method of the present invention on the Texas Coast-I dataset, respectively; (III-a) represents the label of the Texas Coast-II dataset, and (III-b) to (III-j) represent the detection results of RX, CRD, LRASR, LSMAD, GTVLRR, GAED, NJCR, AHMID, and the method of the present invention on the Texas Coast-II dataset, respectively.

[0160] By comparing existing methods, the method of this invention, and the label, it can be seen that the method of this invention has the best effect and is significantly better than the mainstream methods among the eight existing technologies.

[0161] Figure 5 and Figure 6 The methods of this invention and mainstream methods are compared on three datasets. curves and Curves; where (I) represents the Gulfport dataset, (II) represents the Texas Coast-I dataset, and (III) represents the Texas Coast-II dataset.

[0162] The larger the area under the curve, the better the detection performance. Figure 5 It can be seen that the detection effect of the method of the present invention is the best; The smaller the area under the curve, the lower the false alarm rate and the stronger the ability to suppress background noise. Figure 6 It can be seen that the method of the present invention has the lowest false alarm rate, better background suppression effect, and the best detection performance.

[0163] The table below (Table 1) lists the AUC values ​​of the method of this invention and eight mainstream methods on three datasets (i.e., and The AUC value is between 0 and 1. The closer the value is to 1, the better the detection effect; for The closer the value is to 0, the lower the false alarm rate and the better the ability to suppress the background, that is, the better the performance.

[0164] Table 1. Comparison of AUC values ​​of the proposed method and eight mainstream methods on three datasets.

[0165]

[0166] As shown in the table above, the method of this invention has the highest performance on three different datasets (Gulfport, Texas Coast-I, and Texas Coast-II). and the smallest This further demonstrates that the method of the present invention has the highest detection accuracy and the lowest false alarm rate compared to existing methods, i.e., the best performance.

[0167] The above experimental results demonstrate the correctness and effectiveness of the method proposed in this invention.

[0168] The parts of this invention not described in detail are common knowledge to those skilled in the art.

[0169] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Obviously, those skilled in the art, after understanding the content and principle of the present invention, may make various modifications and changes in form and detail without departing from the principle and structure of the present invention. However, these modifications and changes based on the concept of the present invention are still within the scope of protection of the claims of the present invention.

Claims

1. A hyperspectral anomaly detection method based on low-rank representation and cooperative representation, characterized in that, Includes the following steps: (1) Construct a progressive background dictionary: (1.1) Input the original hyperspectral image X 3D ∈R w×h×b Where w represents the width, h represents the height, and b is the number of spectral bands; a sliding window is used to process the original hyperspectral image X. 3D The hyperspectral image is divided into T sub-blocks by setting the sliding window size to m×m. For the t-th sub-block X t 3D ∈R m×m×b Two-dimensionalization yields X t ∈R (n / T)×b n = w × h represents the number of pixels; (1.2) The original hyperspectral image is two-dimensionalized to obtain the hyperspectral image X∈R. n×b The average spectral vector of X is calculated according to the following formula. And use it as the reference vector: Where, x ν Let ν represent the ν-th pixel in X, where ν = 1, 2, ..., n; (1.3) Calculate the relationship between each pixel in each hyperspectral sub-block and the [missing information]. The Rao-SID distance between the elements is used to select the pixels corresponding to the maximum and minimum Rao-SID distances in each sub-block as reference pixels, resulting in a reference dictionary of 2T pixels, i.e., G = [g1, g2, ..., g...]. 2T ]∈R 2T×b , where 2T << n; (1.4) Cluster the reference dictionary G, dividing it into k different clusters ψ = {ψ1, ψ2, ..., ψ3} based on similarity. k }; (1.5) Calculate the approximation of each pixel in the cluster to all pixels within the cluster in turn. and the similarity to pixels outside the cluster. Where, n k This represents the number of pixels in the k-th cluster. Represents the i-th pixel in the k-th cluster. This represents the j-th pixel in the k-th cluster, where i, j = 1, 2, ..., n k ; Represents the current cluster ψ k The j'th pixel outside, j' = 1, 2, ..., (nn) k ),nn k It is the current cluster ψ k All pixels outside; For the current cluster ψ k Each pixel in Perform the following calculations and sort the results in ascending order. Sort the data and select the first p pixels as ψ. k The representative pixel in the image is: Each cluster is calculated sequentially to obtain k×p representative pixels, forming a representative dictionary D = [d1, d2, ..., dp]. k×p ]; (1.6) Calculate the Rao-SID distance between any two pixels in the dictionary, and use the maximum distance as the threshold d. Threshold : Where, d a' It represents the a'-th pixel in the dictionary, d b' Here, a' and b' represent the b'-th pixel in the dictionary, and a' and b' are the pixel indices in the dictionary, where a', b' = 1, 2, ..., k × p; Calculate x ν With the pixel d in the dictionary D a' Rao-SID distance d between RS (x ν ,d a' The smaller the distance, the closer the two pixels are; let the minimum distance be d'. RS (x ν ), will be greater than d Threshold d' RS (x ν The corresponding pixel x) ν Defined as a potential representative pixel, i.e., pixel x is determined according to the following formula. ν Is it a potential representative pixel? Add all potential representative pixels to the representative dictionary to construct the final progressive background dictionary D' = [d'1, d'2, ..., d'']. l ]∈R b×l l is the number of pixels in the progressive background dictionary, l≥(k×p); (2) Establish a low-rank representation model: (2.1) Establish a low-rank representation model for the entire hyperspectral image based on the progressive background dictionary D': X = D'S + E Where S = [s1, s2, ..., s n ]∈R l×n Let E be the coefficient matrix, where E = [e1, e2, ..., e n ]∈R b×n This is an abnormal part; (2.2) The objective function for constructing the low-rank representation model is as follows: st X=D'S+E Among them, ||·|| * The nuclear norm is the sum of the singular values ​​of a matrix, ||·||. 2,1 Indicate l 2,1 Norm, which is the sum of the l2 norms of the columns of a matrix, λ LRR Represents the balance parameters of the low-rank representation; (2.3) The objective function of the low-rank representation model is optimized using the alternating direction multiplier method to obtain the anomaly part E. * ; (2.4) Using E * The response value determines the anomaly level of the v-th pixel: Where u represents the band, u = 1, 2, ..., b; T(x ν ) represents the l2 norm of the v-th column of matrix E*. When it is greater than a threshold, x ν Pixels are identified as anomalous; conversely, x ν For normal pixels; the degree of abnormality of all pixels is represented as a low-rank result R. LRR ; (3) Based on a progressive background dictionary D' with low-rank representation, the pixels x in the hyperspectral image X are... ν As the pixel to be measured, select the pixel in D' that is the same as x. ν The local background dictionary Z = {z1, z2, ..., zn} is composed of the s most similar pixels. s }∈R b×s That is, a similarity-based collaborative representation background dictionary; (4) Establish a collaborative representation model, the steps are as follows: (4.1) Based on the local background dictionary Z, pixel x ν Establish a collaborative representation model: x ν =Zα+r v Where α represents x ν The corresponding representation vector, r v Represents the residual vector; (4.2) The objective function for constructing the collaborative representation model is as follows: Where, λ CR The trade-off parameters for cooperative representation; (4.3) The objective function of the collaborative representation model is rewritten, and the pixel to be measured is rewritten as... Rewrite the background dictionary as follows Here, 1 is a row vector with a value of 1 in 1×s, such that α satisfies the constraint that the sum is 1; at the same time, a distance weighting matrix Γ is introduced to control the size of α; (4.4) Optimize the rewritten objective function and calculate the objective function's performance on the desired outcome. Taking the partial derivatives and setting the result to 0, we get the following result: In solving Then, the pixel x to be measured is calculated according to the following formula. v The residual is represented by: (4.5) Calculate the representation residuals for all pixels in the hyperspectral image X sequentially to obtain the cooperative representation results: R CR ＝[r1 CR ,r2 CR ,...,r n CR ]； (5) Represent the low-rank result R LRR and the results of the cooperative representation R CR Feature fusion is performed using the Hadamard product method, i.e., R = R LRR ⊙R CR The final anomaly detection result is obtained as R = [r1, r2, ..., r]. n ].

2. The method according to claim 1, characterized in that: The Rao-SID distance mentioned in step (1.3) is calculated using the following formula: d RS (x u' ,x v' )=tan(d Rao (x u' ,x v' ))·d SID (x u' ,x v' ) Where, d RS (x u' ,x v' ) represents pixel x u' and x v' The Rao-SID distance between them has a dimension of b×1; B is the band index.

3. The method according to claim 2, characterized in that: The Rao-SID distance is used to characterize the dissimilarity between two pixels; that is, the greater the distance, the greater the difference between the two pixels.

4. The method according to claim 1, characterized in that: In step (1.4), the reference dictionary G is clustered using the density peak clustering method. The steps are as follows: (1.4.1) Input reference dictionary G = [g1, g2, ..., g 2T ]∈R 2T×b Calculate the pairwise similarity matrix F between elements based on Euclidean distance, and estimate the cutoff distance d. c ; (1.4.2) Calculate the local density ρ and center offset distance δ based on the similarity matrix and cutoff distance, and draw the decision graph of ρ and δ; (1.4.3) Select cluster centers based on the decision graph, and assign the remaining samples to clusters according to the principle of highest density and closest distance; (1.4.4) Complete the clustering and obtain the clustering result ψ={ψ1,ψ2,...,ψ k } 5. The method according to claim 4, characterized in that: The similarity matrix F in step (1.4.1) is calculated according to the following formula: f p'q' =||g p' -g q' ||2 Among them, f p'q' The element in the p'-th row and q'-th column of the similarity matrix F is used to represent element g in the reference dictionary G. p' and g q' The similarity between them is given by p',q'=1,2,...,2T, where p',q'=1,2,...,2T are the pixel indices in the reference dictionary G.

6. The method according to claim 4, characterized in that: In step (1.4.1), the cutoff distance d c It is based on d c Draw a circle with radius d, and let the number of data points falling inside the circle be 2% of the total number of data points. Then, deduce d. c The value of .

7. The method according to claim 4, characterized in that: The local density ρ and center offset distance δ in step (1.4.2) are calculated using the following formulas:

8. The method according to claim 1, characterized in that: Step (3) involves selecting from D' the value of x. ν The local background dictionary Z = {z1, z2, ..., zn} is composed of the s most similar pixels. s }∈R b×s Specifically, similarity is measured using Euclidean distance, and the calculation formula is as follows: d(d' l' ,x ν )=||d' l' -x ν ||2, Wherein d(d') l' ,x ν ) is the pixel d' in D' l' With x ν The Euclidean distance between them, where l' is the pixel index in D', and l' = 1, 2, ..., l.

9. The method according to claim 1, characterized in that: In step (4.3), the objective function of the collaborative representation model is rewritten as follows: in, This is the new representation vector.

10. The method according to claim 1 or 9, characterized in that: The distance weighting matrix Γ is represented as follows:

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