Abnormal target detection method in hyperspectral images based on total variation low-rank tensor decomposition

Abstract

The invention relates to a method for detecting abnormal targets in hyperspectral images based on total variation low-rank tensor decomposition, and belongs to the technical field of abnormal target detection in hyperspectral remote sensing images. The invention aims to solve the problem that the current abnormal detection method cannot well separate the background and the abnormality. The invention adopts a total variation regularized low-rank tensor decomposition model to decompose the hyperspectral image into a low-rank data part and a mixed information part; then, the low-rank data part is decomposed into a mixed information part by using the total variation regularized low-rank tensor decomposition model. 2,1 The norm and domain transformation recursive filter are used to detect anomalies in the mixed information part; and the collaborative representation detector is used to extract the anomaly information embedded in the low-rank background data part; the initial detection results of the low-rank data and the mixed information part are fused to obtain the final detection result. It is mainly used for abnormal target detection in hyperspectral images.

Description

Technical Field

[0001] The invention belongs to the technical field of abnormal target detection in hyperspectral remote sensing images, and in particular relates to a method for detecting abnormal targets in hyperspectral remote sensing images. Background Art

[0002] Hyperspectral images (HSI) with hundreds of spectral bands play a key role in remote sensing scenarios. Hyperspectral images contain rich spectral and spatial information, so they have been widely used in many fields, such as mineral exploration, precision agriculture, and urban monitoring. In these applications, hyperspectral anomaly detection is a technique that detects pixels with significant spectral differences from the surrounding background without prior information.

[0003] At present, anomaly detection methods for hyperspectral images have been developed. However, these anomaly detection methods are still insufficient in utilizing the spatial information of hyperspectral images, resulting in the inability to separate background and anomalies well. The total variation regularized low-rank tensor decomposition (LRTDTV) model is first designed to restore hyperspectral images. This method can decompose HSI into a clean HSI part and a mixed noise part. However, any decomposition method cannot completely separate information such as anomalies and noise from the original HSI. Therefore, the hyperspectral image abnormal target detection method based on total variation low-rank tensor decomposition proposed in the present invention first decomposes the hyperspectral image using the LRTDTV model, and then processes the decomposed parts separately. Finally, the detection results of the two parts are fused together to better separate the background and anomalies. Summary of the invention

[0004] In order to solve the problem that the current anomaly detection method cannot separate the background and anomalies well, the present invention proposes a hyperspectral image abnormal target detection method based on total variation low rank tensor decomposition.

[0005] The method for abnormal target detection in hyperspectral images based on total variation low-rank tensor decomposition includes the following steps:

[0006] The total variation regularized low-rank tensor decomposition model is used to decompose the hyperspectral image into low-rank data parts. and mixed information part M; then use l 2,1 The norm and domain transformation recursive filter are used to perform anomaly detection on the mixed information part; and the collaborative representation detector is used to extract the anomaly information embedded in the low-rank background data part; the initial detection results of the low-rank data and the mixed information part are fused to obtain the final detection result.

[0007] Furthermore, the process of decomposing the hyperspectral image into a low-rank data part and a mixed information part by using the total variation regularized low-rank tensor decomposition model comprises the following steps:

[0008] Firstly, the total variation regularized low-rank tensor decomposition model is used to decompose the hyperspectral image; then, based on the augmented Lagrangian multiplier method, the regularized low-rank tensor decomposition model is transformed into a method to minimize the augmented Lagrangian function, thereby reducing the low-rank data part. Expressed as The mixed information part M is expressed as

[0009] In the total variation regularized low-rank tensor decomposition model, is the low-rank data part, is a sparse term, is a Gaussian term.

[0010] Furthermore, the total variation regularized low-rank tensor decomposition model is as follows:

[0011]

[0012] in, represents the original hyperspectral image, C× 1 U 1 × 2 U 2 × 3 U 3 is a core tensor of C and rank r i′ The factor matrix U i′ Tucker decomposition, U 1 , U 2 , U 3 is the factor matrix under the three modes, I is the identity matrix; τ,λ 1 ,β is an auxiliary parameter in the total variation regularized low-rank tensor decomposition model; is the SSTV norm term.

[0013] Furthermore, the regularized low-rank tensor decomposition model is transformed into the minimized augmented Lagrangian function in the process of minimizing the augmented Lagrangian function as follows:

[0014]

[0015] in, are intermediate variables, representing and D w (·)=[w 1 ×D h (·); w 2 ×D v (·); w 3 ×D t (·)] is a weighted three-dimensional difference operator, D h ,D v ,Dt is the first-order difference operator in three different directions of the hyperspectral image cube; Γ i′ is the Lagrange multiplier, i′=1,2,3; <·> represents the inner product operation, τ,λ 1 ,β is an auxiliary parameter in the total variation regularized low-rank tensor decomposition model.

[0016] Furthermore, in the process of detecting anomalies in the mixed information part, l 2,1 Norm regularization is used to perform initial detection on the mixed information part, and then the domain transformation recursive filter is used to smooth the initial detection result.

[0017] Further, the initial detection result of the mixed information part is expressed as:

[0018]

[0019] Where D represents the number of spectral bands of the hyperspectral data, H and W represent the length and width of the hyperspectral image, respectively. is an element in the mixed information part M.

[0020] Further, the domain transform recursive filter is expressed as:

[0021] γ 1 = DTRF(I,G,δ s ,δ r ) (6)

[0022] Among them, I is the use of l 2,1 The detection result diagram of the mixed information part calculated by norm regularization, G represents the guide image, δ s and δ r are two smoothing parameters of the domain transform recursive filter.

[0023] Furthermore, the guide image is as follows:

[0024]

[0025] Where μ is the original hyperspectral image The matrix consisting of the spectral averages of all pixels in .

[0026] Furthermore, the specific process of extracting abnormal information embedded in the low-rank background data part by using the collaborative representation detector includes the following steps:

[0027] The low-rank data part Convert to a two-dimensional matrix D represents the number of spectral bands of hyperspectral data, N is the total number of samples; the low-rank data part is extracted using the collaborative representation detector Abnormal information in, x is the center pixel, and the size of the outer window is W out ×W out , the size of the inner window is W in ×W in , s = W out ×W out -W in ×W in ;

[0028] For a pixel x, its objective function can be expressed as:

[0029]

[0030] Among them, λ 2 represents the Lagrange multiplier, the matrix X s The background set of pixels between the outer window and the inner window, is the weight vector;

[0031]

[0032] Using the matrix X s and weight vector Reconstruct pixel x:

[0033]

[0034] in, is the reconstruction element of element x;

[0035] The residual error with respect to element x can be calculated as:

[0036]

[0037] If γ 2 is greater than a given threshold σ, then Detected as abnormal.

[0038] Furthermore, the process of fusing the initial detection results of the low-rank data and the mixed information part comprises the following steps:

[0039] By transforming the initial detection result γ 1 and γ 2 Fusion, get the final detection result map; the final fusion process is as follows:

[0040] γ=α 1 γ 1 +α 2 γ 2 (12)

[0041] Among them, α 1 and α2 is a tuning parameter, and α 1 +α 2 =1.

[0042] Beneficial effects:

[0043] The hyperspectral anomaly detection algorithm proposed in this paper uses the total variation regularized low-rank tensor decomposition model to divide the hyperspectral into two parts: the low-rank data part and the mixed information part. By considering the global and piecewise smooth structure of the hyperspectral, most of the anomaly information can be decomposed into the mixed information part. Then, using l 2,1 The norm combined with the domain transformation recursive filter performs anomaly detection on the mixed information part, achieving a good noise suppression effect and can well solve the problem of not being able to separate the background and anomalies well.

[0044] In addition, the collaborative representation detector (CRD) is used to extract the abnormal information embedded in the low-rank data part, and the initial results of the low-rank data are fused with the initial results of the mixed information part to obtain the final detection map. After experimental analysis, the method proposed in this invention can obtain AUC values ​​of 0.9954, 0.9804 and 0.9869 on the three data sets respectively. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 Flowchart of anomaly detection method based on total variation regularized low-rank tensor decomposition and collaborative representation;

[0046] Figure 2 shows the pseudo-color image, true value image and detection results of data set I, where Figure 2(a) is the pseudo-color image, Figure 2(b) is the true value image, and Figure 2(c) is the detection image;

[0047] Figure 3 shows the pseudo-color image, true value image and detection results of Dataset II, where Figure 3(a) is the pseudo-color image, Figure 3(b) is the true value image, and Figure 3(c) is the detection image;

[0048] Figure 4 shows the pseudo-color image, true-value image, and detection results of dataset III, where Figure 4(a) is the pseudo-color image, Figure 4(b) is the true-value image, and Figure 4(c) is the detection image. DETAILED DESCRIPTION

[0049] Specific implementation method 1: Combination Figure 1 To explain this embodiment,

[0050] The method for abnormal target detection in hyperspectral images based on total variation low-rank tensor decomposition described in this embodiment includes the following steps:

[0051] S1. The total variation regularized low-rank tensor decomposition model is used to decompose the hyperspectral image into a low-rank data part and a mixed information part;

[0052] S2. Utilize l2,1 Norm and domain transformation recursive filters to detect anomalies in the mixed information part;

[0053] S3, using collaborative representation detector to extract abnormal information embedded in low-rank background data;

[0054] S4. The initial detection results of the low-rank data and the mixed information part are integrated to obtain the final detection result.

[0055] Specifically,

[0056] The process of decomposing a hyperspectral image into a low-rank data part and a mixed information part using a total variation regularized low-rank tensor decomposition model as described in S1 includes the following steps:

[0057] The total variation regularized low-rank tensor decomposition model is a method originally designed to restore hyperspectral images. This method can decompose hyperspectral images into a clean hyperspectral image part and a mixed noise part. The total variation regularized low-rank tensor decomposition model is based on the low-rank tensor Tucker decomposition and the spatial-spectral total variation regularizer, which can describe the piecewise smooth structure of the hyperspectral image and explore the global correlation between all hyperspectral image bands. In addition, different types of noise are also considered in the total variation regularized low-rank tensor decomposition model. According to the definition and characteristics of anomalies in hyperspectral images, it is easy to find that the anomaly information is hidden in the separated noise terms. However, no decomposition method can completely separate the anomaly, noise and other information from the original HSI.

[0058] Therefore, the anomaly detection method based on total variation regularized low-rank tensor decomposition and collaborative representation proposed in the present invention first decomposes the hyperspectral image using the total variation regularized low-rank tensor decomposition model, and then processes the decomposed parts separately. Represents the original hyperspectral image, and the total variation regularized low-rank tensor decomposition model is expressed as:

[0059]

[0060] Among them, C× 1 U 1 × 2 U 2 × 3 U 3 is a core tensor of C and rank r i The factor matrix U i Tucker decomposition, U 1 , U 2 , U 3 is the factor matrix under three modes, I is the identity matrix; Equal in size, is the low-rank data part, is a sparse term, is a Gaussian term; τ,λ 1 ,β is an auxiliary parameter.

[0061] SSTV norm term is represented as:

[0062]

[0063] Among them, x i′,j′,k′ Yes Input The (i′, j′, k′)th layer, w j′ It is along The weight coefficient of the control regularization strength of the j′th mode expansion. Due to the non-convexity of Tucker decomposition, problem (1) is a non-convex optimization problem. By introducing auxiliary variables, the augmented Lagrange multiplier (ALM) method is used to solve the problem. Then, problem (1) can be written as:

[0064]

[0065] in, are intermediate variables, representing and D w (·)=[w 1 ×D h (·); w 2 ×D v (·); w 3 ×D t (·)] is a weighted three-dimensional difference operator, D h ,D v ,D t is the first-order difference operator in three different directions of the hyperspectral image cube. Problem (3) is further transformed into minimizing the augmented Lagrangian function:

[0066]

[0067] Among them, μ is the penalty parameter; Γ i′ is the Lagrange multiplier, i′=1,2,3; <·> represents the inner product operation, ||.|| F represents the F-norm.

[0068] Therefore, we can optimize the augmented Lagrangian function (4) for one variable while fixing the other variables. Finally, the low-rank data part is represented as The mixed information part M is represented as

[0069] The process of performing anomaly detection on the mixed information part described in S2 comprises the following steps:

[0070] In order to detect anomalies in the mixed information part M, we first use l 2,1 Norm regularization performs initial detection on the mixed information part; the initial detection result of the mixed information part is expressed as:

[0071]

[0072] Where D represents the number of spectral bands of the hyperspectral data, H and W represent the length and width of the hyperspectral image, respectively. is an element in the mixed information part M;

[0073] In order to utilize the local spatial information of the hyperspectral image, the domain transform recursive filter is used to smooth the initial detection results; the domain transform recursive filter is expressed as:

[0074] γ 1 = DTRF(I,G,δ s ,δ r ) (6)

[0075] Among them, I is the use of l 2,1 The detection result diagram of the mixed information part calculated by norm regularization, G represents the guide image, δ s and δ r are two smoothing parameters of the domain transform recursive filter;

[0076] The guidance image calculated on the original hyperspectral image using the spectral angle distance can be expressed as:

[0077]

[0078] Where μ is the original hyperspectral image The matrix is ​​composed of the spectral averages of all pixels in the domain, and the initial detection result obtained by the domain transformation recursive filter is recorded as γ 1 .

[0079] The specific process of extracting abnormal information embedded in the low-rank background data part by using the collaborative representation detector in S3 includes the following steps:

[0080] Collaborative Representation Detector (CRD) is used to further extract the hidden low-rank data parts. The abnormal information in the detection result graph is recorded as γ 2 ;let Represents the low-rank data part and transforms it into a two-dimensional matrix D represents the number of spectral bands of the hyperspectral data, N is the total number of samples, and H and W are the length and width of the hyperspectral image.

[0081] x is the center pixel, and the size of the outer window is W out ×W out , the size of the inner window is W in ×W in , s = W out ×W out -W in ×W in , s is the number of samples extracted. For a pixel x, its objective function can be expressed as:

[0082]

[0083] Among them, λ 2 represents the Lagrange multiplier, is the weight vector, the matrix X s is the background set of pixels between the outer window and the inner window, the weight vector This can be done by Compute by taking the derivative and setting the result to zero. After deduction, it can be written into the following equation:

[0084]

[0085] Using the matrix X s and weight vector Reconstruct pixel x:

[0086]

[0087] in, is the reconstruction element of element x;

[0088] The residual error with respect to element x can be calculated as:

[0089]

[0090] If γ 2 is greater than a given threshold σ, then Detected as abnormal.

[0091] The process of fusing the initial detection results of the low-rank data and the mixed information part described in S4 comprises the following steps:

[0092] In order to further effectively utilize all abnormal information, the initial detection result γ 1 and γ 2 Fusion, to obtain the final detection result map. This process can further improve the performance of the method proposed in this patent. The final fusion process is shown as follows:

[0093] γ=α 1γ 1 +α 2 γ 2 (12)

[0094] Among them, α 1 and α 2 is a tuning parameter, and α 1 +α 2 =1.

[0095] The present invention can better utilize the spatial information of the hyperspectral image and enable abnormal targets to be better detected.

[0096] Example

[0097] This embodiment uses three hyperspectral data to illustrate the effect of the anomaly detection method based on total variation regularized low-rank tensor decomposition and collaborative representation proposed in the present invention. The detailed information of the three data used is listed in Table 1. The experimental results use the area under the receiver characteristic curve (AUC) as the evaluation index. The higher the AUC value, the better the detection effect.

[0098] Table 1 Detailed information of the hyperspectral images used

[0099]

[0100] For different data, the optimal parameter settings of the method of the present invention are shown in Table 2. Parameter α 1 , α 2 is the weight coefficient, W in and W out is the size of the inner and outer windows. The language environment is MATLAB, and the experimental hardware platform is: CPU: i5-5200U, memory: 4G.

[0101] Table 2 Optimal parameters and AUC values ​​for three sets of experimental data

[0102]

[0103] The results of detecting different data sets using the present invention are shown in FIG. 2 to FIG. 4 .

[0104] Figure 2 shows the pseudo-color image, true value image and detection results of data set I, where Figure 2(a) is the pseudo-color image, Figure 2(b) is the true value image, and Figure 2(c) is the detection image;

[0105] Figure 3 shows the pseudo-color image, true value image and detection results of Dataset II, where Figure 3(a) is the pseudo-color image, Figure 3(b) is the true value image, and Figure 3(c) is the detection image;

[0106] Figure 4 shows the pseudo-color image, true-value image, and detection results of dataset III, where Figure 4(a) is the pseudo-color image, Figure 4(b) is the true-value image, and Figure 4(c) is the detection image.

[0107] The present invention may also have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art may make various corresponding changes and modifications based on the present invention, but these corresponding changes and modifications should all fall within the scope of protection of the claims attached to the present invention.

Claims

1. A method for abnormal target detection in hyperspectral images based on total variation low-rank tensor decomposition, characterized in that: The following steps are involved: The total variation regularized low-rank tensor decomposition model is used to decompose the hyperspectral image into low-rank data parts. and a mixed information part M; The process of decomposing a hyperspectral image into a low-rank data part and a mixed information part using a total variation regularized low-rank tensor decomposition model includes the following steps: Firstly, the total variation regularized low-rank tensor decomposition model is used to decompose the hyperspectral image; then, based on the augmented Lagrangian multiplier method, the regularized low-rank tensor decomposition model is transformed into a method to minimize the augmented Lagrangian function, thereby reducing the low-rank data part. Expressed as represents the original hyperspectral image, and the mixed information part M is represented as In the total variation regularized low-rank tensor decomposition model, is the low-rank data part, is a sparse term, is the Gaussian term; Then use l 2,1 The norm and domain transformation recursive filter are used to detect anomalies in the mixed information part; and the collaborative representation detector is used to extract the anomaly information embedded in the low-rank data part; the initial detection results of the low-rank data and the mixed information part are fused to obtain the final detection result; The specific process of extracting abnormal information embedded in the low-rank data part by using the collaborative representation detector includes the following steps: The low-rank data part Convert to a two-dimensional matrix D represents the number of spectral bands of hyperspectral data, N is the total number of samples; the low-rank data part is extracted using the collaborative representation detector Abnormal information in, x is the center pixel, and the size of the outer window is W out ×W out , the size of the inner window is W in ×W in , s = W out ×W out -W in ×W in , s is the number of samples drawn; For a pixel x, the objective function is expressed as: Among them, λ2 represents the Lagrange multiplier, and the matrix X s The background set of pixels between the outer window and the inner window, is the weight vector; Using the matrix X s and weight vector Reconstruct pixel x: in, is the reconstruction element of element x; The residual error with element x is calculated as: If γ2 is greater than a given threshold σ, then Detected as abnormal.

2. The method for abnormal target detection in hyperspectral images based on total variation low-rank tensor decomposition according to claim 1 is characterized in that: The total variation regularized low-rank tensor decomposition model is as follows: in, represents the original hyperspectral image, C×1U1×2U2×3U3 is the core tensor of C and rank r i The factor matrix U i Tucker decomposition of , U1, U2, U3 are factor matrices under three modes, I is the identity matrix; τ, λ1, β are auxiliary parameters in the total variation regularized low-rank tensor decomposition model; is the SSTV norm term.

3. The method for abnormal target detection in hyperspectral images based on total variation low-rank tensor decomposition according to claim 1 or 2, characterized in that: The minimized augmented Lagrangian function in the process of converting the regularized low-rank tensor decomposition model into the minimized augmented Lagrangian function is as follows: in, are intermediate variables, representing and D w (·)=[w1×D h (·);w2×D v (·);w3×D t (·)] is a weighted three-dimensional difference operator, D h ,D v ,D t is the first-order difference operator in three different directions of the hyperspectral image cube; Γ i′ is the Lagrange multiplier, i′=1,2,3; <·> represents the inner product operation, τ, λ1, β are auxiliary parameters in the total variation regularized low-rank tensor decomposition model.

4. The method for abnormal target detection in hyperspectral images based on total variation low-rank tensor decomposition according to claim 3 is characterized in that: In the process of detecting anomalies in the mixed information part, l 2,1 Norm regularization is used to perform initial detection on the mixed information part, and then the domain transformation recursive filter is used to smooth the initial detection result.

5. The method for abnormal target detection in hyperspectral images based on total variation low-rank tensor decomposition according to claim 4 is characterized in that: The initial detection result of the mixed information part is expressed as: Where D represents the number of spectral bands of the hyperspectral data, H and W represent the length and width of the hyperspectral image, respectively. is an element in the mixed information part M.

6. The method for abnormal target detection in hyperspectral images based on total variation low-rank tensor decomposition according to claim 5, characterized in that: The domain transform recursive filter is expressed as: γ1=DTRF(I,G,δ s ,d r ) (6) Among them, I is the use of l 2,1 The detection result diagram of the mixed information part calculated by norm regularization, G represents the guide image, δ s and δ r are two smoothing parameters of the domain transform recursive filter.

7. The method for abnormal target detection in hyperspectral images based on total variation low-rank tensor decomposition according to claim 6, characterized in that: The boot image is as follows: Where μ is the original hyperspectral image The matrix consisting of the spectral averages of all pixels in .

8. The method for abnormal target detection in hyperspectral images based on total variation low-rank tensor decomposition according to claim 7, characterized in that: The process of fusing the initial detection results of the low-rank data and the mixed information part comprises the following steps: The final detection result graph is obtained by fusing the initial detection results γ1 and γ2. The final fusion process is shown as follows: γ=α1γ1+α2γ2 (12) Here, α1 and α2 are adjustment parameters, and α1+α2=1.

Images