A hyperspectral anomaly detection method and system based on tensor multi-subspace learning

Abstract

The application discloses a hyperspectral anomaly detection method and system based on tensor multi-subspace learning, and the method comprises the following steps: acquiring hyperspectral image tensor data of a detection area; performing waveband-by-waveband normalization processing; decomposing into an anomaly tensor, a noise tensor and a structural background component; designing a non-convex tensor correlation total variation regularization; constructing an iterative sparse weight tensor; adopting a structured-norm; constructing a robust dictionary tensor; establishing an anomaly detection model; adopting an effective iterative updating algorithm based on an alternating direction multiplier method to perform optimization, acquiring an optimal anomaly tensor; and performing detection on the obtained optimal anomaly tensor to generate an anomaly detection result image. The application realizes effective separation among the background, the anomaly and the noise by respectively performing regularization constraint optimization on the background component, the anomaly component and the noise component and constructing a robust background dictionary.

Description

Technical Field

[0001] This invention relates to the field of optical image processing technology, and more specifically, to a hyperspectral anomaly detection method and system based on tensor multi-subspace learning. Background Technology

[0002] Hyperspectral images are three-dimensional data cubes that combine image and spectrum, simultaneously recording two-dimensional spatial information of ground feature distribution and one-dimensional spectral information reflecting material composition. Anomaly detection, as a key technology in intelligent interpretation of hyperspectral images, aims to identify anomalous targets that are significantly different from the background spectral features without prior spectral information, and has wide applications in military reconnaissance, geological exploration, and disaster monitoring. However, traditional anomaly detection algorithms typically use low-dimensional signal processing methods such as pixel-by-pixel spectral feature analysis or band-by-band spatial feature extraction to interpret hyperspectral images, which inevitably destroys the inherent structural information of hyperspectral images. To preserve the inherent spatial-spectral structural information of hyperspectral images, researchers have proposed a large number of hyperspectral anomaly detection methods based on tensor representations.

[0003] While tensor representation-based methods have achieved initial success in anomaly detection, several challenges remain. First, existing methods often use the sum of two independent regularization terms to characterize the low-rank nature and local smoothness of the background, respectively. This direct addition not only introduces an extra regularization parameter but may also fail to fully represent the background data, leading to a significant discrepancy between the estimated and actual background. Recently, researchers proposed tensor-related total variational (t-CTV) regularization, which models the tensor kernel norm (TNN) in the gradient domain, achieving a unified characterization of background low-rank and local smoothness, and has been successfully applied to tensor restoration tasks. However, due to the inherent limitations of TNNs, directly applying t-CTV to hyperspectral anomaly detection may restrict its detection performance.

[0004] Secondly, most methods employ -norm or - Norms are used to characterize the sparsity of anomalous components. This type of metric imposes the same penalty on all targets, making it difficult to distinguish sparse non-anomalous targets, which can easily lead to an increase in false alarms and thus affect detection accuracy.

[0005] Furthermore, when constructing a background dictionary based on the improved tensor robust principal component analysis method, existing methods typically only utilize the low-rank property of the background while ignoring its local smoothness, which may lead to insufficient representation of background information.

[0006] Finally, most existing methods do not explicitly consider the impact of noise. In real-world scenarios, noise is often mixed between the background and unusual targets, and effective noise modeling can help improve the visibility of unusual targets.

[0007] To address these issues, this patent proposes a hyperspectral anomaly detection method based on tensor multi-subspace learning to achieve effective separation between background, anomalies, and noise. Summary of the Invention

[0008] The purpose of this invention is to overcome the shortcomings of the prior art and provide a hyperspectral anomaly detection method and system based on tensor multi-subspace learning. It aims to solve the problems of insufficient mining of low-rank and local smoothness coupling information of background and sparse structure information of anomalous components in existing hyperspectral anomaly detection methods, and the construction of dictionaries that are easily affected by noise and outliers.

[0009] To achieve the above objectives, the present invention adopts the following technical solution:

[0010] A hyperspectral anomaly detection method based on tensor multi-subspace learning, the method comprising:

[0011] Step S1: Obtain hyperspectral image tensor data of the region to be detected;

[0012] Step S2: Perform band-by-band normalization on the acquired hyperspectral image tensor data;

[0013] Step S3: Decompose the hyperspectral image tensor data into anomaly tensors, noise tensors, and structural background components based on robust dictionary tensors and coefficient tensor tensor products;

[0014] Step S4: Design non-convex tensor correlation total variation regularization for constraining coefficient tensors;

[0015] Step S5, in the tensor Under norm constraints, an iterative sparse weight tensor is constructed to constrain anomalous tensors.

[0016] Step S6, using structured... - Norm-constrained noise tensor;

[0017] Step S7: Combine non-convex tensor correlation total variation regularization and iterative sparse weight tensor and integrate them into the tensor robust principal component analysis framework to construct a robust dictionary tensor.

[0018] Step S8 involves performing total variation regularization on the non-convex tensor correlation, iterating the sparse weight tensor, and structuring. - Norms are integrated into a unified tensor low-rank representation learning framework to build an anomaly detection model;

[0019] Step S9: Optimize the established model using an efficient iterative update algorithm based on the alternating direction multiplier method to obtain the optimal anomaly tensor;

[0020] Step S10: Detect the obtained optimal anomaly tensor and generate an anomaly detection result map.

[0021] Furthermore, in step S4, the design steps for non-convex tensor-dependent total variational regularization are as follows:

[0022] Step S41: Define the traditional tensor-related total variation and clarify its expression in the case of low-rank and local smoothness in the modeling background;

[0023]

[0024] In the formula, It is a coefficient tensor Along the first The gradient tensor of the modulus; Represents the tensor nuclear norm; yes The One singular value; yes The A frontal slice; It is along The result of performing a fast Fourier transform on the third dimension; m, n, and b represent the height, width, and number of bands of the hyperspectral image, respectively; Represents the modal index of a tensor; Indicates the index of the front slice; Indicates singular value index;

[0025] Step S42: Define a non-convex tensor-dependent total variation and overcome the bias of traditional tensor-dependent total variation in describing background structure;

[0026]

[0027] In the formula, It is a non-convex Gamma-norm and has unitary invariance.

[0028] Furthermore, in step S5, the iterative sparse weight tensor is constructed as follows:

[0029]

[0030]

[0031] In the formula, This represents the number of iterations. It is the first An anomaly detection map is obtained after the next iteration; Indicates multiple Stacked into a tensor ; It is a constant; is the anomalous tensor; b represents the number of bands in the hyperspectral image; Represents the modal index of a tensor; Indicates the index of the front slice; This represents a singular value index.

[0032] Furthermore, in step S6, structuring... The method for constraining noise tensors using the -norm is as follows:

[0033]

[0034] In the formula, For noise tensor; Indicates taking the noise tensor The The Frobenius norm of the two-dimensional matrix composed of columns; m, n, and b represent the height, width, and number of bands of the hyperspectral image, respectively; Represents the modal index of a tensor; Indicates the index of the front slice; This represents a singular value index.

[0035] Furthermore, in step S7, the steps for constructing the robust dictionary tensor are as follows:

[0036] Step S71: Construct an objective function based on non-convex tensor correlation total variation regularization and iterative sparse weight tensor;

[0037]

[0038]

[0039]

[0040] In the formula, Represents hyperspectral image tensor data; This represents the low-rank background tensor to be solved; Represents the sparse anomaly tensor to be solved; Represents the low-rank background tensor Along the first The gradient tensor of the modulus; It is a non-convex Gamma-norm; Represents the regularization parameter; Represents the iterative sparse weight tensor; Represents the modal index of a tensor; It represents the Hadamardi (or Hadama) stack;

[0041] Step S72: The objective function is optimized using the alternating direction multiplier method to obtain the optimal low-rank background tensor. ;

[0042] Step S73, define the robust dictionary tensor For the optimal low-rank background tensor .

[0043] Furthermore, in step S8, the anomaly detection model is:

[0044]

[0045]

[0046]

[0047] In the formula, , , , and These represent hyperspectral image tensor data, robust dictionary tensor, coefficient tensor, anomaly tensor, and noise tensor, respectively. and For regularization parameters; It is a coefficient tensor Along the first The gradient tensor of the modulus; It is a non-convex Gamma-norm; Represents the iterative sparse weight tensor; Indicates group sparsity -norm; Represents the structured sparse terms of noise; Represents the modal index of a tensor; It represents the Hadamardi (or Hadama) stack.

[0048] Furthermore, in step S9, the established anomaly detection model is optimized using an efficient iterative update algorithm based on the alternating direction multiplier method. The calculation method is as follows:

[0049]

[0050]

[0051] In the formula, , and Represents the Lagrange multipliers; Indicates the penalty parameter; Indicates auxiliary variables; , , , and These represent hyperspectral image tensor data, robust dictionary tensor, coefficient tensor, anomaly tensor, and noise tensor, respectively. and For regularization parameters; It is a coefficient tensor Along the first The gradient tensor of the modulus; It is a non-convex Gamma-norm; Represents the iterative sparse weight tensor; Indicates group sparsity -norm; Represents the structured sparse terms of noise; Represents the modal index of a tensor; Indicates along the first Gradient operator of the modulus; It is the tensor product; Denotes the Frobenius norm; It represents the Hadamardi (or Hadama) stack.

[0052] Furthermore, in step S10, the anomaly detection structure diagram is generated as follows:

[0053]

[0054] In the formula, Diagram showing the anomaly detection structure The Middle One element; Represents the optimal anomaly tensor The Middle One element; and For spatial location index; For band indexing; This represents the number of bands in the hyperspectral image.

[0055] This invention also proposes a hyperspectral anomaly detection system based on tensor multi-subspace learning, the system comprising:

[0056] The hyperspectral image acquisition unit is used to acquire hyperspectral image tensor data of the region to be detected.

[0057] The preprocessing unit is used to perform band-by-band normalization preprocessing on the hyperspectral image tensor data.

[0058] Background modeling units are used to capture the global low rank and local smoothness of background components;

[0059] Anomaly modeling unit, used to enhance the sparsity of anomalous targets and distinguish sparse non-anomalous targets;

[0060] Noise modeling unit, used to suppress the confusion between noise and anomalous targets;

[0061] Robust dictionary building units are used to capture complex multi-subspace structures in heterogeneous contexts;

[0062] The anomaly detection model establishment and optimization unit is used to establish an anomaly detection model based on tensor multi-subspace learning and optimize it to obtain the optimal anomaly tensor.

[0063] The detection unit is used to construct a detection graph based on the optimal anomaly tensor to obtain an anomaly detection result graph.

[0064] This invention also proposes a hyperspectral anomaly detection device based on tensor multi-subspace learning, comprising:

[0065] Memory, used to store computer programs and data;

[0066] The processor is used to implement the steps of the hyperspectral anomaly detection method based on tensor multi-subspace learning described above when executing a computer program.

[0067] The beneficial effects of this invention are:

[0068] This invention designs a non-convex tensor-correlated total variational regularization method without introducing additional regularization parameters to enhance the coupled modeling capability for low-rank background structure and local smoothness priors. Unlike the traditional t-CTV, the non-convex tensor-correlated total variational method further characterizes the low-rank and inherent sparsity of the gradient tensor, reducing the bias generated by traditional methods in describing background characteristics, thereby obtaining a more accurate low-rank background estimate. Simultaneously, in the tensor... Under the norm constraint, an iterative sparse weight tensor is introduced to constrain the anomalous tensor. Furthermore, considering the influence of strong residuals in anomalous target images, a structured approach is adopted. - Norm constraint on noise components. Finally, based on the tensor robust principal component analysis framework, combined with the designed non-convex tensor correlation total variation regularization and iterative sparse weight tensor, a robust dictionary tensor is constructed, which can fully represent background information and effectively eliminate noise and anomaly interference. This invention can detect anomalous targets of different scales in complex scenes, providing reliable technical support for applications such as military reconnaissance and precision agriculture. Attached Figure Description

[0069] Figure 1 This is a flowchart of a hyperspectral anomaly detection method based on tensor multi-subspace learning in this embodiment;

[0070] Figure 2 This is a structural framework diagram of a hyperspectral anomaly detection system based on tensor multi-subspace learning in this embodiment;

[0071] Figure 3 This is a structural framework diagram of a hyperspectral anomaly detection device based on tensor multi-subspace learning in this embodiment.

[0072] Figure labels: 1. Hyperspectral image acquisition unit; 2. Preprocessing unit; 3. Background modeling unit; 4. Anomaly modeling unit; 5. Noise modeling unit; 6. Robust dictionary construction unit; 7. Anomaly detection model establishment and optimization unit; 8. Detection unit; 9. Memory; 10. Processor. Detailed Implementation

[0073] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0074] Example: A hyperspectral anomaly detection method based on tensor multi-subspace learning. This method first acquires hyperspectral image tensor data, then performs band-by-band normalization, and decomposes it into a structural background component, an anomaly tensor, and a noise tensor. A tensor multi-subspace learning strategy is employed, representing the structural background component as the tensor product of a robust dictionary tensor and its corresponding coefficient tensor to capture the complex distribution characteristics of heterogeneous backgrounds. To effectively characterize the global low-rank and local smoothness of the background component, a non-convex Gamma norm is introduced into the gradient tensor domain and modeled, proposing non-convex tensor correlated total variation (NTCTV) regularization. Compared to traditional t-CTV, NTCTV can more accurately describe the low-rank structural characteristics of the background, thereby improving the accuracy of background modeling. For the anomaly tensor, in the tensor... Under norm constraints, an iterative sparse weight tensor is designed to enhance the contrast between anomalous targets and the background; the noise tensor is structured. - Norm constraints are used to suppress the confusion between noise and anomalous targets. In addition, by combining non-convex tensor correlated total variation (NTCTV) regularization and iterative sparse weight tensors and integrating them into the tensor robust principal component analysis framework, a robust dictionary tensor is constructed, which can fully represent background ground feature information. Finally, an efficient iterative algorithm based on alternating direction multiplier method (ADMM) is used to optimize the proposed model to obtain the optimal anomalous tensor. The optimal anomalous tensor is then used for detection, and anomaly detection result map is output.

[0075] This method achieves effective separation of background, anomalies, and noise by optimizing the regularization constraints on background, anomaly, and noise components separately and constructing a robust background dictionary. For example... Figure 1 As shown, specifically:

[0076] Step S1: Acquire hyperspectral image tensor data of the area to be detected using a hyperspectral imaging device;

[0077] Step S2: Perform band-by-band normalization on the acquired hyperspectral image tensor data.

[0078] The method for band-by-band normalization is as follows:

[0079]

[0080] In the formula, For hyperspectral tensor data The A frontal slice, , , Let m, n, and b be the set of real numbers, representing the height, width, and number of bands of the hyperspectral image, respectively. and These are operations for finding the maximum and minimum values, respectively.

[0081] Step S3: Decompose the hyperspectral image tensor data into a structural background component, an anomaly tensor, and a noise tensor. The structural background component is the tensor product of the robust dictionary tensor and the coefficient tensor, and its expression is as follows:

[0082]

[0083] In the formula, , , , and These represent hyperspectral image tensor data, robust dictionary tensor, coefficient tensor, anomaly tensor, and noise tensor, respectively. , , , , m, n, and b represent the height, width, and number of bands of the hyperspectral image, respectively.

[0084] Step S4: Design non-convex tensor correlation total variation regularization for constraining coefficient tensors.

[0085] The design steps for nonconvex tensor-dependent total variational regularization are as follows:

[0086] Step S41, define the traditional tensor-related total variation ( This clarifies the expression of traditional tensor-related total variation in the context of low-rank and local smoothness in modeling.

[0087]

[0088] In the formula, It is a coefficient tensor Along the first The gradient tensor of the modulus; Represents the tensor nuclear norm; yes The One singular value; yes The A frontal slice; It is along The result of performing a fast Fourier transform on the third dimension; m, n, and b represent the height, width, and number of bands of the hyperspectral image, respectively; Represents the modal index of a tensor. ; Indicates the index of the front slice; Indicates singular value index;

[0089] Step S42 defines a non-convex tensor-dependent total variation and overcomes the bias of traditional tensor-dependent total variation in describing background structure, enhancing the ability to model low rank and smoothness in a unified manner.

[0090]

[0091] In the formula, It is a non-convex Gamma quasi-norm and has unitary invariance, i.e. ,in and It is the size of orthogonal tensors, This is the transpose operator.

[0092] when hour, Approaching the tensor tube rank, i.e. , Tensor The order of administration; when hour, Approaching TNN, i.e. This design does not require the introduction of additional regularization parameters and can more accurately characterize the low-rank structure and local smoothness of the background.

[0093] Step S5, in the tensor - Under norm constraints, construct iterative sparse weight tensors to constrain anomalous tensors.

[0094] To enhance the contrast between anomalous targets and the background, an iterative sparse weight tensor is designed. Used for weighted constraint anomalous tensors The construction of the iterative sparse weight tensor is as follows:

[0095]

[0096]

[0097] In the formula, This represents the number of iterations. It is the first An anomaly detection map is obtained after the next iteration; Indicates multiple Stacked into a tensor ; Let be a constant, set to 0.01; is the anomalous tensor; b represents the number of bands in the hyperspectral image; Represents the modal index of a tensor; Indicates the index of the front slice; This represents a singular value index.

[0098] Iterative sparse weight tensor The system dynamically adjusts its response based on anomalies, reducing the penalty for truly anomalous areas while increasing the penalty for background areas, thereby enhancing the prominence of anomalous targets.

[0099] Step S6, using structured... - Norm-constrained noise tensor.

[0100] To suppress noise interference in anomaly detection, a structured approach is adopted. -norm pairs noise tensor The method for imposing constraints is as follows:

[0101]

[0102] In the formula, For noise tensor; Indicates taking the noise tensor The The Frobenius norm of the two-dimensional matrix composed of columns; m, n, and b represent the height, width, and number of bands of the hyperspectral image, respectively; Represents the modal index of a tensor; Indicates the index of the front slice; This represents a singular value index.

[0103] Structured - The norm encourages structured sparsity of noise in the combined spatial-spectral dimension, which helps distinguish noise from real anomalies.

[0104] Step S7: Under the framework of tensor robust principal component analysis, the ability of non-convex tensor correlation total variation to characterize the low-rank smoothness of the background and the ability of iterative sparse weights to suppress anomalous components are integrated to construct a robust dictionary tensor that can resist noise and anomalous interference.

[0105] The steps for constructing a robust dictionary tensor are as follows:

[0106] Step S71: Construct an objective function based on non-convex tensor correlation total variation regularization and iterative sparse weight tensor;

[0107]

[0108]

[0109]

[0110] In the formula, Represents hyperspectral image tensor data; This represents the low-rank background tensor to be solved; Represents the sparse anomaly tensor to be solved; Represents the low-rank background tensor Along the first The gradient tensor of the modulus; It is a non-convex Gamma-norm; Represents the regularization parameter; Represents the iterative sparse weight tensor; Represents the modal index of a tensor; It represents the Hadamardi (or Hadama) stack;

[0111] The objective function decomposes the hyperspectral image tensor data into the sum of a low-rank background tensor and a sparse anomaly tensor, and enhances the structural properties of both by using non-convex tensor correlation total variation and weighted sparse norm, respectively, aiming to accurately estimate the clean background components from contaminated data.

[0112] Step S72 involves optimizing the objective function using the alternating direction multiplier method. In each iteration, while keeping other variables fixed, a single variable is updated sequentially to ultimately obtain the optimal low-rank background tensor. ;

[0113] Step S73, define the robust dictionary tensor For the optimal low-rank background tensor ,Right now .

[0114] Step S8 involves performing total variation regularization on the non-convex tensor correlation, iterating the sparse weight tensor, and structuring. - Norm integration into a unified tensor low-rank representation learning framework to build an anomaly detection model.

[0115] The anomaly detection model is as follows:

[0116]

[0117]

[0118]

[0119] In the formula, , , , and These represent hyperspectral image tensor data, robust dictionary tensor, coefficient tensor, anomaly tensor, and noise tensor, respectively. and This is a regularization parameter used to balance the contributions of each item; It is a coefficient tensor Along the first The gradient tensor of the modulus; It is a non-convex Gamma-norm; Represents the iterative sparse weight tensor; Indicates group sparsity -norm; Represents the structured sparse terms of noise; Represents the modal index of a tensor; It represents the Hadamardi (or Hadama) stack.

[0120] Step S9: The established model is optimized using an efficient iterative update algorithm based on the alternating direction multiplier method to obtain the optimal anomaly tensor.

[0121] The anomaly detection model, optimized using an efficient iterative update algorithm based on the alternating direction multiplier method, is calculated as follows:

[0122]

[0123]

[0124] In the formula, , and Represents the Lagrange multipliers; Indicates the penalty parameter; Indicates auxiliary variables; , , , and These represent hyperspectral image tensor data, robust dictionary tensor, coefficient tensor, anomaly tensor, and noise tensor, respectively. and Regularization parameter It is a coefficient tensor Along the first The gradient tensor of the modulus; It is a non-convex Gamma-norm; Represents the iterative sparse weight tensor; Indicates group sparsity -norm; Represents the structured sparse terms of noise; Represents the modal index of a tensor; Indicates along the first Gradient operator of the modulus; It is the tensor product; Denotes the Frobenius norm; It means Hadama accumulation

[0125] The optimization problem in the above equation can be decomposed into several subproblems and solved using ADMM; this method updates individual variables one by one while keeping other variables fixed, and finally obtains the optimal anomaly tensor. .

[0126] Step S10: Detect the obtained optimal anomaly tensor and generate an anomaly detection result map.

[0127] The anomaly detection structure diagram is generated as follows:

[0128]

[0129] In the formula, Diagram showing the anomaly detection structure The Middle One element; Represents the optimal anomaly tensor The Middle One element; and For spatial location index; For band indexing; This represents the number of bands in the hyperspectral image.

[0130] This embodiment designs a non-convex tensor-correlated total variational (NTCTV) regularization method that does not require the introduction of additional regularization parameters to enhance the coupled modeling capability for background low-rank structure and local smoothness priors. Unlike the traditional t-CTV, NTCTV further characterizes the low-rank and inherent sparsity of the gradient tensor, reducing the bias generated by traditional methods in describing background characteristics, thereby obtaining a more accurate low-rank background estimate. Simultaneously, in the tensor... Under the norm constraint, an iterative sparse weight tensor is introduced to constrain the anomalous tensor. Furthermore, considering the influence of strong residuals in anomalous target images, a structured approach is adopted. - Norm constraint on noise components. Finally, based on the tensor robust principal component analysis framework, combined with the designed non-convex tensor correlated total variation (NTCTV) regularization and iterative sparse weight tensor, a robust dictionary tensor is constructed, which can fully represent background information and effectively eliminate noise and anomaly interference. The method proposed in this embodiment can detect anomalous targets at different scales in complex scenes, providing reliable technical support for applications such as military reconnaissance and precision agriculture.

[0131] This embodiment also proposes a hyperspectral anomaly detection system based on tensor multi-subspace learning, such as... Figure 2 As shown, the system includes a hyperspectral image acquisition unit 1, a preprocessing unit 2, a background modeling unit 3, an anomaly modeling unit 4, a noise modeling unit 5, a robust dictionary construction unit 6, an anomaly detection model establishment and optimization unit 7, and a detection unit 8.

[0132] Among them, the hyperspectral image acquisition unit 1 is used to acquire hyperspectral image tensor data of the region to be detected.

[0133] Preprocessing unit 2 is used to perform band-by-band normalization preprocessing on hyperspectral image tensor data.

[0134] Background modeling unit 3 is used to capture the global low rank and local smoothness of background components.

[0135] Anomaly modeling unit 4 is used to enhance the sparsity of anomalous targets and distinguish sparse non-anomalous targets.

[0136] Noise modeling unit 5 is used to suppress the confusion between noise and abnormal targets.

[0137] Robust dictionary building unit 6 is used to capture complex multi-subspace structures in heterogeneous backgrounds.

[0138] The anomaly detection model establishment and optimization unit 7 is used to establish an anomaly detection model based on tensor multi-subspace learning and optimize it to obtain the optimal anomaly tensor.

[0139] Detection unit 8 is used to construct a detection map based on the optimal anomaly tensor to obtain an anomaly detection result map.

[0140] This embodiment also proposes a hyperspectral anomaly detection device based on tensor multi-subspace learning, such as... Figure 3 As shown, the device includes a memory 9 and a processor 10; wherein, the memory 9 is used to store computer programs and data; and the processor 10 is used to implement the steps of the above-described hyperspectral anomaly detection method based on tensor multi-subspace learning when executing the computer program.

[0141] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A hyperspectral anomaly detection method based on tensor multi-subspace learning, characterized in that, The method includes: Step S1: Obtain hyperspectral image tensor data of the region to be detected; Step S2: Perform band-by-band normalization on the acquired hyperspectral image tensor data; Step S3: Decompose the hyperspectral image tensor data into anomaly tensors, noise tensors, and structural background components based on robust dictionary tensors and coefficient tensor tensor products; Step S4: Design non-convex tensor correlation total variation regularization for constraining coefficient tensors; Step S5, in the tensor Under norm constraints, an iterative sparse weight tensor is constructed to constrain anomalous tensors. Step S6, using structured... - Norm-constrained noise tensor; Step S7: Combine non-convex tensor correlation total variation regularization and iterative sparse weight tensor and integrate them into the tensor robust principal component analysis framework to construct a robust dictionary tensor. Step S8 involves performing total variation regularization on the non-convex tensor correlation, iterating the sparse weight tensor, and structuring. - Norms are integrated into a unified tensor low-rank representation learning framework to build an anomaly detection model; Step S9: Optimize the established model using an efficient iterative update algorithm based on the alternating direction multiplier method to obtain the optimal anomaly tensor; Step S10: Detect the obtained optimal anomaly tensor and generate an anomaly detection result image; In step S4, the design steps for nonconvex tensor-dependent total variational regularization are as follows: Step S41: Define the traditional tensor-related total variation and clarify its expression in the case of low-rank and local smoothness in the modeling background; In the formula, It is a coefficient tensor Along the first The gradient tensor of the modulus; Represents the tensor nuclear norm; yes The One singular value; yes The A frontal slice; It is along The result of performing a fast Fourier transform on the third dimension; m, n, and b represent the height, width, and number of bands of the hyperspectral image, respectively; Represents the modal index of a tensor; Indicates the index of the front slice; Indicates singular value index; Step S42: Define a non-convex tensor-dependent total variation and overcome the bias of traditional tensor-dependent total variation in describing background structure; In the formula, It is a non-convex Gamma-norm and has unitary invariance; In step S8, the anomaly detection model is: In the formula, , , , and These represent hyperspectral image tensor data, robust dictionary tensor, coefficient tensor, anomaly tensor, and noise tensor, respectively. and For regularization parameters; It is a coefficient tensor Along the first The gradient tensor of the modulus; It is a non-convex Gamma-norm; Represents the iterative sparse weight tensor; Represents the sparse anomaly tensor to be solved; Indicates group sparsity -norm; Represents the structured sparse terms of noise; Represents the modal index of a tensor; It represents the Hadamardi (or Hadama) stack.

2. The hyperspectral anomaly detection method based on tensor multi-subspace learning according to claim 1, characterized in that, In step S5, the iterative sparse weight tensor is constructed as follows: In the formula, This represents the number of iterations. It is the first An anomaly detection map is obtained after the next iteration; Indicates multiple Stacked into a tensor ; It is a constant; is the anomalous tensor; b represents the number of bands in the hyperspectral image; Represents the modal index of a tensor; Indicates the index of the front slice; This represents a singular value index.

3. The hyperspectral anomaly detection method based on tensor multi-subspace learning according to claim 1, characterized in that, In step S6, structuring The method for constraining noise tensors using the -norm is as follows: In the formula, For noise tensor; Indicates taking the noise tensor The The Frobenius norm of the two-dimensional matrix composed of columns; m, n, and b represent the height, width, and number of bands of the hyperspectral image, respectively; Represents the modal index of a tensor; Indicates the index of the front slice; This represents a singular value index.

4. The hyperspectral anomaly detection method based on tensor multi-subspace learning according to claim 1, characterized in that, In step S7, the steps for constructing the robust dictionary tensor are as follows: Step S71: Construct an objective function based on non-convex tensor correlation total variation regularization and iterative sparse weight tensor; In the formula, Represents hyperspectral image tensor data; This represents the low-rank background tensor to be solved; Represents the sparse anomaly tensor to be solved; Represents the low-rank background tensor Along the first The gradient tensor of the modulus; It is a non-convex Gamma-norm; Represents the regularization parameter; Represents the iterative sparse weight tensor; Represents the modal index of a tensor; It represents the Hadamardi (or Hadama) stack; Step S72: The objective function is optimized using the alternating direction multiplier method to obtain the optimal low-rank background tensor. ; Step S73, define the robust dictionary tensor For the optimal low-rank background tensor .

5. The hyperspectral anomaly detection method based on tensor multi-subspace learning according to claim 1, characterized in that, In step S9, the anomaly detection model is optimized using an efficient iterative update algorithm based on the alternating direction multiplier method. The calculation method is as follows: In the formula, , and Represents the Lagrange multipliers; Indicates the penalty parameter; Indicates auxiliary variables; , , , and These represent hyperspectral image tensor data, robust dictionary tensor, coefficient tensor, anomaly tensor, and noise tensor, respectively. and For regularization parameters; It is a coefficient tensor Along the first The gradient tensor of the modulus; It is a non-convex Gamma-norm; Represents the iterative sparse weight tensor; Indicates group sparsity -norm; Represents the structured sparse terms of noise; Represents the modal index of a tensor; Indicates along the first Gradient operator of the modulus; It is the tensor product; Denotes the Frobenius norm; It represents the Hadamardi (or Hadama) stack.

6. The hyperspectral anomaly detection method based on tensor multi-subspace learning according to claim 1, characterized in that, In step S10, the anomaly detection structure diagram is generated as follows: In the formula, Diagram showing the anomaly detection structure The Middle One element; Represents the optimal anomaly tensor The Middle One element; and For spatial location index; For band indexing; This represents the number of bands in the hyperspectral image.

7. A hyperspectral anomaly detection system based on tensor multi-subspace learning for implementing the method of claim 1, characterized in that, The system includes: The hyperspectral image acquisition unit (1) is used to acquire hyperspectral image tensor data of the region to be detected; Preprocessing unit (2) is used to perform band-by-band normalization preprocessing on hyperspectral image tensor data; Background modeling unit (3) is used to capture the global low rank and local smoothness of background components; Anomaly modeling unit (4) is used to enhance the sparsity of anomalous targets and distinguish sparse non-anomalous targets; Noise modeling unit (5) is used to suppress the confusion between noise and abnormal targets; Robust dictionary construction unit (6) is used to capture complex multi-subspace structures in heterogeneous backgrounds; Anomaly detection model establishment and optimization unit (7) is used to establish anomaly detection model based on tensor multi-subspace learning and optimize it to obtain the optimal anomaly tensor; The detection unit (8) is used to construct a detection graph based on the optimal anomaly tensor to obtain an anomaly detection result graph.

8. A hyperspectral anomaly detection device based on tensor multi-subspace learning, characterized in that, include: Memory (9) is used to store computer programs and data; The processor (10) is configured to implement the steps of the hyperspectral anomaly detection method based on tensor multi-subspace learning as described in any one of claims 1-6 when executing a computer program.

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