Hyperspectral anomaly detection method based on non-local structure prior and tensor wheel decomposition
By constructing a hyperspectral anomaly detection model based on nonlocal structure priors and tensor wheel decomposition, the problem of simultaneously representing global low-rank structures and nonlocal texture repeatability in existing technologies is solved, and high-precision background and anomaly separation is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-01-23
- Publication Date
- 2026-03-31
AI Technical Summary
Existing hyperspectral image anomaly detection techniques struggle to simultaneously characterize global low-rank structures and nonlocal texture repeatability, resulting in suboptimal detection results.
We employ a method based on nonlocal structural priors and tensor wheel decomposition. By constructing a tensor wheel decomposition model, we capture the full-dimensional coupling relationships of hyperspectral data. We utilize a four-dimensional nonlocal grouping strategy to preserve the spatial geometric structure, capture long-distance texture relationships, and improve the ability to recover details.
It achieves high-precision separation of background and anomalies, significantly improving detection accuracy, and enables efficient low-rank modeling while maintaining the inherent spatial-spectral geometric features of high-dimensional data.
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Figure CN121767684A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of remote sensing image processing and application technology, and relates to hyperspectral image processing, remote sensing data recovery and multidimensional tensor decomposition technology. In particular, it relates to a method for detecting anomalous targets in hyperspectral images by combining nonlocal spatial structure priors with tensor wheel decomposition. Background Technology
[0002] Hyperspectral images can capture information from hundreds of continuous spectral bands, providing detailed spatial and spectral information, and are therefore applied in various military and civilian fields. Hyperspectral anomaly detection plays a crucial role in the application of hyperspectral imaging by identifying potentially valuable targets within complex datasets of hyperspectral images. Therefore, it is essential to develop hyperspectral anomaly detection techniques to locate targets even without prior knowledge.
[0003] Extensive research has been conducted on hyperspectral anomaly detection methods and models, with the Reed-Xiaoli (RX) detector being a classic approach and a widely used benchmark algorithm. The RX method, based on the statistical characteristics of hyperspectral images, describes the degree of anomaly by calculating the Mahalanobis distance between the detected spectrum and the background spectrum. Based on this, researchers have proposed extended algorithms such as local-RX, subspace-RX, and kernel-RX. However, due to the complex and diverse types of ground features in real-world scenes, the background spectral distribution often fails to satisfy the Gaussian distribution assumption, affecting the detection performance of these algorithms. Subsequently, to avoid this problem, researchers proposed prior-based methods that explore the inherent characteristics of hyperspectral images, such as low rank, sparsity, and non-local self-similarity, to achieve anomaly detection, such as LRR, LSaSMD, and LSMAD. However, these methods typically involve converting a third-order tensor into a second-order matrix, which inevitably leads to the loss of the inherent high-order structure of HSI.
[0004] In recent years, an increasing number of researchers have focused on tensor decomposition-based methods, hoping to preserve the spatial and spectral information of hyperspectral images through tensor data. Examples include methods based on Tucker tensor decomposition (Zhang X, Wen G, Dai W. A tensor decomposition-based anomaly detection algorithm for hyperspectral image[J]. IEEE Transactions on Geoscience and Remote Sensing,2016, 54(10): 5801-5820) and methods based on CANDECOMP / PARAFAC (Zhang X, Wen G, Dai W. Anomaly detecting in hyperspectral imageries based on tensor decomposition with spectral and spatial partitioning[C] 2015 8th International Congress on Image and Signal Processing (CISP). IEEE, 2015: 737-741). Tensor-based methods can preserve the multidimensional structure of hyperspectral images, thus improving anomaly detection performance to some extent. However, these tensor decomposition-based methods suffer from many computational inconveniences. Subsequently, Tensor train (TT) decomposition and its extended Tensor ring (TR) decomposition have attracted attention and have been used in anomaly detection tasks (Feng M, Chen W, Yang Y, et al. Hyperspectral anomaly detection based on tensor ring decomposition with factors TV regularization[J]. IEEE Transactions on Geoscience and RemoteSensing, 2023, 61: 1-14.). However, these methods generally can only capture the structural relationships between adjacent dimensions, and cannot simultaneously model the long-distance coupling characteristics between different dimensions of a high-dimensional tensor. Furthermore, they are insufficient for representing spatially distant but texture-similar nonlocal structures.Another type of method uses the non-local self-similarity features of images to cluster similar patches and construct patch groups. However, such methods usually require flattening the patches into matrices, which destroys the original spatial structure and prevents the model from making full use of the three-dimensional geometric features of hyperspectral data, thus obtaining suboptimal detection results.
[0005] In summary, there is an urgent need for a method that can accurately characterize the high similarity and non-local high similarity between various dimensions while maintaining the original structure, thereby obtaining high-precision detection results. Summary of the Invention
[0006] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a hyperspectral image anomaly detection method based on nonlocal structural priors and tensor wheel decomposition. This method addresses the problem that existing hyperspectral image anomaly detection techniques struggle to simultaneously characterize global low-rank structures and nonlocal texture repeatability, leading to suboptimal detection results. This method constructs tensor wheel decomposition to express the full-dimensional coupling relationships of hyperspectral data, obtaining a stable and highly expressive global structural prior. It utilizes a four-dimensional nonlocal grouping strategy to preserve spatial geometric structure, capture long-distance texture relationships, and improve detail recovery capabilities. This invention enables high-precision background modeling of hyperspectral images under conditions of different spatial-spectral resolutions, spectral ranges, and anomaly categories, providing a robust and high-fidelity solution for hyperspectral anomaly detection, making hyperspectral image anomaly detection technology closer to practical application needs.
[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:
[0008] A hyperspectral anomaly detection method based on nonlocal structure prior and tensor wheel decomposition, comprising the following steps:
[0009] Step 1: Construct a hyperspectral anomaly detection model based on nonlocal structural priors and tensor wheel decomposition.
[0010] Step 1.1, record the hyperspectral data to be detected as follows: , , They are spatial dimensions, For the spectral dimension, the hyperspectral data to be detected satisfies the following degradation model:
[0011] (1)
[0012] in, For the hyperspectral background tensor, It is a hyperspectral anomaly tensor.
[0013] Step 1.2, fix the size of the sliding window as... The sliding step size is The sliding window is moved row by row and column by column in two spatial dimensions to... Perform a traversal scan to obtain all overlapping patch blocks, each patch block being of size [size missing]. .
[0014] Step 1.3: Perform the standard KNN algorithm on all patch blocks obtained in Step 1.2 to group them, fixing the number of patch blocks in each group. After grouping, N patch blocks are obtained. Each group is stacked along a new dimension in its original three-dimensional form to form a four-dimensional tensor, thus obtaining N nonlocal patch groups, denoted as . ,in, , indicating the number of groups, For spatial dimensions, For spectral dimensions, It is a non-local dimension.
[0015] The nonlocal patch groups obtained in steps 1.4 and 1.3 have high similarity in four dimensions (i.e., two spatial dimensions, one spectral dimension and one nonlocal dimension). Tensor wheel decomposition is used to constrain their similarity, and a hyperspectral anomaly detection model as shown in formula (2) is constructed. By accurately characterizing the hyperspectral background component, the effect of separating the background and anomaly from the hyperspectral image is achieved.
[0016] (2)
[0017] in, Indicates tensor wheel decomposition; Indicates the number of groups; Indicates the number of dimensions; Indicates the first The first in the group A factor tensor of dimension; Represents the core tensor of the nth group; For balance parameters; Denotes the Frobenius norm; express Norm.
[0018] Step 2 involves solving the hyperspectral anomaly detection model constructed in Step 1, with the ultimate goal of obtaining the hyperspectral anomaly tensor. Specifically:
[0019] Step 2.1: Acquire raw hyperspectral image data, perform standardization preprocessing on the acquired raw data, normalize the dataset, and obtain the hyperspectral data to be detected. .
[0020] Step 2.2, introduce auxiliary variables ,make , The number of groups is represented by the equivalent model of the hyperspectral anomaly detection model shown in formula (2), as shown in formula (3):
[0021] (3)
[0022] Formula (3) can be solved using the Proximal Alternating Minimization (PAM) framework, updating variables one by one by fixing the rest and updating a certain factor. Specifically, the objective function can be written as:
[0023] (4)
[0024] in, To be in accordance with constraints Relevant penalty parameters; For the related Lagrange multipliers, Indicates the number of groups; To be in accordance with constraints Relevant penalty parameters; These are the Lagrange multipliers associated with it.
[0025] The objective function shown in formula (4) can be broken down into the following five sub-problems:
[0026] (5)
[0027] in, It is a proximal parameter; Indicates the number of iterations; upper right subscript , These represent the first and second digits of the variable. sequence The next iteration; Indicates the first The first in the group A factor tensor of dimension; Represents the core tensor of the nth group; Indicates the first Auxiliary variables of the group; For the hyperspectral background tensor, It is a hyperspectral anomaly tensor.
[0028] Step 2.3: Input the hyperspectral data to be detected obtained in Step 2.1. Initialize the number of iterations Maximum number of iterations Balance parameters Two penalty parameters Two Lagrange multipliers Proximal parameters Fixed sliding window size Sliding step size Number of patch blocks in each group Hyperspectral background tensor Hyperspectral anomaly tensor factor tensor Core tensor Auxiliary variables , Iteration stopping threshold Update step size Maximum penalty parameter threshold While keeping other variables constant, update a single variable individually. The stopping threshold range is... between.
[0029] Step 2.4, Update the factor tensor and core tensor :
[0030] Solving the first and second subproblems corresponding to formula (5), we can obtain the following results:
[0031] (6)
[0032] in, Indicates the transpose operation; This represents the inverse operation; Represents the identity matrix; upper right subscript , These represent the first and second digits of the variable. sequence The next iteration; for The 3D cyclic tensor expansion; for The third-dimensional expansion of the generalized tensor This means that the merger has been completed except for the one that was originally intended to be merged. All factor tensors outside of the sub-wheel tensor ( for (dimensional sequence vectors); yes The classical tensor second-dimensional expansion; This is the inverse operation of the second-dimensional expansion of a classical tensor; and They are respectively and vector expansion, This is the inverse operation of vector expansion; for The fourth-dimensional expansion of the generalized tensor This means only the merger was performed. sub-wheel tensor ( for (a sequence vector of dimensions).
[0033] Step 2.5, Update auxiliary variables :
[0034] Solving the third subproblem in formula (5), we obtain the following result:
[0035] (7)
[0036] Among them, the upper right corner mark , These represent the first and second digits of the variable. sequence The next iteration; Indicates the first The first in the group A factor tensor of dimension; Represents the core tensor of the nth group; Indicates the first Auxiliary variables of the group; This represents the hyperspectral background tensor of the nth group; Representation and Constraints Relevant penalty parameters; Indicates the related first Group Lagrange multipliers; This indicates the proximal parameter.
[0037] Step 2.6, Update the hyperspectral background tensor :
[0038] Solving the fourth subproblem corresponding to formula (5), we obtain the following result:
[0039] (8)
[0040] Among them, the upper right corner mark , These represent the first and second digits of the variable. , The next iteration; Indicates the first Auxiliary variables of the group; Represents the hyperspectral background tensor; Represents the hyperspectral anomaly tensor; This represents the hyperspectral data to be detected; To be in accordance with constraints Relevant penalty parameters; For the related Lagrange multipliers, Indicates the number of groups; To be in accordance with constraints Relevant penalty parameters; These are the Lagrange multipliers associated with it.
[0041] Step 2.7, Update the hyperspectral anomaly tensor :
[0042] The fifth subproblem corresponding to formula (5) is shown below:
[0043] (9)
[0044] Solving formula (9) yields the following results:
[0045] (10)
[0046] in, yes Minimization operator; top right subscript This indicates the first... The next iteration; Represents the hyperspectral anomaly tensor; This represents the hyperspectral data to be detected; Represents the hyperspectral background tensor; Representation and Constraints Relevant penalty parameters; Indicates the Lagrange multipliers associated with it; This represents the equilibrium parameter.
[0047] Step 2.8, update the Lagrange multipliers and penalty parameters.
[0048] (11)
[0049] (12)
[0050] Among them, the upper right corner mark , These represent the first and second digits of the variable. , The next iteration; To be in accordance with constraints Relevant penalty parameters; For the related Lagrange multipliers, Indicates the number of groups; To be in accordance with constraints Relevant penalty parameters; For the Lagrange multipliers associated with it; Indicates the update step size; This represents the threshold value for the maximum penalty parameter.
[0051] Step 2.9, check the convergence conditions as follows:
[0052] (13)
[0053] If the above convergence conditions are met, the iteration terminates and proceeds to step 3. If not, the iteration returns to step 2.4 and continues until the convergence conditions shown in formula (13) are met, and the hyperspectral anomaly tensor is output. .
[0054] Step 3, using the hyperspectral anomaly tensor obtained in Step 2 Anomaly map obtained by pixel-by-pixel calculation For anomaly graphs The first in 1 pixel The specific calculation formula is as follows:
[0055] (14)
[0056] in, Anomaly diagram In position Pixel value at; Represents the hyperspectral anomaly tensor In position The value at; Indicates the first dimension coordinate; Indicates the second-dimensional coordinates; Represents the third-dimensional coordinates.
[0057] The obtained anomaly graph This is the final anomaly detection result.
[0058] Compared with the prior art, the present invention has the following main advantages:
[0059] This invention proposes a hyperspectral image anomaly detection method based on nonlocal structure prior and tensor wheel decomposition. Patches with repetitive texture patterns or similar spectral features in the hyperspectral background tensor are aggregated into nonlocal patch groups, which are then subjected to tensor wheel decomposition. This allows the cross-regional texture repetition and spectral commonality inherent in the nonlocal patch groups to be effectively characterized in a compact low-rank tensor form, fully utilizing internal redundant information and accurately representing the background structure. The tensor wheel structure avoids the structural destruction caused by traditional matrixing, enabling efficient low-rank modeling while maintaining the inherent spatial-spectral geometric features of high-dimensional data. Hyperspectral anomaly tensors, unable to maintain global consistency during tensor wheel decomposition, are automatically weakened. This method solves the problem of existing techniques struggling to simultaneously represent global low-rank structure and nonlocal texture repetition while preserving structural information, significantly improving the accuracy of background and anomaly separation. Attached Figure Description
[0060] Figure 1 This is a flowchart illustrating the principle of the present invention.
[0061] Figure 2 For visualization results; Figure 2 (a) in the image is a pseudo-color image from the Sandiego dataset; Figure 2 (b) in the diagram is the truth graph; Figure 2 (c) in the figure represents the anomaly graph obtained by this method. Detailed Implementation
[0062] The present invention will be further described below with reference to specific embodiments.
[0063] A hyperspectral anomaly detection method based on nonlocal structure prior and tensor wheel decomposition, comprising the following steps:
[0064] Step 1: Construct a hyperspectral anomaly detection model based on nonlocal structural priors and tensor wheel decomposition.
[0065] Step 1.1, record the hyperspectral data to be detected as follows: , , They are spatial dimensions, For the spectral dimension, the hyperspectral data to be detected satisfies the following degradation model:
[0066] (1)
[0067] in, For the hyperspectral background tensor, It is a hyperspectral anomaly tensor.
[0068] Step 1.2, fix the size of the sliding window as... The sliding step size is The sliding window is moved row by row and column by column in two spatial dimensions to... Perform a traversal scan to obtain all overlapping patch blocks, each patch block being of size [size missing]. .
[0069] Step 1.3: Perform the standard KNN algorithm on all patch blocks obtained in Step 1.2 to group them, fixing the number of patch blocks in each group. After grouping, N patch blocks are obtained. Each group is stacked along a new dimension in its original three-dimensional form to form a four-dimensional tensor, thus obtaining N nonlocal patch groups, denoted as . ,in, , indicating the number of groups, For spatial dimensions, For spectral dimensions, It is a non-local dimension.
[0070] The nonlocal patch groups obtained in steps 1.4 and 1.3 have high similarity in four dimensions (i.e., two spatial dimensions, one spectral dimension and one nonlocal dimension). Tensor wheel decomposition is used to constrain their similarity, and a hyperspectral anomaly detection model as shown in formula (2) is constructed. By accurately characterizing the hyperspectral background component, the effect of separating the background and anomaly from the hyperspectral image is achieved.
[0071] (2)
[0072] in, Indicates tensor wheel decomposition; Indicates the number of groups; Indicates the number of dimensions; Indicates the first The first in the group A factor tensor of dimension; Represents the core tensor of the nth group; For balance parameters; Denotes the Frobenius norm; express Norm.
[0073] Step 2 involves solving the hyperspectral anomaly detection model constructed in Step 1, with the ultimate goal of obtaining the hyperspectral anomaly tensor. Specifically:
[0074] Step 2.1: This example uses the Sandiego dataset collected by the AVIRIS sensor over San Diego Airport in California, USA. The spatial size of this hyperspectral data is... (Right now The spatial resolution is approximately 3.5 meters. After removing low signal-to-noise ratio and water vapor absorption bands, 189 bands remain (i.e., The wavelength range is 400–2500 nm, and the spectral resolution is 10 nm. This data undergoes standardization preprocessing to normalize the dataset, yielding the hyperspectral data to be detected. Size is .
[0075] Step 2.2, introduce auxiliary variables ,make , The number of groups is represented by the equivalent model of the hyperspectral anomaly detection model shown in formula (2), as shown in formula (3):
[0076] (3)
[0077] Formula (3) can be solved using the Proximal Alternating Minimization (PAM) framework, updating variables one by one by fixing the rest and updating a certain factor. Specifically, the objective function can be written as:
[0078] (4)
[0079] in, To be in accordance with constraints Relevant penalty parameters; For the related Lagrange multipliers, Indicates the number of groups; To be in accordance with constraints Relevant penalty parameters; These are the Lagrange multipliers associated with it.
[0080] The objective function shown in formula (4) can be broken down into the following five sub-problems:
[0081] (5)
[0082] in, It is a proximal parameter; Indicates the number of iterations; upper right subscript , These represent the first and second digits of the variable. sequence The next iteration; Indicates the first The first in the group A factor tensor of dimension; Represents the core tensor of the nth group; Indicates the first Auxiliary variables of the group; For the hyperspectral background tensor, It is a hyperspectral anomaly tensor.
[0083] Step 2.3: Input the hyperspectral data to be detected obtained in Step 2.1. Initialize the number of iterations Maximum number of iterations Balance parameters Two penalty parameters Two Lagrange multipliers All are 0, near-end parameters Fixed sliding window size Sliding step size Number of patch blocks in each group Hyperspectral background tensor Hyperspectral anomaly tensor All are 0, tensor rank is 2, factor tensor and core tensor Randomized generation using tensor round rank, auxiliary variable =0, Iteration stopping threshold Update step size Maximum penalty parameter threshold While keeping other variables constant, update a single variable individually.
[0084] Step 2.4, Update the factor tensor and core tensor :
[0085] Solving the first and second subproblems corresponding to formula (5), we can obtain the following results:
[0086] (6)
[0087] in, Indicates the transpose operation; This represents the inverse operation; Represents the identity matrix; upper right subscript , These represent the first and second digits of the variable. sequence The next iteration; for The 3D cyclic tensor expansion; for The third-dimensional expansion of the generalized tensor This means that the merger has been completed except for the one that was originally intended to be merged. All factor tensors outside of the sub-wheel tensor ( for (dimensional sequence vectors); yes The classical tensor second-dimensional expansion; This is the inverse operation of the second-dimensional expansion of a classical tensor; and They are respectively and vector expansion, This is the inverse operation of vector expansion; for The fourth-dimensional expansion of the generalized tensor This means only the merger was performed. sub-wheel tensor ( for (a sequence vector of dimensions).
[0088] Step 2.5, Update auxiliary variables :
[0089] Solving the third subproblem in formula (5), we obtain the following result:
[0090] (7)
[0091] Among them, the upper right corner mark , These represent the first and second digits of the variable. sequence The next iteration; Indicates the first The first in the group A factor tensor of dimension; Represents the core tensor of the nth group; Indicates the first Auxiliary variables of the group; This represents the hyperspectral background tensor of the nth group; Representation and Constraints Relevant penalty parameters; Indicates the related first Group Lagrange multipliers; This indicates the proximal parameter.
[0092] Step 2.6, Update the hyperspectral background tensor :
[0093] Solving the fourth subproblem corresponding to formula (5), we obtain the following result:
[0094] (8)
[0095] Among them, the upper right corner mark , These represent the first and second digits of the variable. , The next iteration; Indicates the first Auxiliary variables of the group; Represents the hyperspectral background tensor; Represents the hyperspectral anomaly tensor; This represents the hyperspectral data to be detected; To be in accordance with constraints Relevant penalty parameters; For the related Lagrange multipliers, Indicates the number of groups; To be in accordance with constraints Relevant penalty parameters; These are the Lagrange multipliers associated with it.
[0096] Step 2.7, Update the hyperspectral anomaly tensor :
[0097] The fifth subproblem corresponding to formula (5) is shown below:
[0098] (9)
[0099] Solving formula (9) yields the following results:
[0100] (10)
[0101] in, yes Minimization operator; top right subscript This indicates the first... The next iteration; Represents the hyperspectral anomaly tensor; This represents the hyperspectral data to be detected; Represents the hyperspectral background tensor; Representation and Constraints Relevant penalty parameters; Indicates the Lagrange multipliers associated with it; This represents the equilibrium parameter.
[0102] Step 2.8, update the Lagrange multipliers and penalty parameters.
[0103] (11)
[0104] (12)
[0105] Among them, the upper right corner mark , These represent the first and second digits of the variable. , The next iteration; To be in accordance with constraints Relevant penalty parameters; For the related Lagrange multipliers, Indicates the number of groups; To be in accordance with constraints Relevant penalty parameters; For the Lagrange multipliers associated with it; Indicates the update step size; This represents the threshold value for the maximum penalty parameter.
[0106] Step 2.9, check the convergence conditions as follows:
[0107] (13)
[0108] If the above convergence conditions are met, the iteration terminates and proceeds to step 3. If not, the iteration returns to step 2.4 and continues until the convergence conditions shown in formula (13) are met, and the hyperspectral anomaly tensor is output. .
[0109] Step 3, using the hyperspectral anomaly tensor obtained in Step 2 Anomaly map obtained by pixel-by-pixel calculation For anomaly graphs The first in 1 pixel The specific calculation formula is as follows:
[0110] (14)
[0111] in, Anomaly diagram In position Pixel value at; Represents the hyperspectral anomaly tensor In position The value at; Indicates the first dimension coordinate; Indicates the second-dimensional coordinates; Represents the third-dimensional coordinates.
[0112] The obtained anomaly graph This is the final anomaly detection result.
[0113] To evaluate detection accuracy, four commonly used AUC indices for anomaly detection in hyperspectral images were further calculated as evaluation metrics: , , and The higher the first, second, and fourth indicators, and the lower the third indicator, the better the effect. Table 1 lists the AUC index for different methods.
[0114] Table 1: AUC index of the Sandiego dataset in this example
[0115]
[0116] As shown in Table 1, the method of this invention achieves an excellent AUC index, indicating a relatively accurate separation of background and anomalies. Furthermore, the visualization results are as follows... Figure 2 As shown. The method of the present invention achieves excellent detection results, simultaneously highlighting abnormalities and suppressing background.
[0117] The above-described embodiments are merely illustrative of the implementation methods of the present invention, but should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the protection scope of the present invention.
Claims
1. A hyperspectral anomaly detection method based on nonlocal structure prior and tensor wheel decomposition, characterized in that, The hyperspectral anomaly detection method includes the following steps: Step 1: Construct a hyperspectral anomaly detection model based on nonlocal structure priors and tensor wheel decomposition; Step 2 involves solving the hyperspectral anomaly detection model constructed in Step 1, with the ultimate goal of obtaining the hyperspectral anomaly tensor. ; Step 3, using the hyperspectral anomaly tensor obtained in Step 2 Anomaly map obtained by pixel-by-pixel calculation For anomaly graphs The first in 1 pixel The specific calculation formula is as follows: （14）； in, Anomaly diagram In position Pixel value at; Represents the hyperspectral anomaly tensor In position The value at; Indicates the first dimension coordinate; Indicates the second-dimensional coordinates; Represents the third-dimensional coordinates; The obtained anomaly graph This is the final anomaly detection result.
2. The hyperspectral anomaly detection method based on nonlocal structure prior and tensor wheel decomposition according to claim 1, characterized in that, Step 1 specifically includes: Step 1.1, record the hyperspectral data to be detected as follows: , , They are spatial dimensions, For the spectral dimension; the hyperspectral data to be detected satisfies the following degradation model: （1）； in, For the hyperspectral background tensor, For hyperspectral anomaly tensors; Step 1.2, fix the size of the sliding window as... The sliding step size is The sliding window is moved row by row and column by column in two spatial dimensions to... Perform a traversal scan to obtain all overlapping patch blocks, each patch block being of size [size missing]. ; Step 1.3: Perform the standard KNN algorithm on all patch blocks obtained in Step 1.2 to group them, fixing the number of patch blocks in each group. After grouping, N patch blocks are obtained; each group is stacked along the new dimension according to the original three-dimensional shape to form a four-dimensional tensor, resulting in N nonlocal patch groups, denoted as ,in, , indicating the number of groups, For spatial dimensions, For spectral dimensions, It is a non-local dimension; The nonlocal patch groups obtained in steps 1.4 and 1.3 are similar in four dimensions. Tensor wheel decomposition is used to constrain their similarity, and a hyperspectral anomaly detection model as shown in formula (2) is constructed. By accurately characterizing the hyperspectral background component, the effect of separating the background and anomaly from the hyperspectral image is achieved. （2）； in, Indicates tensor wheel decomposition; Indicates the number of groups; Indicates the number of dimensions; Indicates the first The first in the group A factor tensor of dimension; Represents the core tensor of the nth group; For balance parameters; Denotes the Frobenius norm; express Norm.
3. The hyperspectral anomaly detection method based on nonlocal structure prior and tensor wheel decomposition according to claim 2, characterized in that, The four dimensions in step 1.4 include two spatial dimensions, one spectral dimension, and one nonlocal dimension.
4. The hyperspectral anomaly detection method based on nonlocal structure prior and tensor wheel decomposition according to claim 3, characterized in that, Step 2 specifically refers to: Step 2.1: Acquire raw hyperspectral image data, perform standardization preprocessing on the acquired raw data, normalize the dataset, and obtain the hyperspectral data to be detected. ; Step 2.2, introduce auxiliary variables ,make , The number of groups is represented by the equivalent model of the hyperspectral anomaly detection model shown in formula (2), as shown in formula (3): （3）； Formula (3) is solved using the proximal alternation minimization PAM framework, updating variables one by one by "fixing the rest and updating a certain factor"; specifically, the objective function is written as: （4）； in, To be in accordance with constraints Relevant penalty parameters; For the related Lagrange multipliers, Indicates the number of groups; To be in accordance with constraints Relevant penalty parameters; For the Lagrange multipliers associated with it; The objective function shown in formula (4) is decomposed into five sub-problems and solved separately; Step 2.3: Input the hyperspectral data to be detected obtained in Step 2.
1. While keeping other variables constant, update a single variable individually. Step 2.4, Update the factor tensor and core tensor Solve the first and second subproblems corresponding to formula (5); Step 2.5, Update auxiliary variables Solve the third subproblem corresponding to formula (5); Step 2.6, Update the hyperspectral background tensor Solve the fourth subproblem corresponding to formula (5). Step 2.7, Update the hyperspectral anomaly tensor Solve the fifth subproblem corresponding to formula (5); Step 2.8, update the Lagrange multipliers and penalty parameters; Step 2.9: Check the convergence condition. If the convergence condition is met, terminate the iteration and proceed to step 3. If not, return to step 2.4 to continue iterating and updating until the convergence condition shown in formula (13) is met, and output the hyperspectral anomaly tensor. .
5. The hyperspectral anomaly detection method based on nonlocal structure prior and tensor wheel decomposition according to claim 4, characterized in that, In step 2.2, the five sub-problems are as follows: （5）； in, It is a proximal parameter; Indicates the number of iterations; upper right subscript , These represent the first and second digits of the variable. sequence The next iteration; Indicates the first The first in the group A factor tensor of dimension; Represents the core tensor of the nth group; Indicates the first Auxiliary variables of the group; For the hyperspectral background tensor, It is a hyperspectral anomaly tensor.
6. The hyperspectral anomaly detection method based on nonlocal structure prior and tensor wheel decomposition according to claim 5, characterized in that, In step 2.3, the other variables are: the number of initial iterations. Maximum number of iterations Balance parameters Two penalty parameters Two Lagrange multipliers Proximal parameters Fixed sliding window size Sliding step size Number of patch blocks in each group Hyperspectral background tensor Hyperspectral anomaly tensor factor tensor Core tensor Auxiliary variables , Iteration stopping threshold Update step size Maximum penalty parameter threshold The stop threshold range is: between.
7. The hyperspectral anomaly detection method based on nonlocal structure prior and tensor wheel decomposition according to claim 6, characterized in that, Steps 2.4 to 2.9 are specifically as follows: Step 2.4, Update the factor tensor and core tensor : Solving the first and second subproblems corresponding to formula (5), we can obtain the following results: （6）； in, Indicates the transpose operation; This represents the inverse operation; Represents the identity matrix; upper right subscript , These represent the first and second digits of the variable. sequence The next iteration; for The 3D cyclic tensor expansion; for The third-dimensional expansion of the generalized tensor This means that the merger has been completed except for the one that was originally intended to be merged. All factor tensors outside of the sub-wheel tensor ( for (dimensional sequence vectors); yes The classical tensor second-dimensional expansion; This is the inverse operation of the second-dimensional expansion of a classical tensor; and They are respectively and vector expansion, This is the inverse operation of vector expansion; for The fourth-dimensional expansion of the generalized tensor. This means only the merger was performed. The sub-wheel tensor; Step 2.5, Update auxiliary variables : Solving the third subproblem in formula (5), we obtain the following result: （7）； Among them, the upper right corner mark , These represent the first and second digits of the variable. sequence The next iteration; Indicates the first The first in the group A factor tensor of dimension; Represents the core tensor of the nth group; Indicates the first Auxiliary variables of the group; This represents the hyperspectral background tensor of the nth group; Representation and Constraints Relevant penalty parameters; Indicates the related first Group Lagrange multipliers; Indicates the proximal parameter; Step 2.6, Update the hyperspectral background tensor : Solving the fourth subproblem corresponding to formula (5), we obtain the following result: （8）； Among them, the upper right corner mark , These represent the first and second digits of the variable. , The next iteration; Indicates the first Auxiliary variables of the group; Represents the hyperspectral background tensor; Represents the hyperspectral anomaly tensor; This represents the hyperspectral data to be detected; To be in accordance with constraints Relevant penalty parameters; For the related Lagrange multipliers, Indicates the number of groups; To be in accordance with constraints Relevant penalty parameters; For the Lagrange multipliers associated with it; Step 2.7, Update the hyperspectral anomaly tensor : The fifth subproblem corresponding to formula (5) is shown below: （9）； Solving formula (9) yields the following results: （10）； in, yes Minimization operator; top right subscript This indicates the first... The next iteration; Represents the hyperspectral anomaly tensor; This represents the hyperspectral data to be detected; Represents the hyperspectral background tensor; Representation and Constraints Relevant penalty parameters; Indicates the Lagrange multipliers associated with it; Indicates the balance parameters; Step 2.8, update the Lagrange multipliers and penalty parameters; （11）； （12）； Among them, the upper right corner mark , These represent the first and second digits of the variable. , The next iteration; To be in accordance with constraints Relevant penalty parameters; For the related Lagrange multipliers, Indicates the number of groups; To be in accordance with constraints Relevant penalty parameters; For the Lagrange multipliers associated with it; Indicates the update step size; This represents the threshold value for the maximum penalty parameter; Step 2.9, the convergence condition is as follows: （13）。