Hyperspectral target detection method based on third-order tensor decomposition and adaptive reconstruction

Abstract

The application provides a hyperspectral target detection method based on third-order tensor decomposition and adaptive reconstruction, comprising the following steps: S1, hyperspectral data preprocessing; S2, Tucker decomposition and adaptive reconstruction of the data; S3, multi-measure method is used to extract targets respectively; S4, multi-measure information is fused to obtain a target of interest; and S5, a threshold segmentation method is used to segment the target and the background. Global constraint energy minimization, Pearson correlation coefficient and Euclidean distance are used to obtain part of target pixels respectively, and the three methods are fused to obtain more accurate target pixels of interest. Experiments prove that the method exhibits good detection performance.

Description

Technical Field

[0001] This invention relates to the field of hyperspectral image target detection technology, and in particular to a hyperspectral target detection method based on third-order tensor decomposition and adaptive reconstruction, which is especially suitable for the detection and identification of camouflaged and concealed low-contrast targets in urban low-altitude environments and complex ground scenes. Background Technology

[0002] In modern urban environments, the complexity of low-altitude and ground-level scenes presents significant challenges to target detection. These environments often contain a wide variety of targets, including buildings, vehicles, people, and other objects. These targets can easily be concealed or disguised due to their shapes, colors, and textures closely resembling their surroundings. Targets with subtle camouflage and low contrast are particularly difficult to detect and identify accurately. However, the combined advantages of hyperspectral imaging and spatial-spectral mapping can overcome this challenge, enabling the effective detection and identification of even minute targets. Therefore, in-depth research into hyperspectral target detection technology is crucial for improving the accuracy and reliability of target detection in urban environments.

[0003] Based on the degree of information utilization, current hyperspectral target detection methods are mainly divided into traditional detection methods based on spectral domain information, joint detection methods based on spatial and spectral information, and methods based on deep feature extraction. With the development of hyperspectral technology, many traditional hyperspectral target detection algorithms have emerged. The constrained energy minimization (CEM) method designs a filter that outputs the minimum amount of information under the constraint of the prior target spectrum. Spectral angle mapper (SAM) does not require any information distribution assumptions and can be considered one of the simpler target detectors. The matching filter (MF) is also an early detector. The adaptive coherence estimator (ACE) uses different methods to expand the detection statistics, achieving greater separation between the target and the background. Spectral information divergence (SID) achieves target detection by calculating the information divergence between two spectra. The ensemble-based constrained energy minimization (E-CEM) model is designed based on CEM, including cascaded detection, random averaging, and multi-scale scanning strategy design. These methods are simple in design, but they neglect to utilize specular 3D structural information, and their detection performance still needs to be improved.

[0004] In joint detection algorithms based on spatial-spectral information, some researchers have proposed transform-domain adaptive constrained energy minimization detectors, utilizing local constrained energy minimization for target detection. Li et al. proposed a novel hyperspectral detection technique called combined sparse and collaborative representation technology (CSCR). This algorithm uses target and background libraries to describe the features of test pixels, thus achieving effective target detection. Yang et al. proposed a sparse spatial constrained energy minimization (SSCEM) method that integrates a total variational regularization term, making the output sparse through an L1-norm regularization term. Sun et al. proposed a tree structure encoding-based algorithm for target detection (TDTSE). This algorithm constructs a binary tree using data features and uses this structure to segment targets from the background. Chen et al. proposed a global-to-local approach for hyperspectral layered target detection (G2LHTD). However, these methods suffer from low detection accuracy because they ignore the three-dimensional structural information of the hyperspectral spectrum itself.

[0005] In terms of deep feature extraction, Li et al. proposed a deep convolutional neural network for hyperspectral imagery target detection (HTD-NET), a deep convolutional neural network for detecting targets in hyperspectral images. This method increases the amount of data through pixel pairing and data augmentation, extracts multi-layer information, and constructs a pixel similarity discrimination model. Shi et al. proposed a deep spatial-spectral network (DSSN) for unsupervised hyperspectral target detection. This method uses a traditional detector and edge-preserving filter to identify regions of interest and extracts relevant features from the processed image. Shen et al. proposed a dyadic sparse constraint (DSC) algorithm for target detection. Dong et al. combined relevance distance constraints and density peak clustering to construct a lightweight convolutional neural network (LCNN) for hyperspectral target detection. However, these methods suffer from low robustness due to limited sample size.

[0006] Research has shown that tensor theory methods can better utilize the three-dimensional structural information of data, and this theory has been applied to hyperspectral image segmentation and classification. However, existing work on hyperspectral target detection using tensor representations is scarce. Li Wei et al. proposed prior-based tensor approximation for anomaly detection (PTA), which improves anomaly detection performance by utilizing some prior constraints. Gu Yanfeng et al. proposed tensor matched subspace detector (MSD). This method defines the tensor quantum space projection for the first time, and the tensor quantum space projection can be calculated without iteration using three predetermined orthogonal direction mapping matrices. Then, the test tensor block is projected into the tensor quantum space, and finally, the ratio of remaining energy is used for measurement, and the target is obtained through a likelihood ratio test. However, these methods fail to adaptively achieve tensor reconstruction, resulting in poor preservation of the intrinsic ability of the target and background, and low target-background discriminability. Summary of the Invention

[0007] Considering that tensors can better preserve the three-dimensional structural information of hyperspectral data, this invention provides a hyperspectral target detection framework based on third-order tensor decomposition and adaptive reconstruction (TTDAR). First, the Tucker decomposition and reconstruction strategy is used to eliminate the influence of noise and other factors in complex background hyperspectral data, preserving the intrinsic structural features of the data and improving the separation between the target and the background. This includes determining the principal components of the factor matrix through a logarithmic singular value summation strategy, followed by calculating the energy difference between the measured spectrum and the prior spectrum to fine-tune the principal components and obtain more suitable principal component values. Second, based on the reconstructed data, a multi-metric information strategy is proposed to obtain the target of interest. This includes using global constraint energy minimization to obtain energy metric information, using local Pearson correlation coefficients to obtain local related information, and using local Euclidean distance to obtain distance information. Finally, the multi-metric information is fused to obtain the target of interest.

[0008] The specific technical solution is as follows:

[0009] A hyperspectral target detection method based on third-order tensor decomposition and adaptive reconstruction includes the following steps:

[0010] S1, Hyperspectral data preprocessing. The acquired hyperspectral data is normalized by maximum and minimum values, and the spectra of the target of interest are extracted from the partially normalized data to construct a priori spectral library;

[0011] S2, Tucker decomposition and adaptive reconstruction of the data. The hyperspectral data is represented as a third-order tensor, and Tucker decomposition is performed to obtain a core tensor and three factor matrices. The principal components of different factor matrices are initially obtained using the logarithmic energy summation method. Further principal components of different factor matrices are obtained by minimizing the energy difference between the prior spectrum and the target spectrum of the measured data. The hyperspectral data is then reconstructed using the obtained refined principal components.

[0012] S3, multiple metric methods are used to extract the target. Global constraint energy minimization is used to obtain energy metric information, local Pearson correlation coefficient is used to obtain local related information, and local Euclidean distance is used to obtain local distance information.

[0013] S4, fusing multiple metrics to obtain the target of interest. Fusion of three metrics improves the target of interest detection rate.

[0014] S5 uses a threshold segmentation method to separate the target from the background. By setting a certain threshold, the target and background are assigned values ​​of 1 and 0 respectively.

[0015] Specifically:

[0016] S1 specifically includes the following sub-steps:

[0017] S101, the acquired data is normalized using the maximum and minimum value method, as shown in the following formula:

[0018]

[0019] in This represents the raw hyperspectral data collected. This represents the data obtained after normalization;

[0020] S102, select the prior spectrum of the target of interest from the partially acquired hyperspectral images, and normalize these spectra to obtain the prior spectrum d.

[0021] S2 specifically includes the following sub-steps:

[0022] S201, Tucker decomposition of hyperspectral data;

[0023] The three-dimensional spatial structure information of hyperspectral data is represented using tensor methods; a hyperspectral image is represented as a third-order tensor. Where T1, T2, and T3 represent the rows, columns, and bands of the hyperspectral data, respectively;

[0024] The hyperspectral dataset is reconstructed using Tucker decomposition; the tensor X is represented as:

[0025]

[0026] in This is called the core tensor, whose elements represent the level of interaction between different components; and Given three factor matrices, considered as principal components under each mode, the optimization problem is formulated as follows:

[0027]

[0028] The solution to the above equation is obtained by solving it in an alternating manner, wherein each factor matrix is ​​obtained by eigenvalue decomposition when the other two matrices are fixed;

[0029] S202, adaptive principal component selection for different factor matrices after hyperspectral decomposition;

[0030] Tucker decomposition decomposes a third-order tensor matrix into three factor matrices (U, V, W) and a core tensor. The columns of each factor matrix serve as the eigenvectors of the modulus-n mode, sorted in descending order of the corresponding eigenvalues, where n is 1, 2, or 3.

[0031] For different factor matrices (U, V, W), the number of principal components r for determining different factor matrices... i The number of (i = 1, 2, 3) is introduced, and a strategy of selecting principal components using the logarithmic singular value summation ratio is adopted. The formula for selecting principal components using the logarithmic singular value summation is as follows:

[0032]

[0033] Where a i =[a1,a2,...,a s ] is the singular value factor matrix, s is the number of singular values, r is the number of principal components selected, and ε is a constant 1; by setting the value of the logarithmic singular value summation ratio η, the corresponding r in different factor matrices is automatically determined;

[0034] After initially determining the number of principal components, a fine search is performed in the vicinity of the principal components; the principal component with the smallest difference from the prior target spectral energy is selected as the final principal component, as shown in the following formula:

[0035]

[0036] Where E X Represents data X reconstructed with different factor matrices and different numbers of principal components. r+k The energy of the spectrum corresponding to the target location, k = 2, representing the fine search range, t represents the t-th band, T3 represents the band number, E T Let E represent the energy of the prior target spectrum, and let E represent the spectral energy difference. The number of principal components that minimizes the spectral energy difference is selected.

[0037] S203, hyperspectral data reconstruction based on the selected principal components;

[0038] Reconstructed and For spectral dimensions, the formula is as follows:

[0039]

[0040] in U r =U(:,1:r1),V r =V(:,1:r2),W r =W(:,1:r3), r i The principal components of different factor matrices.

[0041] S3 specifically includes the following sub-steps:

[0042] S301 uses global constraint energy minimization to obtain energy metric information;

[0043] Hyperspectral data unfolded into a two-dimensional matrix is The design of a globally constrained energy-minimizing filter must satisfy the following formula:

[0044]

[0045] Where N is the number of pixels, which is T1×T2. denoted by a pixel, R is the correlation matrix of the sample set, which in this case is the correlation matrix of all pixels in the hyperspectral image; w is the filter, and d is the target spectrum;

[0046] For conditional extremum problems, the value of the filter w can be obtained by using the Lagrange multiplier method. The filter value is as follows:

[0047]

[0048] The CEM operator is used to traverse the entire hyperspectral image data to obtain the distribution of pixels similar to the known target spectrum d in the entire image, thereby achieving target detection; the detection formula is as follows:

[0049]

[0050] Where w is the filter for reconstructing the data, d is the target spectrum of the reconstructed data, R is the autocorrelation matrix of the reconstructed data, and x is the spectrum of the pixel to be measured in the reconstructed data;

[0051] S302, local Pearson correlation coefficient is used to obtain local relevant information;

[0052] The formula for the distance similarity between the prior spectrum and the spectrum to be measured is as follows:

[0053]

[0054] Among them o i Let represent the distance similarity between the prior spectrum and the i-th test spectrum. The mean distance similarity of the four neighbors is as follows:

[0055]

[0056] S303 uses local Euclidean distance to obtain distance information;

[0057] The Pearson correlation coefficient, which represents the similarity between the prior target spectrum and the measured spectrum, is expressed by the following formula:

[0058]

[0059] in T3 represents the Pearson correlation coefficient between the measured spectrum and the prior spectrum, and T3 represents the number of bands in the spectrum. The mean Pearson correlation coefficients for the four-neighbor region are as follows:

[0060]

[0061] Where x (i,j) This represents the spectrum of the i-th pixel to be measured in the fractional domain. The mean of the Pearson correlation coefficients in the four neighborhoods of the fractional domain is given.

[0062] S4 integrates the three information acquisition methods to obtain the target detection result, as shown in the following formula:

[0063]

[0064] In S5, the determination of r is made by comparing it with a specified threshold Th:

[0065]

[0066] Where 1 indicates that r is the target and 0 indicates that r belongs to the background.

[0067] This invention proposes a hyperspectral target detection method based on third-order tensor decomposition and adaptive reconstruction. First, a Tucker decomposition and reconstruction strategy is used to suppress background and enhance target features. A logarithmic singular value summation strategy is employed to initially determine the principal components of the factor matrix, and the minimum energy difference between the measured spectrum and the prior spectrum is used to further determine more accurate principal component values. Second, multiple metric methods are fused to obtain a more complete picture of the target of interest. Global constraint energy minimization, Pearson correlation coefficient, and Euclidean distance are used to obtain partial target pixels, and the fusion of these three methods yields more accurate target pixels of interest. Experiments demonstrate that the proposed method exhibits good detection performance. Attached Figure Description

[0068] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0069] Figure 1 This is a flowchart of the present invention;

[0070] Figure 2 This is a flowchart of the hyperspectral data Tucker decomposition and adaptive reconstruction process of the present invention;

[0071] Figure 3 This is a flowchart of the adaptive principal component selection process of the present invention;

[0072] Figure 4 This is a flowchart of the multi-measurement method of the present invention;

[0073] Figure 5 The examples show the pseudo-color images, ground truth images, and detection result images of camouflaged vehicle data against a bare soil cement background using different methods.

[0074] (a) Pseudo-color image (b) Truth image (c) SAM (d) MF (e) ECEM (f) ACE (g) PTA (h) DSC (i) LCNN (j) Proposed;

[0075] Figure 6 The examples show pseudo-color images, ground truth images, and detection result images of different methods used in the camouflage vehicle data in the bushes.

[0076] (a) Pseudo-color image (b) Truth image (c) SAM (d) MF (e) ECEM (f) ACE (g) PTA (h) DSC (i) LCNN (j) Proposed;

[0077] Figure 7 ROC curves of camouflaged vehicle data against bare soil and cement backgrounds using different methods;

[0078] Figure 8 ROC curves for different methods of camouflaging vehicle data in bushes. Detailed Implementation

[0079] The specific technical solution of the present invention will be described in conjunction with the accompanying drawings.

[0080] The framework diagram of the hyperspectral target detection algorithm using third-order tensor decomposition and adaptive reconstruction in this invention is as follows: Figure 1 As shown, the hyperspectral data undergoes tensor decomposition and adaptive reconstruction. The original data is decomposed using tensor Tucker decomposition. For each mode after decomposition, singular value decomposition, logarithmic singular value summation for coarse principal component selection, and minimization of the energy difference between the prior target and the measured data for finer principal component selection are performed to reconstruct the data. Secondly, based on the reconstructed data, three metrics are used to extract partial targets: global constraint energy minimization, local Pearson correlation coefficient, and local Euclidean distance. Finally, these three types of information are fused to obtain a more complete picture of the target of interest.

[0081] The specific steps are as follows:

[0082] S1 involves preprocessing the acquired hyperspectral data to address the issue of low model adaptability caused by data bias. This mainly includes normalizing the acquired data and extracting the prior spectra of interest.

[0083] S101, the acquired data is normalized using the maximum and minimum value method, as shown in the following formula:

[0084]

[0085] in This represents the raw hyperspectral data collected. This indicates the data obtained after normalization.

[0086] S102, select some prior spectra of targets of interest from the partially acquired hyperspectral images, and normalize these spectra to obtain the prior spectrum d.

[0087] S2, as Figure 2 As shown, the acquired data is subjected to tensor Tucker decomposition and adaptive reconstruction.

[0088] S201, Tucker decomposition of hyperspectral data.

[0089] Hyperspectral target detection against complex backgrounds is one of the major challenges in remote sensing. Spectral information alone is insufficient for effectively detecting pixel or region targets. To fully utilize the three-dimensional spatial structure information of hyperspectral data, a tensor method is employed to represent the data. A hyperspectral image can be represented as a third-order tensor. Where T1, T2, and T3 represent the rows, columns, and bands of the hyperspectral data, respectively.

[0090] Due to various factors (such as sensor shooting angle), the spectral curves of targets against complex backgrounds exhibit certain differences. To obtain more robust features, Tucker decomposition is used to reconstruct the hyperspectral dataset. Tensor It can be approximated as:

[0091]

[0092] in This is called the core tensor, whose elements represent the level of interaction between different components. and The matrix consists of three factors, which can be considered as principal components under each mode. The optimization problem is formulated as follows:

[0093]

[0094] The solution to the above equation can be obtained by solving it in an alternating manner, where each factor matrix is ​​obtained by eigenvalue decomposition when the other two matrices are fixed.

[0095] S202, such as Figure 3 As shown, adaptive principal component selection is performed on different factor matrices after hyperspectral decomposition.

[0096] Generally, Tucker decomposition can be viewed as a higher-order principal component analysis. It provides a simple compression method that retains the most important information while truncating less important information. Through Tucker decomposition, a third-order tensor matrix is ​​decomposed into three factor matrices (U, V, W) and a core tensor. The columns of each factor matrix serve as eigenvectors in the modulus-n (n = 1, 2, 3) mode, sorted in descending order of their corresponding eigenvalues. Larger eigenvalues ​​retain more information, and important information can be obtained by truncating appropriate principal components. Therefore, finding the optimal singular values ​​is a key challenge in high-order principal component extraction.

[0097] In this scenario, each factor matrix corresponds to different eigenvalues, resulting in varying abilities to extract important information. For different factor matrices (U, V, W), how do we determine r? i The number of singular values ​​(i = 1, 2, 3) is crucial. Some studies have directly used the singular value energy ratio method in anomaly detection; however, this method suffers from significant singular value differences, and different principal component selections can lead to substantial image bias. Considering that logarithmic functions can reduce data variability, this invention introduces a logarithmic singular value summation ratio strategy. This method is more robust and achieves better detection performance. The formula for selecting principal components using logarithmic singular value summation is as follows:

[0098]

[0099] Where a i =[a1,a2,...,a s [] is the singular value factor matrix, s is the number of singular values, r is the number of principal components selected, and ε is a constant 1 (to prevent logarithmic loss). i (Biased towards negative infinity). By setting the value of the logarithmic singular value summation ratio η, the corresponding r in different factor matrices can be automatically determined. In this experiment, η is generally taken as 0.2.

[0100] After initially determining the number of principal components, a fine-grained search is performed near the principal components to obtain more robust features and suppress background interference that highlights the target. The principal component with the smallest spectral energy difference from the prior target is selected as the final principal component, as shown in the following formula:

[0101]

[0102] Where E X Represents data X reconstructed with different factor matrices and different numbers of principal components. r+k The energy of the spectrum corresponding to the target location, k = 2, representing the fine search range, t represents the t-th band, T3 represents the band number, E T Let E represent the energy of the prior target spectrum, and let E represent the spectral energy difference. The number of principal components that minimizes the spectral energy difference is selected.

[0103] S203, hyperspectral data reconstruction based on the selected principal components.

[0104] Tucker decomposition provides an effective feature selection method. During reconstruction, by preserving the principal components of different factor matrices, the intrinsic features of the target and background are maintained, improving the separation of the target and background spectra. The reconstructed... and For spectral dimensions, the formula is as follows:

[0105]

[0106] in U r =U(:,1:r1),V r =V(:,1:r2),W r =W(:,1:r3), r i The principal components of different factor matrices.

[0107] S3, as Figure 4 As shown, multiple metrics are used to extract the target separately.

[0108] S301 uses global constraint energy minimization to obtain energy metric information.

[0109] Hyperspectral data unfolded into a two-dimensional matrix is The design of a globally constrained energy-minimizing filter must satisfy the following formula:

[0110]

[0111] Where N is the number of pixels, which is T1×T2. Let represent a pixel, R be the correlation matrix of the sample set, and in this case, the correlation matrix of all pixels in the hyperspectral image. w is the filter, and d is the target spectrum.

[0112] For conditional extremum problems, the value of the filter w can be obtained by using the Lagrange multiplier method. The filter value is as follows:

[0113]

[0114] By applying the CEM operator to the entire hyperspectral image data, the distribution of pixels similar to the known target spectrum d within the entire image can be obtained, thus achieving target detection. The detection formula is as follows:

[0115]

[0116] Where w is the filter for reconstructing the data, d is the target spectrum of the reconstructed data, R is the autocorrelation matrix of the reconstructed data, and x is the spectrum of the pixel to be measured in the reconstructed data.

[0117] S302 uses the local Pearson correlation coefficient to obtain local relevant information.

[0118] The formula for the distance similarity between the prior spectrum and the spectrum to be measured is as follows:

[0119]

[0120] Among them o i Let represent the distance similarity between the prior spectrum and the i-th test spectrum. The mean distance similarity of the four neighbors is as follows:

[0121]

[0122] S303 uses local Euclidean distance to obtain distance information.

[0123] The Pearson correlation coefficient, which represents the similarity between the prior target spectrum and the measured spectrum, is expressed by the following formula.

[0124]

[0125] in T3 represents the Pearson correlation coefficient between the measured spectrum and the prior spectrum, and T3 represents the number of spectral bands. The mean Pearson correlation coefficients for the four-neighbor region are as follows.

[0126]

[0127] Where x (i,j) This represents the spectrum of the i-th pixel to be measured in the fractional domain. The mean of the Pearson correlation coefficients in the four neighborhoods of the fractional domain is given.

[0128] S4, Multi-metric information fusion to obtain the target of interest

[0129] The three information acquisition methods are fused to obtain the target detection result, as shown in the following formula:

[0130]

[0131] S5, Threshold segmentation to separate target from background

[0132] The determination of r can be made by comparing it with a specified threshold Th:

[0133]

[0134] Where 1 indicates that r is the target and 0 indicates that r belongs to the background.

[0135] Results analysis:

[0136] The two datasets tested in this invention were acquired using the GaiaSkymini2 spectral imaging instrument from Shuangli Spectroscopy. Their spectral range is from 400 nm to 1000 nm, with a spatial resolution of 0.14 m and a spectral resolution of 3.5 nm at a distance of 500 m. The background includes bare soil, cement, and shrubs; the targets include camouflaged vehicles; and the prior target spectra used were obtained from a subset of the acquired images. Figure 5 and Figure 6 Figures (a) and (b) show the pseudo-color plot and the truth plot of these two data points, respectively.

[0137] Figure 5 and Figure 6 Figures (c)-(j) respectively show the qualitative detection results of different methods on these two datasets. Figure 5 and Figure 6 As can be seen from (c) to (i), the contrastive methods detect very few target pixels, and some methods can hardly detect any target pixels at all. Although the proposed method has some false alarms, it can detect more target pixels, and the proposed method has better detection performance.

[0138] Figure 7 and Figure 8 The receiver operating characteristic (ROC) curves are shown for different methods on two collected datasets. Figure 7 In the study, when the false alarm probability is 0.1, the proposed method achieves a detection probability of 0.9825, while other methods have detection probabilities below 0.9649, demonstrating a significantly better detection rate than other algorithms. Figure 8 When the false alarm probability is 0.1, the proposed method has a detection probability of 1.0, while the PTA method has the highest detection rate of 0.99. Furthermore, the ROC curve of the proposed method is located in the upper left of the comparison methods in both figures, indicating that the proposed method significantly outperforms the other algorithms in detection performance.

Claims

1. A hyperspectral target detection method based on third-order tensor decomposition and adaptive reconstruction, characterized in that, Includes the following steps: S1, Hyperspectral data preprocessing; The collected hyperspectral data were normalized by maximum and minimum values, and the spectra of the target of interest were extracted from the partially normalized data to construct a priori spectral library. S2, perform Tucker decomposition and adaptive reconstruction on the data; represent the hyperspectral data as a third-order tensor, perform Tucker decomposition on it to obtain a core tensor and three factor matrices; use the logarithmic energy summation method to initially obtain the principal components of different factor matrices, and use the minimization of the energy difference between the prior spectrum and the target spectrum of the test data to further obtain the principal components of different factor matrices; use the obtained fine principal components to reconstruct the hyperspectral data; S3, multiple metric methods are used to extract the target separately; global constraint energy minimization is used to obtain energy metric information, local Pearson correlation coefficient is used to obtain local related information, and local Euclidean distance is used to obtain local distance information; Specifically, it includes the following sub-steps: S301 uses global constraint energy minimization to obtain energy metric information; Hyperspectral data unfolded into a two-dimensional matrix is The design of a globally constrained energy-minimizing filter must satisfy the following formula: （7）； Where N is the number of pixels. , Represents a pixel. This is the correlation matrix of the sample set, which in this case is the correlation matrix of all pixels in the hyperspectral image; For filters, For the target spectrum; For conditional extremum problems, the solution using the Lagrange multiplier method is the filter. The filter values ​​are as follows: （8）； The CEM operator is applied to the entire hyperspectral image data to obtain the spectrum of the known target. The distribution of similar pixels throughout the image is analyzed to achieve target detection; the detection formula is as follows: （9）； in Filters for reconstructing data, To reconstruct the target spectrum of the data, To reconstruct the autocorrelation matrix of the data, To reconstruct the spectrum of the pixels to be measured in the data; S302, local Pearson correlation coefficient is used to obtain local relevant information; The formula for the distance similarity between the prior spectrum and the spectrum to be measured is as follows: （10）； in Let represent the distance similarity between the prior spectrum and the i-th test spectrum. The mean distance similarity of the four neighbors is as follows: （11）； S303 uses local Euclidean distance to obtain distance information; The Pearson correlation coefficient, which represents the similarity between the prior target spectrum and the measured spectrum, is expressed by the following formula: (12)； in The Pearson correlation coefficient represents the relationship between the measured spectrum and the prior spectrum. This indicates the number of spectral bands; the mean of the four-neighbor Pearson correlation coefficients is as follows: (13)； in This represents the spectrum of the i-th pixel to be measured in the fractional domain. The mean of the Pearson correlation coefficients in the four neighborhoods of the fractional domain; S4, fuse multi-metric information to obtain the target of interest; fuse three metric methods to improve the detection rate of the target of interest; The three information acquisition methods are fused to obtain the target detection result, as shown in the following formula: (14)； S5 uses a threshold segmentation method to separate the target from the background; by setting a certain threshold, the target and the background are assigned values ​​of 1 and 0 respectively.

2. The hyperspectral target detection method based on third-order tensor decomposition and adaptive reconstruction according to claim 1, characterized in that, S1 specifically includes the following sub-steps: S101, the acquired data is normalized using the maximum and minimum value method, as shown in the following formula: （1）； in This represents the raw hyperspectral data collected. This represents the data obtained after normalization; S102, Select the prior spectrum of the target of interest from the partially acquired hyperspectral images, and also normalize these spectra to obtain the prior spectrum. .

3. The hyperspectral target detection method based on third-order tensor decomposition and adaptive reconstruction according to claim 2, characterized in that, S2 specifically includes the following sub-steps: S201, Tucker decomposition of hyperspectral data; The three-dimensional spatial structure information of hyperspectral data is represented using tensor methods; a hyperspectral image is represented as a third-order tensor. ,in , and These represent the rows, columns, and bands of hyperspectral data, respectively. The hyperspectral dataset was reconstructed using Tucker decomposition; tensors Represented as: （2）； in This is called the core tensor, whose elements represent the level of interaction between different components; , and Given three factor matrices, considered as principal components under each mode, the optimization problem is formulated as follows: （3）； The solution to the above equation is obtained by solving it in an alternating manner, wherein each factor matrix is ​​obtained by eigenvalue decomposition when the other two matrices are fixed; S202, adaptive principal component selection for different factor matrices after hyperspectral decomposition; Tucker decomposition decomposes a third-order tensor matrix into three factor matrices. , , and a core tensor The columns of each factor matrix serve as the eigenvectors of the modulus-n mode, sorted in descending order of the corresponding eigenvalues, where n is 1, 2, or 3. For different factor matrices , , To determine the number of principal components for different factor matrices The number of elements, i, is 1, 2, or 3. A strategy of selecting principal components using the logarithmic singular value summation ratio is introduced. The formula for selecting principal components using the logarithmic singular value summation is as follows: （4）； in It is a singular value factor matrix. It is the number of singular values. It is the number of principal components selected. It is a constant of 1; by setting the ratio of the sum of logarithmic singular values. The value is automatically determined in different factor matrices. ; After initially determining the number of principal components, a fine search is performed in the vicinity of the principal components; the principal component with the smallest difference from the prior target spectral energy is selected as the final principal component, as shown in the following formula: （5）； in Represents data reconstructed with different factor matrices and different numbers of principal components. The energy of the spectrum at the location corresponding to the target. A value of 2 indicates a more precise search range. Indicates the first band, Indicates the number of bands. This represents the energy of the prior target spectrum. This represents the spectral energy difference, and the number of principal components that minimizes the spectral energy difference is selected. S203, hyperspectral data reconstruction based on the selected principal components; Reconstructed and For spectral dimensions, the formula is as follows: （6）； in , , , , The principal components of different factor matrices.

4. The hyperspectral target detection method based on third-order tensor decomposition and adaptive reconstruction according to claim 1, characterized in that, S5 The determination is made by comparing it with a specified threshold. To determine by comparison: （15）； Where 1 represents It is the target, 0 represents It belongs to the background.

Images