A robust deep nonnegative matrix factorization method for hyperspectral image unmixing

Abstract

This invention relates to the field of image processing and remote sensing analysis technology, and provides a robust deep non-negative matrix factorization method for hyperspectral image unmixing. The method includes: decomposing hyperspectral data into a product of multiple non-negative low-rank matrices using a multi-level non-negative matrix factorization method; representing the similarity and differences of data in each non-negative low-rank matrix based on a dual-graph adversarial learning mechanism; constraining the Gram matrix during the decomposition process using inner product-based structural sparsity regularization; and constructing a comprehensive optimization model to obtain the unmixing results of the hyperspectral data. This invention represents hyperspectral data as multiple non-negative low-rank matrices, and introduces adversarial graph regularization terms, hierarchical sparsity constraints, and truncated activation mechanisms to improve the robustness and expressive power of the model. Finally, it utilizes the alternating direction multiplier method (ADMM) for efficient optimization, enabling the proposed method to accurately extract endmembers and abundance in complex noisy environments, achieving robust hyperspectral image unmixing.

Description

Technical Field

[0001] This invention relates to the field of image processing and remote sensing analysis technology, and more specifically, to a robust deep nonnegative matrix factorization method for hyperspectral image unmixing. Background Technology

[0002] Hyperspectral images (HSI) are widely used in agricultural monitoring, environmental assessment, and mineral exploration due to their high spectral resolution across continuous narrow bands. However, due to the limited spatial resolution of sensors, the problem of "mixed pixels" is common in these images, meaning that a single pixel contains spectral information from multiple different materials. Hyperspectral unmixing (HU) technology has therefore become a prerequisite for hyperspectral data analysis, with its core objective being to estimate endmembers and their corresponding abundance distributions from mixed pixels.

[0003] Currently, linear mixture models (LMMs) are widely used due to their strong physical interpretability and high computational efficiency, and have spurred the development of various typical unmixing methods, including:

[0004] (1) Geometric methods (such as VCA, N-FINDR, etc.) are based on the pure pixel assumption and find endmembers distributed on the data convex hull boundary in the image, but their performance is poor in cases of high mixing or no pure pixels;

[0005] (2) Sparse regression methods (such as SUnSAL and SUnSAL-TV) achieve efficient endmember estimation by using a predefined spectral library and combining L1 or TV regularization constraints, but are limited by the redundancy and high coherence of the library, resulting in high computational cost and sensitivity to noise.

[0006] (3) Statistical methods, especially nonnegative matrix factorization (NMF), avoid the pure pixel assumption by decomposing the observation matrix into nonnegative endmember matrices and abundance matrices, and have good physical interpretability. To overcome the nonconvexity problem of NMF, researchers have further introduced prior constraints such as sparsity (L1, L1 / 2), total variation (TV), and manifold regularization.

[0007] In recent years, Deep Nonnegative Matrix Factorization (DNMF) has gradually become a research hotspot, leveraging the multi-layer feature representation capabilities of deep learning. DNMF, by constructing a multi-layer factorization framework, can effectively extract hierarchical structural information from hyperspectral images, improving the accuracy of unmixing results. Typical works such as MLNMF, SDNMF-TV, and SSRDMF enhance model capabilities by introducing sparsity and spatial regularization. However, existing DNMF methods still face the following key challenges:

[0008] (1) Insufficient ability to maintain spatial structure: Traditional regularization terms are difficult to effectively characterize intra-class continuity and inter-class separation, which limits the model's adaptability to complex boundaries or spatial transition regions;

[0009] (2) Unclear hierarchical sparsity constraints: Existing sparsity mechanisms mostly act on shallow layers and lack in-depth modeling of sparse structures of multi-layer abundance components;

[0010] (3) Poor robustness to noise and outliers: Most methods rely on the F-norm or have no truncation mechanism, making them susceptible to outlier interference.

[0011] (4) Weak cross-layer information fusion mechanism: Although a deep structure has been introduced, there is a lack of effective information feedback and interaction between the front and back layers, which limits the ability to express ambiguity. Summary of the Invention

[0012] In view of this, the present invention proposes a robust deep non-negative matrix factorization method for hyperspectral image unmixing. It adopts a deep non-negative matrix unmixing framework that integrates adversarial graph structure modeling, inner product sparsity constraints and truncation activation mechanisms, so as to comprehensively improve the performance of the model in terms of spatial representation ability, sparse modeling accuracy, robustness and computational efficiency, thereby solving the problems existing in the above-mentioned prior art.

[0013] To achieve the above objectives, this invention proposes a robust deep nonnegative matrix factorization method for hyperspectral image unmixing, comprising:

[0014] The hyperspectral data is decomposed into a product of multiple non-negative low-rank matrices using a multi-level non-negative matrix decomposition method.

[0015] The similarity and difference of data in each layer of non-negative low-rank matrix are represented based on a dual-graph adversarial learning mechanism;

[0016] Structural sparsity regularization based on inner product is used to constrain the Gram matrix in the decomposition process;

[0017] A comprehensive optimization model is constructed, and the unmixing results of hyperspectral data are obtained based on the comprehensive optimization model.

[0018] Furthermore, in the process of decomposing hyperspectral data into a product of multiple non-negative low-rank matrices using a multi-level non-negative matrix factorization method, a nonlinear mapping based on a truncated activation function is performed to enhance the model's expressive power, as detailed below:

[0019]

[0020] in, This indicates the truncation of the nonlinear activation function. This represents the observation matrix, which has B bands and N pixels. Represents the endmember matrix, This represents the abundance matrix of pixels.

[0021] Furthermore, in the process of decomposing hyperspectral data into a product of multiple non-negative low-rank matrices using a multi-level non-negative matrix factorization method, by introducing... The norm redefines the optimization objective, as shown below:

[0022]

[0023] in Norm is defined as , This represents the endmember matrix of each layer. This represents the abundance matrix for each layer.

[0024] Furthermore, the dual-graph adversarial learning mechanism includes:

[0025] Reward maps enhance the consistency of pixel abundance distribution within local neighborhoods;

[0026] Increase the difference between non-neighbor pixels based on the penalty map;

[0027] Construct an objective function based on the reward graph and the penalty graph.

[0028] Furthermore, when pixels are K-nearest neighbors, the reward map constructs the similarity between samples of the same type using the K-nearest neighbor criterion, as shown below:

[0029]

[0030] in, Represents pixels of Neighbor, For temperature parameters, and Each represents two pixels. This represents the 2-norm.

[0031] Furthermore, when pixels are not K-nearest neighbors, the penalty graph constructs connecting edges and assigns weights:

[0032]

[0033] in, Indicates not a pixel of Neighbor, This refers to the temperature parameter.

[0034] Furthermore, the objective function is as follows:

[0035]

[0036] in, , and To balance the parameters, The form representing the trace. Indicates the first The abundance matrix of the layer, The Laplace matrix represents the reward graph. Represents the Laplace matrix of the penalty graph. This represents the transpose of a matrix.

[0037] Furthermore, the inner product-based structural sparsity regularization is used to represent the sum of off-diagonal elements in the Gram matrix, as shown below:

[0038]

[0039] in, It is a matrix of all ones. Indicates the first Column and number The inner product of column abundance vectors This represents the Gram matrix. To represent the transpose of a matrix, The form representing the trace, Indicates the first Abundance matrix of the layer.

[0040] Furthermore, the comprehensive optimization model is as follows:

[0041] in, These represent the parameters for the reward graph, penalty graph, and inner product sparse regularization term, respectively. The form representing the trace, Indicates the first The abundance matrix of the layer, Indicates the first The endmember matrix of the layer. The expression after St represents two constraints on the abundance matrix: the nonnegativity constraint and the sum-to-one constraint.

[0042] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0043] This invention represents observed hyperspectral data as the product of multiple non-negative low-rank matrices, and introduces adversarial graph regularization, hierarchical sparsity constraints, and truncated activation mechanisms to enhance the robustness and expressive power of the model. Specifically, firstly, based on graph structure priors, local similarity graphs and outlier exclusion graphs are constructed, and adversarial graph regularization is designed to enhance the intra-class continuity and inter-class separability of abundance estimation; secondly, sparse regularization based on inner product is introduced into the abundance matrices of each layer, and the discriminativeness and sparsity of abundance are improved by constraining their Gram matrices; thirdly, a truncated activation function is used in the hierarchical iterative update to suppress low-amplitude noise interference and improve the robustness of the model to outliers; finally, the alternating direction multiplier method (ADMM) is used for efficient optimization, enabling the proposed method to accurately extract endmembers and abundance in complex noisy environments and achieve robust hyperspectral image demixing. Attached Figure Description

[0044] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. In the drawings:

[0045] Figure 1 This is a schematic diagram of the overall process of the method proposed in this invention;

[0046] Figure 2 This is a diagram of the deep nonnegative matrix factorization framework for integrating adversarial graph regularization in this invention.

[0047] Figure 3 shows the endmember spectra and synthetic images on the synthetic dataset (SC1) in the embodiment of the present invention, where (a) is the endmember spectrum and (b) is the synthetic image;

[0048] Figure 4 shows the endmember spectra and synthetic images on the synthetic dataset (SC2) in this embodiment of the invention, where (a) is the endmember spectrum and (b) is the synthetic image;

[0049] Figure 5 The abundance map of all algorithms in SC1 in the embodiments of this invention;

[0050] Figure 6 shows the convergence curve of the algorithm proposed in this invention, where (a) is the objective function value, (b) is the reconstruction residual value, and (c) is the endmember residual and abundance residual.

[0051] Figure 7 The abundance maps of all algorithms in SC2 in the embodiments of this invention are shown.

[0052] Figure 8 shows a comparison of the endmember curves extracted by different algorithms in the embodiments of the present invention on the Samson dataset, where (a) represents soil, (b) represents trees, and (c) represents water.

[0053] Figure 9Abundance maps estimated on the Samson dataset by different algorithms in embodiments of the present invention;

[0054] Figure 10 shows a comparison of endmember curves extracted by different algorithms in the embodiments of the present invention on the Jasper dataset, where (a) represents trees, (b) represents water, (c) represents soil, and (d) represents roads.

[0055] Figure 11 The above are abundance maps of different algorithms in the embodiments of the present invention on the Jasper dataset. Detailed Implementation

[0056] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the disclosure to those skilled in the art. It should be noted that, unless otherwise specified, the embodiments and features described herein can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0057] This embodiment proposes a robust deep nonnegative matrix factorization method for hyperspectral image demixing, such as... Figure 1 As shown, it includes:

[0058] The hyperspectral data is decomposed into a product of multiple non-negative low-rank matrices using a multi-level non-negative matrix decomposition method.

[0059] The similarity and difference of data in each layer of non-negative low-rank matrix are represented based on a dual-graph adversarial learning mechanism;

[0060] Structural sparsity regularization based on inner product is used to constrain the Gram matrix in the decomposition process;

[0061] A comprehensive optimization model is constructed, and the unmixing results of hyperspectral data are obtained based on the comprehensive optimization model.

[0062] The technical solution of this embodiment will be described in detail based on the above content, as follows:

[0063] (1) Robust deep nonnegative matrix factorization with truncated activation function

[0064] Traditional nonnegative matrix factorization (NMF) relies on linear decomposition and nonnegativity constraints to perform matrix factorization on data. However, in practical hyperspectral unmixing tasks, the abundance matrix is ​​often disturbed by noise and outliers, causing some elements to deviate from their physical feasible region, thus affecting the unmixing accuracy and model stability. To address this, this embodiment introduces a truncated activation function (such as a ReLU variant). By truncating negative values ​​or small minimum values ​​to zero, a nonlinear mapping is achieved to enhance the model's expressive power while suppressing the interference of outliers on the optimization process. Furthermore, this strategy can improve the stability and physical feasibility of abundance estimation while maintaining data sparsity. The mathematical formalization is as follows:

[0065]

[0066] in, This indicates the truncation of the nonlinear activation function. This represents the observation matrix, which has B bands and N pixels. Represents the endmember matrix, This represents the abundance matrix of pixels.

[0067] Traditional Non-Multi-Factor (NMF) typically employs a loss function based on the F-norm. However, the F-norm exhibits significant instability when dealing with noise and outliers. This is fundamentally because the error term is usually represented as the sum of squared Euclidean norms of the residuals. When extreme values ​​exist, the squared terms significantly amplify the error, causing a small number of outliers to have a disproportionate impact on the decomposition results, thereby reducing the model's stability and unmixing accuracy. To overcome this problem, this embodiment proposes a robust NMF method by introducing a more robust... The norm redefines the optimization objective, effectively reducing the interference caused by outliers.

[0068]

[0069] In norm selection, Norm and The norms are significantly different. For a given matrix , Norm is defined as ,and The norm is then .because Norms avoid the calculation of squared errors and are more effective than standard deviations when dealing with noisy data. Norms demonstrate greater effectiveness.

[0070] Activation function subject to truncation and Inspired by the theoretical advantages of norms in improving NMF performance, the deep NMF problem is established as follows:

[0071]

[0072] in Norm is defined as , This represents the endmember matrix of each layer. This represents the abundance matrix for each layer.

[0073] (2) Adversarial graph regularization

[0074] Graph theory and manifold learning theory show that constructing nearest-neighbor graphs can effectively preserve the local geometric structure of data. However, existing graph regularization methods (such as Laplace regularization) often over-rely on the local manifold assumption, focusing only on the similarity between samples and ignoring the differences between them. This limitation leads to an overly strong continuity in the abundance matrix space, thereby damaging detailed information. To address this, this embodiment proposes a dual-graph adversarial learning mechanism, which effectively optimizes the intra-class compactness and inter-class separability of the abundance matrix through the dynamic balance between the reward graph and the penalty graph, overcoming the shortcomings of traditional graph regularization methods (such as Laplace regularization). Figure 2 (As shown).

[0075] Reward maps aim to enhance the consistency of pixel abundance distribution within local neighborhoods. Specifically, given a data matrix... If pixels yes The K-Nearest Neighbors (KNN) criterion is used to construct similarity connections between samples of the same type:

[0076]

[0077] in, Represents pixels of Neighbor, Temperature is a parameter that controls the similarity decay rate. This is based on the Laplace matrix. , For degree matrix, The reward map constrains the abundance vectors of pixels of the same class to be as close as possible in the manifold space, suppressing loose intra-class distributions caused by noise or gradual changes in mixing ratios. and Each represents two pixels. This represents the 2-norm.

[0078] Penalty maps are used to enhance the dissimilarity between non-neighboring pixels, preventing potential overlap of out-of-class samples in the abundance space. If pixels... no If the K nearest neighbors are found, then connecting edges are constructed and weights are assigned:

[0079]

[0080] Wherein, the corresponding Laplace matrix Its regularization term improves inter-class discriminability by maximizing the abundance difference between non-neighborhood samples. Therefore, by jointly optimizing the Laplace constraints of the reward graph and the penalty graph, the objective function in each layer of the deep NMF model is defined as follows:

[0081]

[0082] in, , and To balance parameters and control the equilibrium between intra-class compactness and inter-class separation, the first term minimizes the abundance difference between samples of the same class, while the second term maximizes the abundance distance between samples of different classes, forming an adversarial optimization. The form representing the trace. Indicates the first The abundance matrix of the layer, The Laplace matrix represents the reward graph. Represents the Laplace matrix of the penalty graph. This represents the transpose of a matrix.

[0083] (3) Inner product sparsity regularization

[0084] From a statistical perspective, each pixel in a hyperspectral image (HSI) is typically composed of a proportional blend of the spectra of multiple land cover materials, i.e., a linear combination of multiple endmembers. However, in an instantaneous field of view (IFOV), only a small fraction of the endmembers actually participate in the blending, making the column vectors of the abundance matrix naturally sparse in most cases. Introducing sparsity constraints not only helps generate simpler representations, highlighting the main land cover components and suppressing the interference of minor or irrelevant features, but also improves the robustness and discriminative ability of the model. In NMF-related research, various sparsity regularization techniques based on L0, L1, and Lp norms have been widely used. These methods each have their advantages but also face their own challenges. For example, L0 regularization can induce sparsity more strongly, but the solution process is complex and belongs to the NP-hard problem; while L1 regularization is more efficient in optimization, it is relatively mild in terms of sparsity control. To overcome the limitations of traditional element-level sparsity constraints, this embodiment introduces a structural sparsity regularization based on inner product in the proposed deep NMF framework, which is rooted in the concept of inner product.

[0085] Specifically, in the deep NMF framework, the first Layer abundance matrix ,in Gram matrix This can be expressed as:

[0086]

[0087] in Indicates the first Column and number The inner product of column abundance vectors. Off-diagonal elements of the Gram matrix. This reflects the cooperative or competitive relationship between different endmembers during the mixing process. It is easy to see that the expression... Corresponding to the Gram matrix The sum of the diagonal elements in the middle and lower bounds. Simply put:

[0088]

[0089] in It is an N*N matrix of all ones, if and only if or Approaching zero, inner product It approaches zero. To represent the transpose of a matrix, The form representing the trace, Indicates the first The abundance matrix of the layer. Therefore, this optimization process can induce sparsity in the inter-column dimension of the abundance matrix, suppressing the global participation of redundant endmembers.

[0090] (4) Final Model

[0091] Considering the preceding discussion, the model's structure consists of three main parts: (1) robust deep nonnegative matrix factorization with truncated activation functions; (2) exploring adversarial graph problems; and (3) learning inner product sparsity regularization. Based on this, the optimization problem of the model is formulated as follows:

[0092]

[0093] The first term is a robust deep nonnegative matrix factorization reconstruction term with a truncated activation function; the second and third terms are adversarial graph and inner product sparsity regularization terms, respectively. Indicates the number of floors. It is an improved nonlinear activation function. , , and represents the parameters corresponding to the reward graph, penalty graph, and abundance inner product sparsity regularization, respectively. The form representing the trace, Indicates the first The abundance matrix of the layer, Indicates the first The endmember matrix of the layer. The expression after St represents two constraints on the abundance matrix: the nonnegativity constraint and the sum-to-one constraint.

[0094] In summary, this embodiment constructs a multi-layer non-negative matrix factorization structure to decompose the observed data into the product of multiple non-negative low-rank matrices. During this process, an adversarial graph regularization term combining local similarity graphs and outlier exclusion graphs is introduced to enhance the spatial structure representation of abundance estimation. Simultaneously, sparsity constraints based on inner product are added to each layer of abundance matrices to guide more discriminative components. Furthermore, an activation function with a truncation mechanism is employed to improve sparsity and noise resistance. Finally, the model is optimized using the Alternating Directional Multiplier Method (ADMM) to obtain accurate and robust hyperspectral unmixing results.

[0095] To comprehensively and rigorously verify the effectiveness of the proposed method, this embodiment conducts a series of systematic experiments on two synthetic datasets and four publicly available real datasets. For quantitative evaluation, spectral angular distance (SAD) and root mean square error (RMSE) are used. Their definitions are as follows:

[0096]

[0097]

[0098] in and . respectively represent the first Each estimated endmember matrix and the corresponding true endmembers; and They represent the first Estimated abundance and actual abundance.

[0099] (1) Simulated dataset experiment

[0100] The data generation process comprises two core steps: endmember selection and abundance estimation. To verify the effectiveness of this method in hyperspectral unmixing tasks, this embodiment conducts experiments on simulated SC1 and SC2.

[0101] For the simulated dataset (SC1), six spectra were first randomly selected from the U.S. Geological Survey (USGS) Digital Spectral Library, as shown in Figure 3, for use in the following experiments. The simulated image has a spatial resolution of 57*57 pixels and a spectral dimension of 188 bands.

[0102] For the simulated data cube 2 (SC2), five spectra were first randomly selected from the USGS digital spectral library, and then the endmembers and abundances were synthesized into simulated hyperspectral data according to the LMM, as shown in Figure 4. This simulated image has 75 × 75 pixels and 188 bands.

[0103] This experiment compared the SAD and RMSE indices of various algorithms under different noise scenarios with signal-to-noise ratios (SNR) of 20, 30, and 40 dB, as shown in Table 1. The experimental results show that the proposed method achieves the lowest SAD and RMSE under all three noise intensities, significantly outperforming existing comparative methods and verifying its stability and outlier resistance under noise interference. It should be noted that the comparative algorithm FaSUn, based on a sparse regression framework, does not require endmember matrix estimation and therefore cannot calculate the SAD index; thus, it is not presented in Table 1. Figure 3 shows the abundance plots of six endmembers using different algorithms under a signal-to-noise ratio of 30 dB. Figure 5 As can be clearly seen, the method in this embodiment can always correctly provide an estimate of the distribution of ground features, and the obtained abundance map is smooth and clear, and highly consistent with the actual abundance.

[0104] Table 1

[0105] 20dB 0.1349 0.0851 0.0714 0.1135 0.0725 0.1079 0.0927 0.0539 / 0.0397 30 dB 0.1273 0.0737 0.0694 0.0801 0.0518 0.0766 0.0625 0.0358 / 0.0267 40 dB 0.1058 0.0702 0.0404 0.0614 0.0581 0.0737 0.0248 0.0212 / 0.0166

[0106] Table 2

[0107] 20dB 0.1187 0.9849 0.0899 0.1022 0.0691 0.0966 0.0976 0.0590 0.0996 0.0446 30 dB 0.1088 0.0910 0.0884 0.0962 0.0427 0.0946 0.0808 0.0557 0.0428 0.0344 40 dB 0.0915 0.0713 0.0487 0.0639 0.0410 0.0849 0.0493 0.0298 0.0275 0.0204

[0108] This experiment analyzed the convergence of the proposed algorithm. The number of endmembers was set to 6, and the signal-to-noise ratio (SNR) was set to 30 dB. Figures 6(a) and (b) show the curves of the objective function value and the main residual term, respectively. It can be seen that the objective function value decreases rapidly after the first few iterations and eventually converges to a stable value; the main residual term also shows a gradual decreasing trend, consistent with the expected results. In addition, Figure 6(c) shows the iterative residual curves of endmembers and abundance estimation. As can be seen from the figure, with the increase of the number of iterations, the residuals of these two matrices gradually approach zero, further verifying the good convergence of the algorithm.

[0109] (2) Simulated dataset 2

[0110] This experimental group systematically evaluated the demixing performance of the algorithm under different noise intensities on SC2, with the signal-to-noise ratio (SNR) set to 20, 30, and 40 dB, respectively. All comparison methods used the same initialization conditions and number of endmembers to ensure fairness. As shown in Table 3, in terms of SAD index, the proposed algorithm achieved the best demixing effect. In terms of abundance inversion (Table 4), the proposed algorithm outperformed the comparison algorithms in most cases. Figure 7The visualization results of the 30dB abundance map further confirm that the algorithm can better preserve the fine spatial structure features in the transition zone of land cover boundaries. These quantitative and qualitative results together show that the algorithm proposed in this embodiment achieves synergistic optimization of endmember spectral separation accuracy and abundance spatial resolution in complex noise scenarios.

[0111] Table 3

[0112] 20dB 0.0205 0.0284 0.0659 0.0644 0.0523 0.0369 0.0253 0.0277 / 0.0189 30 dB 0.0068 0.0272 0.0624 0.0367 0.0423 0.0353 0.0191 0.0058 / 0.0057 40 dB 0.0038 0.0254 0.0619 0.0123 0.0349 0.0109 0.0058 0.0020 / 0.0018

[0113] Table 4

[0114] 20dB 0.0284 0.0300 0.0512 0.0296 0.0388 0.0357 0.0289 0.1005 0.1090 0.0269 30 dB 0.0184 0.0217 0.0440 0.0231 0.0316 0.0218 0.0183 0.0807 0.1012 0.0176 40 dB 0.0096 0.0158 0.0436 0.0165 0.0111 0.0076 0.0094 0.0809 0.1005 0.0065

[0115] Samson Real Dataset

[0116] This experiment validates the algorithm's performance using the Samson hyperspectral dataset, which contains a 95×95 pixel spatial distribution and 156 spectral bands. The dataset's land cover is primarily composed of three typical materials: trees, soil, and water. As shown in Figure 8, the endmember spectral features extracted by the algorithm in this paper exhibit a high degree of consistency with the reference spectrum, intuitively verifying the accuracy of the endmember estimation. Figure 9 Table 5 shows the abundance maps estimated by different algorithms. To further verify the effectiveness of the proposed algorithm, Table 5 lists the SAD values ​​of different algorithms on the Samson dataset. It can be seen that the proposed method exhibits superior performance for both trees and water. More importantly, the proposed algorithm achieves the best overall performance, fully demonstrating its advantage over other methods in hyperspectral unmixing.

[0117] Table 5

[0118] Tree 0.0207 0.0359 0.0316 0.0377 0.0301 0.0307 0.0357 0.0293 / 0.0077 Soil 0.0495 0.0611 0.0559 0.0632 0.0556 0.0549 0.0608 0.0466 / 0.0394 Water 0.1299 0.1503 0.1409 0.1787 0.1406 0.1474 0.1822 0.1235 / 0.1224 Mean 0.0667 0.0824 0.0761 0.0932 0.0754 0.0777 0.0929 0.0665 / 0.0565

[0119] (4) Jasper Ridge real dataset

[0120] This experiment selected a 100 × 100 pixel sub-region of the Jasper dataset as the research object and reserved 198 bands for the experiment. Within this sub-region, we assumed it contained four main land cover endmembers: trees, water, soil, and roads. To evaluate the spectral decoupling capability of the proposed method, the endmember spectra of all comparative algorithms were compared with reference endmembers in the USGS spectral library (as shown in Figure 10). The results show that the endmembers estimated by the proposed algorithm are highly consistent with the reference endmembers in spectral features, intuitively verifying the effectiveness of the proposed method in the spectral unmixing task. In addition, the abundance distribution map (Figure 11) further reveals the spatial resolution capability of the algorithm. Table 6 compares the spectral angular distance (SAD) of different methods on the Jasper dataset. The results show that the proposed method achieves the lowest SAD values ​​for most land cover categories, and its average SAD is also better than other comparative methods.

[0121] Table 6

[0122] Tree 0.4889 0.4671 0.1073 0.1636 0.0849 0.4585 0.4642 0.1592 / 0.0774 Water 0.1016 0.0832 0.4267 0.0764 0.0901 0.0650 0.0603 0.7027 / 0.0488 Soil 0.1902 0.0715 0.0641 0.1537 0.0560 0.0700 0.0846 0.1147 / 0.1158 Road 0.2492 0.0866 0.0676 0.3953 0.4473 0.1189 0.0829 0.2185 / 0.0800 Mean 0.2575 0.1771 0.1664 0.1973 0.1696 0.1781 0.1730 0.2988 / 0.0830

[0123] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A robust deep nonnegative matrix factorization method for hyperspectral image unmixing, characterized in that, include: The hyperspectral data is decomposed into a product of multiple non-negative low-rank matrices using a multi-level non-negative matrix decomposition method. The similarity and difference of data in each layer of non-negative low-rank matrix are represented based on a dual-graph adversarial learning mechanism; Structural sparsity regularization based on inner product is used to constrain the Gram matrix in the decomposition process; A comprehensive optimization model is constructed, and the unmixing results of hyperspectral data are obtained based on the comprehensive optimization model. In the process of decomposing hyperspectral data into a product of multiple non-negative low-rank matrices using a multi-level non-negative matrix factorization method, a nonlinear mapping based on a truncated activation function is performed to enhance the model's expressive power, as detailed below: ， in, This indicates the truncation of the nonlinear activation function. This represents the observation matrix, which has B bands and N pixels. Represents the endmember matrix, A matrix representing the abundance of pixels; In the process of decomposing hyperspectral data into a product of multiple non-negative low-rank matrices using a multi-level non-negative matrix factorization method, the following steps are taken: The norm redefines the optimization objective, as shown below: ， in Norm is defined as , This represents the endmember matrix of each layer. This represents the abundance matrix for each layer; The inner product-based structural sparse regularization is used to represent the sum of off-diagonal elements in the Gram matrix, as shown below: ， in, It is a matrix of all ones. Indicates the first Column and number The inner product of column abundance vectors Represents the Gram matrix, Represents the transpose of a matrix. The form representing the trace, Indicates the first The abundance matrix of the layer; The comprehensive optimization model is shown below: ， ， in, represent the parameters of the reward graph, penalty graph, and inner product sparse regularization term, respectively. The form representing the trace, Indicates the first The abundance matrix of the layer, Indicates the first The endmember matrix of the layer, after St, represents two constraints on the abundance matrix: the non-negativity constraint and the sum-to-one constraint.

2. The robust deep nonnegative matrix factorization method for hyperspectral image unmixing according to claim 1, characterized in that, The dual-graph adversarial learning mechanism includes: Reward maps enhance the consistency of pixel abundance distribution within local neighborhoods; Increase the difference between non-neighbor pixels based on the penalty map; Construct an objective function based on the reward graph and the penalty graph.

3. The robust deep nonnegative matrix factorization method for hyperspectral image unmixing according to claim 2, characterized in that, When pixels are K-nearest neighbors, the reward map constructs the similarity between samples of the same type using the K-nearest neighbor criterion, as shown below: ， in, Represents pixels of Neighbor, For temperature parameters, and Each represents two pixels. It represents the 2-norm.

4. The robust deep nonnegative matrix factorization method for hyperspectral image unmixing according to claim 2, characterized in that, When pixels are not K-nearest neighbors, the penalty graph constructs connecting edges and assigns weights: ， in, Indicates not a pixel of Neighbor, This refers to the temperature parameter.

5. The robust deep nonnegative matrix factorization method for hyperspectral image unmixing according to claim 2, characterized in that, The objective function is as follows: ， in, , and To balance the parameters, The form representing the trace, Indicates the first The abundance matrix of the layer, The Laplace matrix represents the reward graph. Represents the Laplace matrix of the penalty graph. This represents the transpose of a matrix.

Images