A hyperspectral image unmixing method based on graph wavelet transform convolution network

Abstract

The present application relates to a hyperspectral image unmixing method based on graph wavelet transform convolution network, belonging to the technical field of hyperspectral image unmixing. The method comprises: using a Mexican Hat graph wavelet filter to perform frequency domain decomposition on the undirected graph of the original hyperspectral image, obtaining low-frequency components and high-frequency components and inputting them into a parallel double-branch feature encoder network for feature learning and extraction and adaptive recalibration, obtaining enhanced low-frequency features and enhanced high-frequency features and performing element-by-element addition fusion, obtaining multi-frequency comprehensive features and inputting them into an endmember constraint and reconstruction module for abundance estimation, thereby obtaining the reconstructed hyperspectral image and comparing it with the original hyperspectral image, and constructing and optimizing a multi-dimensional joint loss function to obtain a hyperspectral unmixing model for hyperspectral image unmixing. The present application aims to solve the technical problem that the existing technology cannot effectively distinguish the mixed characteristics of high-frequency boundary regions and low-frequency homogeneous regions, resulting in blurred boundaries and spectral distortion.

Description

Technical Field

[0001] This invention relates to a hyperspectral image demixing method based on graph wavelet transform convolutional networks, belonging to the field of hyperspectral image demixing technology. Background Technology

[0002] Hyperspectral remote sensing technology integrates imaging and spectral detection capabilities to acquire the spatial distribution and continuous spectral characteristics of ground objects. However, due to limitations in sensor spatial resolution and the interaction between the sensor and complex surface scenes, pixel-level data commonly exhibits spectral mixing, meaning that a single pixel contains spectral information from multiple ground objects. Hyperspectral demixing is a key technology for addressing the problem of mixed pixels. Its core objective is to estimate the spectral characteristics and corresponding proportion coefficients (abundance) of the basic constituent substances (endmembers) in each mixed pixel.

[0003] In recent years, the continuous advancement of deep learning (DL) technology has brought significant changes to the field of remote sensing, and has also provided new ideas for hyperspectral unmixing. Currently, unmixing methods built upon deep learning are gradually becoming the core mainstream technology for addressing mixed pixel problems in hyperspectral remote sensing. Hong et al. proposed the Endmember-Guided Unmixing Network (EGU-Net), which employs a two-stream Siamese network structure, with one branch processing mixed pixels and the other branch guided by clean endmember spectra extracted from the image. Han et al. proposed the Deep Semi-Siamese Network (Deep HSNet), which effectively integrates endmember information obtained from multiple endmember extraction algorithms by introducing an auxiliary subnetwork, and uses this to guide the learning process of the main unmixing network. Rasti et al. proposed a hyperspectral unmixing method based on deep image priors (UnDIP), which uses deep image priors and a convolutional neural network to combine extracted endmembers and observational data to estimate abundance. Hyperspectral unmixing research has evolved from single spectral feature extraction to spatial-spectral co-modeling, demonstrating that the diversity of feature representations plays a crucial role in improving the performance of deep learning unmixing.

[0004] However, existing methods, such as multi-scale structures or multiple attention mechanisms, are limited to operations within the original spatial-spectral domain and fail to effectively distinguish the essential differences in mixing mechanisms and noise sensitivity between high-frequency boundary regions and low-frequency homogeneous regions in images, leading to mutual interference between features. Han et al. proposed a multimodal hyperspectral unmixing network called MUNet, which introduces LiDAR data to help improve unmixing performance, but it relies on external sensors and is difficult to acquire synchronously, limiting its practicality. Considering the significant differences in the difficulty of mining different frequency components and their mixing characteristics in hyperspectral data, relying solely on single-domain features is insufficient to capture discriminative information. Therefore, it is urgent to construct a physically driven multi-scale representation system through multi-dimensional feature expansion in the frequency domain and other dimensions to synergistically optimize unmixing performance and enhance the model's adaptability to mixed scenes. Summary of the Invention

[0005] The purpose of this invention is to provide a hyperspectral image unmixing method based on graph wavelet transform convolutional networks, aiming to solve the following problems existing in the prior art: First, it extracts features only in the spatial domain, which cannot effectively distinguish the mixing characteristics of high-frequency boundary regions and low-frequency homogeneous regions, resulting in blurred boundaries and spectral distortion in the unmixing results; second, it has insufficient ability to represent irregular spatial structures; and third, it relies on external data, which limits its practicality.

[0006] To achieve the above objectives, the technical solution of this invention is: a hyperspectral image demixing method based on a graph wavelet transform convolutional network. This method first models the hyperspectral image as an undirected graph structure, and uses graph wavelet transform to extend the data from the spatial spectral domain to the frequency domain, decomposing it into low-frequency and high-frequency components with clear physical meaning. Then, a parallel dual-branch convolutional encoder is used to extract specialized features from the high and low frequency information respectively, and a channel attention mechanism is introduced to adaptively recalibrate the features. The dual-path features are then fused and input into an endmember constraint and reconstruction module. The network is jointly trained using a combined loss function, ultimately outputting high-precision endmember spectra and abundance maps. The method includes the following steps:

[0007] Step 1: Construct an undirected graph of the original hyperspectral image, calculate connection weights based on the spectral similarity and spatial distance between pixels and construct an adjacency matrix, calculate the normalized graph Laplacian matrix based on the adjacency matrix, and use a Mexican Hat graph wavelet filter to perform frequency domain decomposition on the undirected graph of the original hyperspectral image to obtain low-frequency and high-frequency components.

[0008] Step 2: Input the low-frequency component and the high-frequency component into a parallel dual-branch feature encoder network to obtain enhanced low-frequency features and enhanced high-frequency features. The parallel dual-branch feature encoder network includes a low-frequency branch and a high-frequency branch. The low-frequency branch performs feature learning and extraction on the low-frequency component to obtain initial low-frequency features. Then, through the channel attention mechanism at the end of the low-frequency branch, the initial low-frequency features are adaptively recalibrated in terms of channel dimension to obtain enhanced low-frequency features. The high-frequency branch performs feature learning and extraction on the high-frequency component to obtain initial high-frequency features. Then, through the channel attention mechanism at the end of the high-frequency branch, the initial high-frequency features are adaptively recalibrated in terms of channel dimension to obtain enhanced high-frequency features.

[0009] Step 3: Add and fuse the enhanced low-frequency features and the enhanced high-frequency features element by element to obtain multi-frequency comprehensive features;

[0010] Step 4: Input the multi-frequency integrated features into the endmember constraint and reconstruction module to obtain the reconstructed hyperspectral image; wherein, the endmember constraint and reconstruction module includes an abundance constraint estimation submodule and a hyperspectral image reconstruction submodule. The abundance constraint estimation submodule performs channel dimension mapping on the multi-frequency integrated features and applies abundance non-negativity constraints and abundance sum-to-one constraints to obtain an abundance matrix. The hyperspectral image reconstruction submodule uses the kernel weights of an unbiased 1×1 convolutional layer as the endmember matrix and combines it with the abundance matrix to perform hyperspectral image reconstruction to obtain the reconstructed hyperspectral image;

[0011] Step 5: Compare the reconstructed hyperspectral image with the original hyperspectral image, and construct a multi-dimensional joint loss function. By minimizing the multi-dimensional joint loss function, a hyperspectral unmixing model is obtained. The hyperspectral image to be processed is input into the hyperspectral unmixing model to obtain the hyperspectral image unmixing result.

[0012] Optionally, Step 1 specifically includes:

[0013] Step 1.1: Construct an undirected graph from the original hyperspectral image ,in, Represents the set of vertices in an undirected graph, where each pixel is a node. edge set This represents the local correlation between pixels, any two pixels and Connection weights The expression is:

[0014]

[0015] In the formula, For pixels spectral vector, For pixels spectral vector, For pixels spatial coordinates, For pixels spatial coordinates, To control the parameters of the spectral similarity scale, Parameters for controlling spatial distance scale;

[0016] Step 1.2: Construct the adjacency matrix , The total number of pixels in the original hyperspectral image, based on the adjacency matrix. Define the degree matrix , Construct a function for a diagonal matrix. The weighted degree of pixel i is used to calculate the normalized graph Laplacian matrix. The expression is:

[0017]

[0018] In the formula, It is the identity matrix;

[0019] Step 1.3: The Mexican Hat function is used as the graph wavelet filter, and its frequency domain expression is as follows:

[0020]

[0021] In the formula, This is the frequency domain response function of the Mexican Hat plot wavelet filter. These are the eigenvalues ​​of the graph Laplacian matrix corresponding to the frequency of the graph signal. This is a scaling parameter used to control the center frequency and bandwidth of the filter;

[0022] Step 1.4: Define each spectral band The image signal is After wavelet filtering of the Mexican Hat diagram, the spectral bands are obtained. The high-frequency components are expressed as:

[0023]

[0024] In the formula, For the first The high-frequency component map signal corresponding to each spectral band. For Mexican Hat plot wavelet filter operators, For the normalized graph Laplace matrix eigenvector matrix, and This is represented as eigenvalue decomposition. For the normalized graph Laplace matrix The eigenvalue diagonal matrix, Represented as a transpose matrix, These are the filter response values ​​corresponding to the eigenvalues ​​of the graph Laplacian matrix. For the normalized graph Laplace matrix eigenvalues;

[0025] Spectral bands are obtained through a complementary approach. low-frequency components The expression is:

[0026]

[0027] Reconstruct all band results to obtain the low-frequency component. With high frequency components ,in, This represents the total number of bands in the original hyperspectral image. The height of the hyperspectral image, The width of the original hyperspectral image.

[0028] Optionally, Step 2 specifically includes:

[0029] Step 2.1: Construct a parallel dual-branch feature encoder network, which includes a low-frequency branch and a high-frequency branch. The parameters of the low-frequency branch and the high-frequency branch are completely independent and do not share. The low-frequency branch uses three stacked 3×3 convolutional blocks with large receptive fields containing batch normalization and LeakyReLU activation functions. The high-frequency branch uses three stacked residual 3×3 convolutional blocks containing batch normalization and LeakyReLU activation functions.

[0030] Step 2.2: Introduce a global average pooling layer (GAP) at the end of both the low-frequency and high-frequency branches to compress the spatial dimension to a one-dimensional vector;

[0031] Step 2.3: In the low-frequency branch, the low-frequency components Initial low-frequency features are extracted using three convolutional blocks. In the high-frequency branch, the high-frequency components Initial high-frequency features are extracted using three convolutional blocks. Both feature weights and adaptive recalibration are calculated using global average pooling and channel attention mechanisms, expressed as follows:

[0032]

[0033]

[0034]

[0035]

[0036] In the formula, This represents the global feature vector of the low-frequency branch. This represents the global feature vector of the high-frequency branch. This is the global average pooling function. This is the channel attention weight vector for the low-frequency branch. Here is the channel attention weight vector for the high-frequency branch. It is the Sigmoid activation function. It is a linear rectified activation function. , Here is the learnable weight matrix for the channel attention module. To enhance the low-frequency characteristics, For the enhanced high-frequency features, This represents broadcast multiplication along the channel dimension.

[0037] Optionally, Step 4 specifically includes:

[0038] Step 4.1: In the abundance-constrained estimation submodule, integrate multi-frequency features. The number of input-to-output channels is equal to the total number of endpoints. The abundance matrix is ​​obtained after processing a 1×1 convolutional layer with the Softmax activation function. The expression is:

[0039]

[0040] In the formula, This is a 1×1 convolution operation;

[0041] Step 4.2: In the hyperspectral image reconstruction submodule, an unbiased 1×1 convolutional layer is used as the decoder, and the kernel weights are used as the estimated endmember matrix. Thus, the reconstructed hyperspectral image is obtained. .

[0042] Optionally, the multi-dimensional joint loss function includes spectral angular distance loss, mean squared error loss, and total variation regularization loss, expressed as:

[0043]

[0044] in, For multi-dimensional joint loss function, For spectral angular distance loss, For mean square error loss, The loss is the regularization loss of the total variation. , To balance the hyperparameters of each loss.

[0045] The beneficial effects of this invention are:

[0046] (1) Based on the multi-domain feature fusion mechanism of graph wavelet transform, this invention combines the spatial domain, spectral domain and graph frequency domain to collaboratively construct a multi-scale representation with clear physical meaning, which significantly improves the adaptability to complex spectral changes.

[0047] (2) The present invention uses a dual-branch structure to process low-frequency and high-frequency features respectively, avoiding the problems of introducing high-frequency noise interference in uniform regions and weakening low-frequency continuity at the boundary of a single network.

[0048] (3) This invention introduces a channel attention feature fusion strategy to achieve semantic-guided optimization of feature fusion, which effectively solves the problems of boundary blurring and spectral distortion when the mixed pixel is resolved in traditional methods. It exhibits strong noise robustness and leading demixing accuracy in both simulated and real datasets. Attached Figure Description

[0049] Figure 1 This is a diagram of the overall architecture of the present invention;

[0050] Figure 2 This is a comparison chart of abundance maps obtained by different unmixing methods on a simulated dataset, according to embodiments of the present invention.

[0051] Figure 3 This is a comparison chart of abundance maps obtained by different unmixing methods on the Moffett dataset according to embodiments of the present invention;

[0052] Figure 4 This is a comparison chart of abundance maps obtained by different unmixing methods on the Houston dataset according to embodiments of the present invention;

[0053] Figure 5 This is a comparison chart of abundance maps obtained by different unmixing methods on the Apex dataset according to embodiments of the present invention. Detailed Implementation

[0054] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0055] Example 1: As Figure 1 As shown, a hyperspectral image demixing method based on graph wavelet transform convolutional networks (GWCNet) includes the following steps:

[0056] Step 1: Construct an undirected graph of the original hyperspectral image, calculate connection weights based on spectral similarity and spatial distance between pixels and construct an adjacency matrix, calculate the normalized graph Laplacian matrix based on the adjacency matrix, and use a Mexican Hat graph wavelet filter to perform frequency domain decomposition on the undirected graph of the original hyperspectral image to automatically decouple the spatial-spectral correlations at different scales in the original image signal, and obtain low-frequency components that characterize the global smoothness characteristics inside similar land features and high-frequency components that contain abrupt changes in land feature boundaries, textures and small target details;

[0057] Step 1.1: Construct an undirected graph from the original hyperspectral image ,in, Represents the set of vertices in an undirected graph, where each pixel is a node. edge set This represents the local correlation between pixels, any two pixels and Connection weights The expression is:

[0058]

[0059] In the formula, For pixels spectral vector, For pixels spectral vector, For pixels spatial coordinates, For pixels spatial coordinates, To control the parameters of the spectral similarity scale, Parameters for controlling spatial distance scale;

[0060] Step 1.2: Construct the adjacency matrix , It is a symmetric nonnegative matrix, reflecting the content-oriented local correlation between pixels, where, The total number of pixels in the original hyperspectral image, i.e., the total number of nodes in the undirected graph, is based on the adjacency matrix. Define the degree matrix , Construct a function for a diagonal matrix. The weighted degree of pixel i is used to calculate the normalized graph Laplacian matrix. The expression is:

[0061]

[0062] In the formula, It is the identity matrix;

[0063] Step 1.3: The Mexican Hat function is used as the graph wavelet filter, and its frequency domain expression is as follows:

[0064]

[0065] In the formula, This is the frequency domain response function of the Mexican Hat plot wavelet filter. These are the eigenvalues ​​of the graph Laplacian matrix corresponding to the frequency of the graph signal. These are scaling parameters used to control the center frequency and bandwidth of the filter. In this embodiment, Take 1;

[0066] Understandably, this embodiment applies the Mexican Hat function to the frequency domain decomposition of hyperspectral undirected graph signals, achieving targeted separation of low-frequency global smooth components and high-frequency detail abrupt change components to meet the input requirements of subsequent dual-branch feature learning networks.

[0067] Step 1.4: Define each spectral band The image signal is After wavelet filtering of the Mexican Hat diagram, the spectral bands are obtained. The high-frequency components are expressed as:

[0068]

[0069] In the formula, For the first The high-frequency component map signal corresponding to each spectral band. For Mexican Hat plot wavelet filter operators, For the normalized graph Laplace matrix eigenvector matrix, and This is represented as eigenvalue decomposition. For the normalized graph Laplace matrix The eigenvalue diagonal matrix, Represented as a transpose matrix, These are the filter response values ​​corresponding to the eigenvalues ​​of the graph Laplacian matrix. For the normalized graph Laplace matrix eigenvalues;

[0070] Spectral bands are obtained through a complementary approach. low-frequency components The expression is:

[0071]

[0072] Reconstruct all band results to obtain the low-frequency component. With high frequency components ,in, This represents the total number of bands in the original hyperspectral image. The height of the hyperspectral image, The width of the original hyperspectral image.

[0073] It is important to understand that existing technologies typically employ a fixed single graph structure, assuming the entire image domain has uniform and smooth characteristics. This makes it impossible to simultaneously characterize the spatial heterogeneity features of "spectral smoothness within ground features and spectral abrupt changes between ground feature boundaries and small ground features" in hyperspectral images, nor can it solve the problem of multi-scale spectral mixing. Therefore, Step 1 of this embodiment introduces graph wavelet transform, which is not a simple graph convolution preprocessing. Instead, it utilizes the multi-scale decomposition characteristics of wavelets to achieve structured frequency domain decoupling of graph signals in the field of hyperspectral unmixing. This automatically separates the original mixed graph signal into physically meaningful low-frequency smooth components and high-frequency detail components, providing targeted input for subsequent specialized feature learning and overcoming the defect of conventional graph convolution indiscriminately modeling information of different frequencies.

[0074] Step 2: Input the low-frequency component and the high-frequency component into a parallel dual-branch feature encoder network to obtain enhanced low-frequency features and enhanced high-frequency features. The parallel dual-branch feature encoder network includes a low-frequency branch and a high-frequency branch. The low-frequency branch performs feature learning and extraction on the low-frequency component to obtain initial low-frequency features. Then, through the channel attention mechanism at the end of the low-frequency branch, the initial low-frequency features are adaptively recalibrated in terms of channel dimension to obtain enhanced low-frequency features. The high-frequency branch performs feature learning and extraction on the high-frequency component to obtain initial high-frequency features. Then, through the channel attention mechanism at the end of the high-frequency branch, the initial high-frequency features are adaptively recalibrated in terms of channel dimension to obtain enhanced high-frequency features.

[0075] Step 2.1: To address the heterogeneity of physical semantics, numerical distribution, and signal-to-noise ratio of high and low frequency components after graph wavelet decomposition, a parallel dual-branch feature encoder network is constructed. The parallel dual-branch feature encoder network includes a low-frequency branch and a high-frequency branch. The parameters of the low-frequency branch and the high-frequency branch are completely independent and not shared. The low-frequency branch is designed for global smoothness information and uses three stacked 3×3 convolutional blocks with large receptive fields containing batch normalization and LeakyReLU activation function (negative slope of 0.2) to capture the spectral consistency of large-area ground features. The high-frequency branch is designed for detail abrupt changes and noise information and uses three stacked residual 3×3 convolutional blocks containing batch normalization and LeakyReLU activation function (negative slope of 0.2) to enhance weak edge signals and suppress sensor noise. The stride and padding of the high-frequency branch are all 1.

[0076] Step 2.2: A global average pooling layer (GAP) is introduced at the end of both the low-frequency and high-frequency branches to compress the spatial dimension to a one-dimensional vector. The low-frequency branch is used to learn structural features that represent global smoothness, while the high-frequency branch is used to learn detailed features that represent local mutations.

[0077] Step 2.3: In the low-frequency branch, the low-frequency components Initial low-frequency features are extracted using three convolutional blocks. In the high-frequency branch, the high-frequency components Initial high-frequency features are extracted using three convolutional blocks. Both feature weights and adaptive recalibration are calculated using global average pooling and channel attention mechanisms, expressed as follows:

[0078]

[0079]

[0080]

[0081]

[0082] In the formula, This represents the global feature vector of the low-frequency branch. This represents the global feature vector of the high-frequency branch. This is the global average pooling function. This is the channel attention weight vector for the low-frequency branch. Here is the channel attention weight vector for the high-frequency branch. It is the Sigmoid activation function. It is a linear rectified activation function. , Here is the learnable weight matrix for the channel attention module. To enhance the low-frequency characteristics, For the enhanced high-frequency features, This represents broadcast multiplication along the channel dimension.

[0083] It is understandable that the parallel dual-branch feature encoder network constructed in Step 2 of this embodiment is deeply coupled with the wavelet decomposition of the pre-image. It is a heterogeneous specialized network customized for the heterogeneity of high and low frequency components: for the characteristics of global smoothness and high signal-to-noise ratio of low frequency components, the low frequency branch adopts a large receptive field convolution structure to capture the spectral consistency of large-area ground objects and suppress irrelevant detail interference; for the characteristics of sparse abrupt changes and the presence of noise and weak edge signals of high frequency components, the high frequency branch adopts residual convolution and channel attention structure to distinguish the effective signal of ground object edge from sensor noise artifacts and enhance weak detail features.

[0084] Step 3: The enhanced low-frequency features and the enhanced high-frequency features are added and fused element by element to obtain a multi-frequency comprehensive feature that integrates global structure and local detail information, thereby achieving complementary optimization of global structure information and local detail information;

[0085] Optionally, the enhanced low-frequency features and enhanced high-frequency features after channel attention recalibration are added and fused element by element to construct a dynamic fusion mechanism with frequency domain contribution awareness. The dynamic fusion mechanism can adaptively and dynamically adjust the contribution weights of low-frequency global structural information and high-frequency local detail information according to the local context of the input image (such as flat areas or ground feature boundaries). This solves the problem that traditional static stitching / linear weighted fusion cannot adapt to the demixing requirements of different regions and achieves the optimal balance between noise suppression and detail preservation.

[0086] Understandably, this embodiment, through Steps 1-3, firstly uses graph wavelet frequency domain decomposition to provide specialized inputs with clear physical meaning for the heterogeneous dual branches. Then, it provides high-quality complementary features for dynamic attention fusion through targeted feature extraction from the heterogeneous dual branches. Finally, it achieves optimal integration of the two feature paths through dynamic attention fusion. Steps 1-3 are deeply coupled and synergistically enhance each other, effectively solving the problems of boundary blurring, spectral distortion, and poor spatial continuity in hyperspectral unmixing.

[0087] Step 4: Input the multi-frequency integrated features into the endmember constraint and reconstruction module to obtain the reconstructed hyperspectral image; wherein, the endmember constraint and reconstruction module includes an abundance constraint estimation submodule and a hyperspectral image reconstruction submodule. The abundance constraint estimation submodule performs channel dimension mapping on the multi-frequency integrated features and applies abundance non-negativity constraints and abundance sum-to-one constraints to obtain an abundance matrix. The hyperspectral image reconstruction submodule uses the kernel weights of an unbiased 1×1 convolutional layer as the endmember matrix and combines it with the abundance matrix to perform hyperspectral image reconstruction to obtain the reconstructed hyperspectral image;

[0088] Step 4.1: In the abundance-constrained estimation submodule, integrate multi-frequency features. The number of input-to-output channels is equal to the total number of endpoints. The abundance matrix is ​​obtained after processing a 1×1 convolutional layer with the Softmax activation function. The expression is:

[0089]

[0090] In the formula, This is a 1×1 convolution operation;

[0091] It is understandable that this embodiment utilizes the exponential normalization mathematical property of the Softmax function to naturally and strictly satisfy the abundance non-negativity constraint (ANC) and the abundance sum to 1 constraint (ASC), ensuring that the abundance values ​​of various endmembers in each pixel are non-negative and sum to 1, thus giving the output results a clear meaning.

[0092] Step 4.2: In the hyperspectral image reconstruction submodule, an unbiased 1×1 convolutional layer is used as the decoder, with the number of input channels being... The endmember matrix is ​​estimated using the convolution kernel weights. Thus, the reconstructed hyperspectral image is obtained. .

[0093] Optionally, the decoder weights are initialized with the initial endmember spectra extracted by the vertex component analysis (VCA) algorithm.

[0094] Step 5: Compare the reconstructed hyperspectral image with the original hyperspectral image, and construct a multi-dimensional joint loss function. By minimizing the multi-dimensional joint loss function, a hyperspectral unmixing model is obtained. The hyperspectral image to be processed is input into the hyperspectral unmixing model to obtain the hyperspectral image unmixing result.

[0095] Optionally, the multi-dimensional joint loss function includes spectral angular distance (SAD) loss, mean squared error (MSE) loss, and total variation regularization (TV) loss, which synergistically achieve multi-objective optimization of spectral fidelity, accuracy improvement, and noise suppression, and is expressed as:

[0096]

[0097] in, For multi-dimensional joint loss function, Spectral angular distance loss is used to measure the spectral shape similarity between the reconstructed hyperspectral image and the original hyperspectral image. It is insensitive to changes in illumination intensity and can effectively ensure the fidelity of the endmember spectrum. Mean squared error loss is used to measure the pixel-level numerical difference between the reconstructed hyperspectral image and the original hyperspectral image, ensuring the overall reconstruction accuracy of the hyperspectral image. The total variation regularization loss is used to constrain the spatial smoothness of the abundance map, suppress noise and artifacts in the unmixed results, and enhance the spatial continuity of abundance in homogeneous material regions. , To balance the various losses, hyperparameters are used to adjust the weights among spectral fidelity, reconstruction accuracy, and spatial continuity.

[0098] Based on the specific implementation details, the effectiveness of the technical solution of the present invention will be demonstrated through experiments.

[0099] Specifically, this embodiment conducted experiments on one simulated dataset and three real datasets, and compared them with seven classic and state-of-the-art unmixing models: vertex component analysis (VCA), minimum volume simplex analysis (MVSA), convolutional neural network autoencoder unmixing (CNNAEU), transformer autoencoder unmixing (TAEU), nonlinear autoencoder unmixing (NLAEU), U-shaped transformer network using shifted windows (USTNet), and temperature scaling unmixing framework based on convolutional autoencoder (TSUCAE).

[0100] Specifically, the experimental hardware environment in this embodiment is: a 12th generation Intel Core i5-12600KF CPU, 32GB RAM, and an NVIDIA GeForce RTX 4060 Ti GPU (16GB VRAM). The model is trained using the Adam optimizer, and the batch size is adjusted according to the dataset: 128 for the simulated dataset, Moffett and Apex datasets, and 256 for the Houston dataset. The number of training epochs is 400-600, and the learning rate is determined through cross-validation.

[0101] Specifically, the simulated dataset was generated using the Hyperspectral Image Synthesis Toolbox (HSIST), containing five endmembers and Gaussian white noise with signal-to-noise ratios of 10, 20, 30, and 40 dB. Moffett removed water absorption bands from the original 224 spectral bands, ultimately retaining 189 spectral bands with wavelengths ranging from 0.4 μm to 2.5 μm and a nominal bandwidth of 10 nm. These bands cover the visible and near-infrared regions. The research scene of interest to Moffett is 50 × 50 pixels in size, which includes... The image depicts a portion of a lake and its surrounding area, comprised of soil and vegetation. The Houston dataset covers the visible to near-infrared bands from 0.364 to 1.046 μm, containing 144 spectral bands. The original image size is 349 × 1905 pixels. This experiment selected a typical sub-region of 170 × 170 pixels as the region of interest for analysis. The scene mainly contains four typical endmembers: parking lot 1, parking lot 2, running track, and grassland. The original image size of the Apex dataset is 111 × 122 pixels, containing 285 bands. After removing low signal-to-noise ratio bands, the image size is 110 × 110 pixels, containing 285 bands. Four endmembers were manually selected from the hyperspectral image: water, trees, roads, and rooftops.

[0102] Specifically, in this embodiment, the root mean square error (RMSE) is used to measure the accuracy of abundance estimation, and the spectral angular distance (SAD) is used to measure the accuracy of endmember extraction. The smaller the value, the better the performance.

[0103] Specifically, the experimental content and results are as follows:

[0104] (1) To evaluate the noise robustness of the model, different levels of Gaussian white noise were added to the simulated dataset to construct test sets with signal-to-noise ratios (SNR) of 10, 20, 30 and 40 dB. The quantitative evaluation results based on this synthetic dataset are shown in Table 1.

[0105] Table 1. Quantitative experimental results of the simulated dataset under different signal-to-noise ratios (best results are bolded).

[0106]

[0107] As shown in Table 1, the performance of most methods is significantly limited by the large amount of noise in the dataset, with VCA performing the worst. In contrast, GWCNet of this invention maintains excellent unmixing capabilities even under high signal-to-noise ratio (SNR) conditions. The unmixing performance of all models decreases with increasing SNR due to added noise. This is because noise disrupts the fundamental structure and prior assumptions upon which the unmixing model relies, leading to geometric distortion, target shift in optimization, and difficulty in satisfying physical constraints. GWCNet decomposes the original hyperspectral image into high-frequency and low-frequency components using graph wavelet transform. The low-frequency components retain global structural information of ground features and are insensitive to noise, while the high-frequency components, although containing details, effectively avoid over-response to high-frequency noise due to the use of a bandpass Mexican Hat filter. Experimental results demonstrate that GWCNet maintains excellent unmixing robustness and accuracy under hyperspectral data containing complex noise.

[0108] Furthermore, to intuitively compare the unmixing performance of GWCNet with existing methods, the abundance plots output by each method were visualized on a simulated dataset (SNR=30dB). The results are as follows: Figure 2 As shown in the figure, the results obtained by VCA and MVSA differ significantly. This is because the geometric methods VCA and MVSA rely on the data forming a clear simplex in the spectral space. Noise causes point cloud diffusion, leading to inaccurate vertex or minimum volume estimation, resulting in severe endmember estimation bias. Although deep learning methods have stronger expressive power, they are not entirely immune to noise interference. CNNAEU's local convolution is prone to misclassifying noise as texture, and its pixel-by-pixel processing lacks a global error correction mechanism. TAEU's self-attention mechanism incorrectly associates distorted spectra with other regions when noise is strong, amplifying error propagation. NLAEU is designed for nonlinear hybrid modeling and is more prone to overfitting noise patterns, especially without additional regularization or prior constraints. The network may learn false nonlinear mapping relationships, leading to simultaneous distortion of endmembers and abundance. TSUCAE's reliance on spatial similarity is distorted at low SNR, causing adaptive sparsity failure. Although UST-Net is relatively robust due to its multi-scale and whole-image modeling, noise severely interferes with the construction of the similarity matrix, leading to incorrect region partitioning, inaccurate temperature parameter allocation, and a weakening of its adaptive advantages. GWCNet fully mines the hidden multi-scale and multi-directional information in images through graph wavelet transform, thereby constructing and providing a more discriminative multi-frequency feature representation for subsequent unmixing operations. Secondly, the model uses a dual-branch network to process feature information and introduces a channel attention mechanism to adaptively weight and fuse low-frequency and high-frequency features, so that their contribution is automatically suppressed in areas with severe noise pollution, thereby effectively preserving valuable spectral spatial details while suppressing noise.

[0109] (2) The results of quantitative evaluation on the Moffett dataset are shown in Table 2.

[0110] Table 2. Quantitative experimental results of endmember segmentation on the Moffett dataset (bolded for best results).

[0111]

[0112] As shown in Table 2, GWCNet achieved the best SAD and RMSE results for the three typical land cover categories of water, soil, and vegetation. Specifically, GWCNet's average SAD value was 0.013, a 43.48% reduction in error compared to the second-ranked method; its average RMSE was 0.037, a 21.28% reduction in error compared to the second-ranked method. This demonstrates that the method exhibits leading accuracy in the spectral and abundance estimation of all land cover types.

[0113] Furthermore, to intuitively compare the unmixing performance of GWCNet with existing methods, the abundance plots output by each method were visualized on the Moffett dataset. The results are as follows: Figure 3 As shown, from Figure 3 As can be seen, the abundance map obtained by GWCNet is visually most similar to the real abundance map on the ground. The lack of clean pixels in real-world scenes prevents VCA and MVSA methods, which rely on simplex vertex structures, from accurately locating endmember spectra. Simultaneously, the limited spatial range restricts the acquisition of spatial context information, making it difficult for deep learning models based on local or global dependencies, such as CNNAEU, TAEU, and UST-Net, to effectively model ground cover distribution. Furthermore, nonlinear effects and sensor noise in the actual mixing process further deviate from the linear assumption, exposing models like NLAEU to the risk of overfitting. TSUCAE's adaptive mechanism fails due to the lack of clear clean region delineation; all seven methods struggle to maintain high-precision unmixing performance in highly mixed and feature-fuzzy real-world scenes. In GWCNet, low-frequency components effectively characterize the globally smooth spectral properties of lakes, while high-frequency components focus on abrupt changes at the water-vegetation boundary. Simultaneously, the introduction of the Mexican Hat filter makes the high-frequency response highly sensitive to second-order spectral changes, avoiding boundary fuzziness and significantly improving the resolution accuracy of mixed pixels.

[0114] (3) The results of quantitative evaluation on the Houston dataset are shown in Table 3.

[0115] Table 3. Quantitative experimental results of endmember segmentation on the Houston dataset (best results are in bold).

[0116]

[0117] As shown in Table 3, NLAEU achieved the highest accuracy in extracting the "Parking Lot 2" endmember. For the remaining three land cover endmembers, GWCNet yielded the best results. Regarding RMSE, TSUCAE outperformed other methods in estimating the abundance of the "Parking Lot 1" endmember. GWCNet was more accurate in estimating the abundance of the endmembers "Grassland," "Runway," and "Parking Lot 2." In the overall performance evaluation, GWCNet achieved the best average SAD and average RMSE among all methods. Compared to the best comparison method, GWCNet significantly improved accuracy in endmember extraction, with an average spectral angular distance of 0.064, an improvement of 9.86%. Simultaneously, GWCNet significantly reduced the error in abundance estimation, with an average root mean square error of 0.029, a reduction of 14.71%. In summary, GWCNet demonstrated superior performance compared to other unmixing methods in the unmixing task.

[0118] Furthermore, Figure 4 This paper presents the abundance visualization results of eight unmixing methods on the Houston dataset. The urban environmental characteristics presented by the Houston dataset pose unique challenges to various unmixing methods. VCA relies on pure pixels to construct simplex vertices, but in the campus scene, the spectra of parking lot 1 and parking lot 2 are highly similar, causing vertex recognition failure. MVSA fits the data through a minimum volume simplex, but the high proportion of mixed pixels in the city leads to a serious offset in the simplex volume estimation, resulting in distortion of the estimated endmember spectra. CNNAEU's convolutional feature extraction mechanism struggles to distinguish subtle differences on the parking lot surface, misclassifying similar spectra as the same land cover, resulting in spatial confusion in the abundance map. TAEU's self-attention mechanism incorrectly associates the spectral features of the runway and parking lot when modeling long-range dependencies, amplifying the estimation error of the mixed region. NLAEU's nonlinear model design is mismatched with the relatively linear characteristics of urban mixing, leading to the network overfitting noise rather than the true mixing mechanism. Although UST-Net's multi-scale processing can preserve details, the sharp boundaries of land cover in the city and the over-smoothing of the U-shaped structure's feature fusion result in the loss of key spatial information in the transition area between parking lot and grass. TSUCAE's temperature scaling mechanism relies on spatial similarity to divide regions. However, the spectral overlap between parking lots 1 and 2 leads to misjudgment of the similarity matrix, causing adaptive sparsity control to fail and resulting in biased abundance estimation. GWCNet accurately responds to high-frequency abrupt changes through graph wavelet filters, enhances dynamic features of mixed regions through bi-branch feature learning, and ensures physical rationality through endmember constraint reconstruction. This effectively solves the problem of mixed pixel resolution in densely populated urban areas, and its demixing performance is significantly better than other methods.

[0119] (4) The quantitative results of different unmixing methods on the Apex dataset are shown in Table 4.

[0120] Table 4. Quantitative experimental results of endmember segmentation on the Apex dataset (best results are in bold).

[0121]

[0122] As shown in Table 4, the compact spatial scale and high spectral dimensionality of the Apex dataset pose significant challenges to various unmixing algorithms. In this urban scene, the spectral responses of water bodies, vegetation, roads, and building rooftops exhibit high overlap in specific bands, significantly weakening the spectral separability of endmembers. TSUCAE achieved the best results in extracting the "road" endmember, while CNNAEU achieved the best results in extracting the "water" endmember. In the remaining scenes, GWCNet demonstrated better unmixing performance. Specifically, compared to the best-performing competing method, GWCNet reduced the average spectral angular distance by 9.78% and the average root mean square error by 22.81%. Overall, GWCNet exhibits better and more stable unmixing performance compared to other methods.

[0123] Furthermore, the abundance visualization results obtained from the eight unmixing methods are as follows: Figure 5 As shown, GWCNet's abundance results are closer to the actual values. The VCA method relies on vertex identification of clean pixels, but the Apex data has a high proportion of mixed pixels and lacks clear clean regions, causing its endmember extraction process to fail. MVSA suffers from volume calculation bias due to spectral redundancy and noise interference, resulting in systematic distortion of endmember spectra. CNNAEU's convolutional feature extraction mechanism is limited by its local receptive field and cannot effectively capture subtle spectral differences between roads and rooftops. TAEU's self-attention mechanism is susceptible to interference from similar spectral patterns in high-dimensional bands, incorrectly associating pixel features from irrelevant regions and amplifying estimation errors. NLAEU assumes a nonlinear mixing mechanism, but most regions in the Apex scene still approximately satisfy the linear mixing assumption; its complex model structure introduces too many parameters, exacerbating the risk of overfitting. UST-Net's multi-scale feature fusion strategy is difficult to fully implement in a limited space; the windowing operation disrupts the continuous boundary between rooftops and roads, destroying crucial spatial consistency. TSUCAE's adaptive mechanism relies on spatial similarity to divide regions; however, endmember spectral overlap leads to misjudgment of the similarity matrix, inaccurate temperature scaling parameters, and sparsity constraints deviating from the actual abundance distribution. GWCNet introduces graph wavelet transform, which is highly sensitive to second-order spectral abrupt changes and accurately captures subtle spectral differences at endmember boundaries. The dual-branch network collaboratively processes global spectral consistency and local mixing details, and the channel attention mechanism dynamically enhances the response of key bands, effectively solving the unmixing and blurring problem in highly overlapping spectral mixtures, and significantly outperforming the processing results of other datasets.

[0124] (5) The running time of the eight unmixing methods on each dataset is shown in Table 5.

[0125] Table 5. Comparison of runtime for each method on different datasets (unit: seconds)

[0126]

[0127] As can be seen from Table 5, GWCNet ranks third in terms of time spent. Without increasing computational complexity, this method still shows good execution efficiency, and its running speed has a significant advantage over existing solutions.

[0128] (6) The experiment also conducted ablation experiments on the graph wavelet transform and dynamic fusion mechanism proposed in this embodiment. The experimental results are shown in Table 6.

[0129] Table 6. Ablation Experiment Results of Core Modules (Best Results in Bold)

[0130]

[0131] As shown in Table 6, GWCNet maintains excellent global unmixing performance even when only graph wavelet transform is applied. This fully verifies the core value of graph wavelet transform in constructing diverse feature representations, proving its effectiveness and irreplaceability as a feature enhancement mechanism. When combined with a dynamic fusion mechanism, the unmixing performance is significantly improved. Graph wavelet transform constructs a frequency domain foundation that fits the geometry of the ground features, while attention fusion achieves intelligent feature scheduling oriented towards the unmixing objective. Together, they form a structure-aware, semantically guided closed loop, significantly improving the model's generalization ability and physical interpretability in real-world complex scenarios.

[0132] In summary, this invention extends hyperspectral images to the frequency domain using graph wavelet transform, and the low-frequency and high-frequency components obtained through dual-branch network collaborative processing are enhanced by a dynamic fusion mechanism. Specifically, graph wavelet transform constructs a graph topology based on spectral-spatial similarity, mapping the original hyperspectral cube to a non-Euclidean domain implicitly defined by ground cover distribution. A Mexican Hat filter is then used to extract high- and low-frequency components with clear physical meaning from this domain: low frequencies correspond to smoothly varying main regions on the graph, while high frequencies focus on structural perturbation regions corresponding to large Laplacian eigenvalues. The dual-branch network architecture addresses the need for collaborative optimization of global semantics and local details in hyperspectral unmixing, achieving accurate feature representation through a separation processing mechanism. The dynamic fusion mechanism adaptively learns weight coefficients for each channel of the low-frequency and high-frequency feature maps, enabling the model to automatically identify and enhance spectral features truly important for the unmixing task while suppressing noise interference or redundant channel information. Finally, endmember constraint reconstruction is used to achieve abundance estimation and endmember extraction. Comparative experiments on multiple datasets show that the present invention has excellent and stable unmixing performance. Ablation experiments prove the effectiveness and necessity of the graph wavelet transform combined with dynamic fusion mechanism, effectively solving the problems of boundary ambiguity and spectral distortion in hyperspectral unmixing, significantly improving unmixing accuracy and spatial continuity, and providing a solution for hyperspectral unmixing tasks that combines theoretical rigor and practical value.

[0133] The specific embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A hyperspectral image demixing method based on graph wavelet transform convolutional networks, characterized in that, The method includes the following steps: Step 1: Construct an undirected graph of the original hyperspectral image, calculate connection weights based on the spectral similarity and spatial distance between pixels and construct an adjacency matrix, calculate the normalized graph Laplacian matrix based on the adjacency matrix, and use a Mexican Hat graph wavelet filter to perform frequency domain decomposition on the undirected graph of the original hyperspectral image to obtain low-frequency and high-frequency components. Step 2: Input the low-frequency component and the high-frequency component into a parallel dual-branch feature encoder network to obtain enhanced low-frequency features and enhanced high-frequency features. The parallel dual-branch feature encoder network includes a low-frequency branch and a high-frequency branch. The low-frequency branch performs feature learning and extraction on the low-frequency component to obtain initial low-frequency features. Then, through the channel attention mechanism at the end of the low-frequency branch, the initial low-frequency features are adaptively recalibrated in terms of channel dimension to obtain enhanced low-frequency features. The high-frequency branch performs feature learning and extraction on the high-frequency component to obtain initial high-frequency features. Then, through the channel attention mechanism at the end of the high-frequency branch, the initial high-frequency features are adaptively recalibrated in terms of channel dimension to obtain enhanced high-frequency features. Step 3: Add and fuse the enhanced low-frequency features and the enhanced high-frequency features element by element to obtain multi-frequency comprehensive features; Step 4: Input the multi-frequency integrated features into the endmember constraint and reconstruction module to obtain the reconstructed hyperspectral image; wherein, the endmember constraint and reconstruction module includes an abundance constraint estimation submodule and a hyperspectral image reconstruction submodule. The abundance constraint estimation submodule performs channel dimension mapping on the multi-frequency integrated features and applies abundance non-negativity constraints and abundance sum-to-one constraints to obtain an abundance matrix. The hyperspectral image reconstruction submodule uses the kernel weights of an unbiased 1×1 convolutional layer as the endmember matrix and combines it with the abundance matrix to perform hyperspectral image reconstruction to obtain the reconstructed hyperspectral image; Step 5: Compare the reconstructed hyperspectral image with the original hyperspectral image, and construct a multi-dimensional joint loss function. By minimizing the multi-dimensional joint loss function, a hyperspectral unmixing model is obtained. The hyperspectral image to be processed is input into the hyperspectral unmixing model to obtain the hyperspectral image unmixing result.

2. The hyperspectral image demixing method based on graph wavelet transform convolutional network according to claim 1, characterized in that, Step 1 specifically includes: Step 1.1: Construct an undirected graph from the original hyperspectral image ,in, Represents the set of vertices in an undirected graph, where each pixel is a node. edge set This represents the local correlation between pixels, any two pixels and Connection weights The expression is: ； In the formula, For pixels spectral vector, For pixels spectral vector, For pixels spatial coordinates, For pixels spatial coordinates, To control the parameters of the spectral similarity scale, Parameters for controlling spatial distance scale; Step 1.2: Construct the adjacency matrix , The total number of pixels in the original hyperspectral image, based on the adjacency matrix. Define the degree matrix , Construct a function for a diagonal matrix. The weighted degree of pixel i is used to calculate the normalized graph Laplacian matrix. The expression is: ； In the formula, It is the identity matrix; Step 1.3: The Mexican Hat function is used as the graph wavelet filter, and its frequency domain expression is as follows: ； In the formula, This is the frequency domain response function of the Mexican Hat plot wavelet filter. These are the eigenvalues ​​of the graph Laplacian matrix corresponding to the frequency of the graph signal. This is a scaling parameter used to control the center frequency and bandwidth of the filter; Step 1.4: Define each spectral band The image signal is After wavelet filtering of the Mexican Hat diagram, the spectral bands are obtained. The high-frequency components are expressed as: ； In the formula, For the first The high-frequency component map signal corresponding to each spectral band. For Mexican Hat plot wavelet filter operators, For the normalized graph Laplace matrix eigenvector matrix, and This is represented as eigenvalue decomposition. For the normalized graph Laplace matrix The eigenvalue diagonal matrix, Represented as a transpose matrix, These are the filter response values ​​corresponding to the eigenvalues ​​of the graph Laplacian matrix. For the normalized graph Laplace matrix eigenvalues; Spectral bands are obtained through a complementary approach. low-frequency components The expression is: ； Reconstruct all band results to obtain the low-frequency component. With high frequency components ,in, This represents the total number of bands in the original hyperspectral image. The height of the hyperspectral image, The width of the original hyperspectral image.

3. The hyperspectral image demixing method based on graph wavelet transform convolutional network according to claim 2, characterized in that, Step 2 specifically refers to: Step 2.1: Construct a parallel dual-branch feature encoder network, which includes a low-frequency branch and a high-frequency branch. The parameters of the low-frequency branch and the high-frequency branch are completely independent and do not share. The low-frequency branch uses three stacked 3×3 convolutional blocks with large receptive fields containing batch normalization and LeakyReLU activation functions. The high-frequency branch uses three stacked residual 3×3 convolutional blocks containing batch normalization and LeakyReLU activation functions. Step 2.2: Introduce a global average pooling layer (GAP) at the end of both the low-frequency and high-frequency branches to compress the spatial dimension to a one-dimensional vector; Step 2.3: In the low-frequency branch, the low-frequency components Initial low-frequency features are extracted using three convolutional blocks. In the high-frequency branch, the high-frequency components Initial high-frequency features are extracted using three convolutional blocks. Both feature weights and adaptive recalibration are calculated using global average pooling and channel attention mechanisms, expressed as follows: ； ； ； ； In the formula, This represents the global feature vector of the low-frequency branch. This represents the global feature vector of the high-frequency branch. This is the global average pooling function. This is the channel attention weight vector for the low-frequency branch. Here is the channel attention weight vector for the high-frequency branch. It is the Sigmoid activation function. It is a linear rectified activation function. , Here is the learnable weight matrix for the channel attention module. To enhance the low-frequency characteristics, For the enhanced high-frequency features, This represents broadcast multiplication along the channel dimension.

4. The hyperspectral image demixing method based on graph wavelet transform convolutional network according to claim 1, characterized in that, Step 4 specifically refers to: Step 4.1: In the abundance-constrained estimation submodule, integrate multi-frequency features. The number of input-to-output channels is equal to the total number of endpoints. The abundance matrix is ​​obtained after processing a 1×1 convolutional layer with the Softmax activation function. The expression is: ； In the formula, This is a 1×1 convolution operation; Step 4.2: In the hyperspectral image reconstruction submodule, an unbiased 1×1 convolutional layer is used as the decoder, and the kernel weights are used as the estimated endmember matrix. Thus, the reconstructed hyperspectral image is obtained. .

5. The hyperspectral image demixing method based on graph wavelet transform convolutional network according to claim 1, characterized in that, The multi-dimensional joint loss function includes spectral angular distance loss, mean squared error loss, and total variation regularization loss, and its expression is: ； in, For multi-dimensional joint loss function, For spectral angular distance loss, For mean square error loss, The loss is the regularization loss of the total variation. , To balance the hyperparameters of each loss.

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