Research On Hyperspectral Image Unmixing Method Based On Tensor Decompositio

Hyperspectral satellite remote sensing images are three-dimensional cubes containing multiple wavelength-range images obtained through imaging spectrometers mounted on satellites.These images contain a rich spectrum of information and play a crucial role in many fields.However,due to the limitations of satellite remote sensing imaging,the spectra of multiple objects are linearly or nonlinearly mixed during transmission,resulting in mixed pixels in hyperspectral images that often contain spectral information from multiple pure objects.This poses a significant challenge for subsequent applications.In recent years,matrix factorization-based unmixing methods using low-rank matrix approximation have been widely researched and applied to obtain pure spectral information of objects and their composition proportions.However,reducing hyperspectral remote sensing images to two-dimensional matrices can destroy the spectral correlation between adjacent spectral bands,and researchers typically add multiple regularization terms to ensure the accuracy of unmixing without losing this spatial-spectral information.Due to the large data volume of hyperspectral images,these methods are usually computationally inefficient and complex in the solution process.Therefore,to improve the accuracy of unmixing and obtain more accurate pure object information and corresponding composition proportions,this study explored unmixing methods based on tensor and autoencoder network frameworks to further improve the performance of extracting endmember spectra and abundance inversion of hyperspectral images.The main contributions include:（1）A blind unmixing method for hyperspectral images based on Tucker tensor decomposition and L1 norm is proposed.This method maintains the third-order tensor structure of the hyperspectral image during processing,utilizes the low-rank characteristics of the hyperspectral image through Tucker tensor decomposition,realizes the utilization of the spatial information of the hyperspectral image in the form of tensor.At the same time,the L₁ norm is added to the model to realize the utilization of hyperspectral image sparsity.In the experiments,the proposed method was compared with the currently best-performing unmixing methods,and the results showed that this method was superior in both endmember extraction and abundance inversion.（2）A hyperspectral image unmixing method based on deep singular value decomposition network is proposed.This method is based on the autoencoder network and uses one-dimensional convolution instead of the fully connected network in the encoder for encoder dimensionality reduction encoding,to maintain the three-dimensional structure of the hyperspectral image and make full use of the spatial information of the hyperspectral image.In addition,the autoencoding network structure is used to simulate the singular value decomposition to describe the low-rank structure of the hyperspectral image.At the same time,the sparse characteristics of the hyperspectral image are deeply mined through the custom threshold activation function in the deep singular value decomposition module.In this method,a differential regularization term is also added to the loss function to utilize the correlation spatial information between adjacent spectral bands.The superiority of the proposed method was verified through simulated data with different signal-to-noise ratios and publicly available real data.