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Sparse unmixing is a semisupervised unmixing method based on the linear mixture model, in which the spectral library is known a prior, and has received considerable attention recently. It has been confirmed that the spatial information in hyperspectral images plays a crucial role in improving the performance of sparse unmixing algorithms. However, the spatial information extracted or captured in most unmixing algorithms is inaccurate and robust enough, which leads to artificial block noise or outliers in the estimated abundance maps, especially as the noise level increases. To address these problems and more efficiently utilize the spatial information, this paper proposes a graph learning and denoising-based weighted sparse mixing (GLDWSU) algorithm, which includes three stages in the unmixing procedure: graph learning, denoising and unmixing. In the first stage, the graph Laplacian matrix is adaptively learned to capture the spatial structure of HSI with the relative total variation (RTV) regularization. In the next stage, HSI is denoised with the learned Laplacian matrix by using Laplacian smoothing. In the final stage, the denoised HSI is unmixed with the reweighted-norm regularization based on the alternating direction method of multipliers (ADMM) framework. The experimental results on both simulated and real data sets show that the proposed GLDWSU algorithm can more accurately capture and utilize the spatial structure information of HSI with a low computational cost and outperforms all the compared methods.

Graph learning and denoising-based weighted sparse unmixing for hyperspectral images