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Coupled denoising and unmixing with low rank constraint and hypergraph regularization for hyperspectral image

The noise removal and endmember unmixing are two pivotal problems for the hyperspectral image (HSI) data exploitation. Different from the traditional approach that treating these two schemes separately, the proposed coupled Denoising and Unmixing (cDeUn) model integrates them into a uniform framework. To obtain the desired denoising and unmixing performances, three issues are included. First, the weighted nuclear norm minimization (WNNM) is adopted to separate the clean HSI from the noisy observation. Second, the sparse representation (SR) based unmixing scheme is incorporated to obtain the endmember abundance matrix. Both denoising and unmixing schemes act as constraints to each other and the effects of them can promote each other. Third, the hypergraph regularization is incorporated to retain the smooth consistency of the abundance matrix and further improve the final performance. Both synthetic and real data experiments confirm that the proposed cDeUn approach can provide superior denoising and unmixing performances for the HSI corrupted by the mixture of Gaussian, salt and pepper, and deadline noise.