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Spatial-Spectral Total Variation (SSTV) can quantify local smoothness ofimage structures, so it is widely used in hyperspectral image (HSI) processingtasks. Essentially, SSTV assumes a sparse structure of gradient maps calculatedalong the spatial and spectral directions. In fact, these gradient tensors arenot only sparse, but also (approximately) low-rank under FFT, which we haveverified by numerical tests and theoretical analysis. Based on this fact, wepropose a novel TV regularization to simultaneously characterize the sparsityand low-rank priors of the gradient map (LRSTV). The new regularization notonly imposes sparsity on the gradient map itself, but also penalize the rank onthe gradient map after Fourier transform along the spectral dimension. Itnaturally encodes the sparsity and lowrank priors of the gradient map, and thusis expected to reflect the inherent structure of the original image morefaithfully. Further, we use LRSTV to replace conventional SSTV and embed it inthe HSI processing model to improve its performance. Experimental results onmultiple public data-sets with heavy mixed noise show that the proposed modelcan get 1.5dB improvement of PSNR.

Low-rank Meets Sparseness: An Integrated Spatial-Spectral Total Variation Approach to Hyperspectral Denoising