ENHANCING SPATIO-SPECTRAL REGULARIZATION BY STRUCTURE TENSOR MODELING FOR HYPERSPECTRAL IMAGE DENOISING

We propose a new regularization function, named Spatio-Spectral Structure Tensor Total Variation (S_3TTV), for hyperspectral image (HSI) denoising. Spatio-Spectral Total Variation (SSTV), defined using spatio-spectral second-order differences, is widely known as a regularization function for HSI that can effectively remove noise while avoiding spatial over-smoothing. However, since SSTV only refers to the information of neighboring pixels or bands, it can corrupt semi-local spatial structure in the process of noise removal. To resolve this problem, we formulate S_3TTV, which is defined by the sum of the nuclear norms of matrices consisting of spatio-spectral second-order differences in small spatial blocks (we call these matrices as spatio-spectral structure tensors). With this formulation, S_3TTV can capture not only the similarity of semi-local spatial structure between adjacent bands but also the spectral correlation across all bands. We also formulate the HSI denoising problem as a convex optimization problem involving S_3TTV and develop an efficient algorithm based on a diagonally preconditioned version of a primal-dual splitting method to efficiently solve this problem. Finally, we demonstrate the effectiveness of S_3TTV by comparing it with state-of-the-art HSI regularization models through mixed noise removal experiments.