Enhancing Spatio-Spectral Regularization by Structure Tensor Modeling for Hyperspectral Image Denoising

Abstract

We propose a new regularization function, named Spatio-Spectral Structure Tensor Total Variation (S <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> TTV), 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 <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> TTV, 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 <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> TTV 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 <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> TTV and develop an efficient algorithm based on a diagonally preconditioned primal-dual splitting method to efficiently solve this problem. Finally, we demonstrate the effectiveness of S <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> TTV by comparing it with state-of-the-art HSI regularization models through mixed noise removal experiments.