Hyperspectral Image Denoising Using Nonconvex Local Low-Rank and Sparse Separation With Spatial-Spectral Total Variation Regularization

Chong Peng, Yang Liu, Kehan Kang, Yongyong Chen, Xinxing Wu, Andrew Cheng, Zhao Kang, Chenglizhao Chen, Qiang Cheng

Abstract: In this article, we propose a novel nonconvex approach to robust principal component analysis (RPCA) for hyperspectral image (HSI) denoising, which focuses on simultaneously developing more accurate approximations to both rank and columnwise sparsity for the low-rank and sparse components, respectively. In particular, the new method adopts the log-determinant rank approximation and a novel <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{2,\log }$ </tex-math></inline-formula> norm, to restrict the local low-rank or columnwisely sparse properties for the component matrices, respectively. For the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{2,\log }$ </tex-math></inline-formula> -regularized shrinkage problem, we develop an efficient, closed-form solution, which is named <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{2,\log }$ </tex-math></inline-formula> -shrinkage operator. The new regularization and the corresponding operator can be generally used in other problems that require columnwise sparsity. Moreover, we impose the spatial–spectral total variation regularization in the log-based nonconvex RPCA model, which enhances the global piecewise smoothness and spectral consistency from the spatial and spectral views in the recovered HSI. Extensive experiments on both simulated and real HSIs demonstrate the effectiveness of the proposed method in denoising HSIs.