Hyperspectral Image Denoising Using Non-convex Local Low-rank and Sparse Separation with Spatial-Spectral Total Variation Regularization

TL;DR

This paper introduces a novel nonconvex method for hyperspectral image denoising that improves low-rank and sparse component separation using log-determinant and log-norm regularizations, combined with spatial-spectral total variation.

Contribution

It develops a new nonconvex RPCA model with log-based approximations and a closed-form $ ext{l}_{2, ext{log}}$ shrinkage operator, enhancing HSI denoising performance.

Findings

Effective in removing noise from simulated HSIs

Outperforms existing methods on real hyperspectral data

Enhances spectral and spatial consistency in denoised images

Abstract

In this paper, we propose a novel nonconvex approach to robust principal component analysis for HSI denoising, which focuses on simultaneously developing more accurate approximations to both rank and column-wise sparsity for the low-rank and sparse components, respectively. In particular, the new method adopts the log-determinant rank approximation and a novel $\ell_{2,\log}$ norm, to restrict the local low-rank or column-wisely sparse properties for the component matrices, respectively. For the $\ell_{2,\log}$-regularized shrinkage problem, we develop an efficient, closed-form solution, which is named $\ell_{2,\log}$-shrinkage operator. The new regularization and the corresponding operator can be generally used in other problems that require column-wise sparsity. Moreover, we impose the spatial-spectral total variation regularization in the log-based nonconvex RPCA model, which enhances the global piece-wise 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.