Hyperspectral Image Denoising with Log-Based Robust PCA

TL;DR

This paper introduces a novel nonconvex RPCA-based method utilizing log-determinant rank approximation and a new $_{2, ext{log}}$ norm for effective hyperspectral image denoising, showing superior results on simulated and real data.

Contribution

It proposes a new nonconvex RPCA approach with log-based rank and norm approximations, including a closed-form $_{2, ext{log}}$-shrinkage operator, for hyperspectral image denoising.

Findings

Effective denoising on simulated HSIs

Superior performance on real hyperspectral images

Efficient $_{2, ext{log}}$-shrinkage solution

Abstract

It is a challenging task to remove heavy and mixed types of noise from Hyperspectral images (HSIs). In this paper, we propose a novel nonconvex approach to RPCA for HSI denoising, which adopts the log-determinant rank approximation and a novel $\ell_{2,\log}$ norm, to restrict the low-rank or column-wise 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, which can be generally used in other problems. Extensive experiments on both simulated and real HSIs demonstrate the effectiveness of the proposed method in denoising HSIs.