  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.
