  Hyperspectral image (HSI) denoising aims to restore clean HSI from the
noise-contaminated one. Noise contamination can often be caused during data
acquisition and conversion. In this paper, we propose a novel spatial-spectral
total variation (SSTV) regularized nonconvex local low-rank (LR) tensor
approximation method to remove mixed noise in HSIs. From one aspect, the clean
HSI data have its underlying local LR tensor property, even though the real HSI
data may not be globally low-rank due to out-liers and non-Gaussian noise.
According to this fact, we propose a novel tensor $L_{\gamma}$-norm to
formulate the local LR prior. From another aspect, HSIs are assumed to be
piecewisely smooth in the global spatial and spectral domains. Instead of
traditional bandwise total variation, we use the SSTV regularization to
simultaneously consider global spatial structure and spectral correlation of
neighboring bands. Results on simulated and real HSI datasets indicate that the
use of local LR tensor penalty and global SSTV can boost the preserving of
local details and overall structural information in HSIs.
