  Several bandwise total variation (TV) regularized low-rank (LR)-based models
have been proposed to remove mixed noise in hyperspectral images (HSIs).
Conventionally, the rank of LR matrix is approximated using nuclear norm (NN).
The NN is defined by adding all singular values together, which is essentially
a $L_1$-norm of the singular values. It results in non-negligible approximation
errors and thus the resulting matrix estimator can be significantly biased.
Moreover, these bandwise TV-based methods exploit the spatial information in a
separate manner. To cope with these problems, we propose a spatial-spectral TV
(SSTV) regularized non-convex local LR matrix approximation (NonLLRTV) method
to remove mixed noise in HSIs. From one aspect, local LR of HSIs is formulated
using a non-convex $L_{\gamma}$-norm, which provides a closer approximation to
the matrix rank than the traditional NN. From another aspect, HSIs are assumed
to be piecewisely smooth in the global spatial domain. The TV regularization is
effective in preserving the smoothness and removing Gaussian noise. These facts
inspire the integration of the NonLLR with TV regularization. To address the
limitations of bandwise TV, we use the SSTV regularization to simultaneously
consider global spatial structure and spectral correlation of neighboring
bands. Experiment results indicate that the use of local non-convex penalty and
global SSTV can boost the preserving of spatial piecewise smoothness and
overall structural information.
