  Spatial-Spectral Total Variation (SSTV) can quantify local smoothness of
image structures, so it is widely used in hyperspectral image (HSI) processing
tasks. Essentially, SSTV assumes a sparse structure of gradient maps calculated
along the spatial and spectral directions. In fact, these gradient tensors are
not only sparse, but also (approximately) low-rank under FFT, which we have
verified by numerical tests and theoretical analysis. Based on this fact, we
propose a novel TV regularization to simultaneously characterize the sparsity
and low-rank priors of the gradient map (LRSTV). The new regularization not
only imposes sparsity on the gradient map itself, but also penalize the rank on
the gradient map after Fourier transform along the spectral dimension. It
naturally encodes the sparsity and lowrank priors of the gradient map, and thus
is expected to reflect the inherent structure of the original image more
faithfully. Further, we use LRSTV to replace conventional SSTV and embed it in
the HSI processing model to improve its performance. Experimental results on
multiple public data-sets with heavy mixed noise show that the proposed model
can get 1.5dB improvement of PSNR.
