  The spatio-spectral total variation (SSTV) model has been widely used as an
effective regularization of hyperspectral images (HSI) for various applications
such as mixed noise removal. However, since SSTV computes local spatial
differences uniformly, it is difficult to remove noise while preserving complex
spatial structures with fine edges and textures, especially in situations of
high noise intensity. To solve this problem, we propose a new TV-type
regularization called Graph-SSTV (GSSTV), which generates a graph explicitly
reflecting the spatial structure of the target HSI from noisy HSIs and
incorporates a weighted spatial difference operator designed based on this
graph. Furthermore, we formulate the mixed noise removal problem as a convex
optimization problem involving GSSTV and develop an efficient algorithm based
on the primal-dual splitting method to solve this problem. Finally, we
demonstrate the effectiveness of GSSTV compared with existing HSI
regularization models through experiments on mixed noise removal. The source
code will be available at https://www.mdi.c.titech.ac.jp/publications/gsstv.
