Spatial-Spectral Texture-Preserved Total Variation: A Novel Regularization for Hyperspectral Image Denoising

Local smoothness is a widely used prior in hyperspectral image (HSI) denoising tasks. The current work mainly realizes the representation of this prior through total variation (TV) regularization. However, the TV regularization applies a uniform penalty to each entry in the image, unable to effectively balance noise removal and texture preservation. Aiming at this problem: 1) We propose a novel regularization for HSI denoising called Spatial-Spectral Texture-Preserved Total Variation (SSTPTV). This naturally expresses the physical phenomenon of the difference in sparsity between textured regions and smooth regions. Specifically, the regularization relaxes the sparsity penalty in textured regions by a weight learning strategy and sparsity measurement method for gradient maps, thereby preserving the spatial-spectral textures of HSIs. 2) An HSI denoising model based on the SSTPTV regularization constraint is given. We propose a tensor alternating subspace representation method that can capture the overall spatial texture features across all bands and the overall spectral texture features across all spectral curves. By applying the SSTPTV regularization constraint to these subspaces, the spatial-spectral texture structures are effectively preserved. An efficient ADMM-based algorithm for solving the model is designed. The simulated and real noise removal experiments of HSI prove that the proposed method has significant superiority and can serve as a framework to optimize other TV-based denoising methods. The code is available at https://github.com/zth-code/SSTPTV.