Spatial–Spectral Total Variation Regularized Low-Rank Tensor Decomposition for Hyperspectral Image Denoising

Several bandwise total variation (TV) regularized low-rank (LR)-based models have been proposed to remove mixed noise in hyperspectral images (HSIs). These methods convert high-dimensional HSI data into 2-D data based on LR matrix factorization. This strategy introduces the loss of useful multiway structure information. 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 regularized LR tensor factorization (SSTV-LRTF) method to remove mixed noise in HSIs. From one aspect, the hyperspectral data are assumed to lie in an LR tensor, which can exploit the inherent tensorial structure of hyperspectral data. The LRTF-based method can effectively separate the LR clean image from sparse noise. From another aspect, HSIs are assumed to be piecewisely smooth in the spatial domain. The TV regularization is effective in preserving the spatial piecewise smoothness and removing Gaussian noise. These facts inspire the integration of the LRTF with TV regularization. To address the limitations of bandwise TV, we use the SSTV regularization to simultaneously consider local spatial structure and spectral correlation of neighboring bands. Both simulated and real data experiments demonstrate that the proposed SSTV-LRTF method achieves superior performance for HSI mixed-noise removal, as compared to the state-of-the-art TV regularized and LR-based methods.