  Low-rankness is important in the hyperspectral image (HSI) denoising tasks.
The tensor nuclear norm (TNN), defined based on the tensor singular value
decomposition, is a state-of-the-art method to describe the low-rankness of
HSI. However, TNN ignores some physical meanings of HSI in tackling denoising
tasks, leading to suboptimal denoising performance. In this paper, we propose
the multi-modal and frequency-weighted tensor nuclear norm (MFWTNN) and the
non-convex MFWTNN for HSI denoising tasks. Firstly, we investigate the physical
meaning of frequency slices and reconsider their weights to improve the
low-rank representation ability of TNN. Secondly, we consider the correlation
among two spatial dimensions and the spectral dimension of HSI and combine the
above improvements to TNN to propose MFWTNN. Thirdly, we use non-convex
functions to approximate the rank function of the frequency tensor and propose
the NonMFWTNN to relax the MFWTNN better. Besides, we adaptively choose bigger
weights for slices mainly containing noise information and smaller weights for
slices containing profile information. Finally, we develop the efficient
alternating direction method of multiplier (ADMM) based algorithm to solve the
proposed models, and the effectiveness of our models are substantiated in
simulated and real HSI datasets.
