Multi-modal and frequency-weighted tensor nuclear norm for hyperspectral image denoising

TL;DR

This paper introduces a novel tensor nuclear norm method that incorporates physical insights and frequency weighting for improved hyperspectral image denoising, demonstrating superior performance on real and simulated datasets.

Contribution

It proposes the MFWTNN and NonMFWTNN models that integrate physical meaning and frequency weights into tensor nuclear norm for enhanced HSI denoising.

Findings

Outperforms existing methods in denoising quality

Effectively suppresses noise while preserving spectral information

Demonstrates robustness on real hyperspectral datasets

Abstract

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.