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

arXiv: https://arxiv.org/abs/2106.12489 · HTML: https://mlsanity.com/paper/2106.12489/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 68 references that are in the map.
- First posted on arXiv 23 Jun 2021.

## Builds on (most cited first, 18 of 18)

- [More Diverse Means Better: Multimodal Deep Learning Meets Remote Sensing Imagery Classification](https://mlsanity.com/paper/2008.05457/) (2020)
- [Tensor Robust Principal Component Analysis with A New Tensor Nuclear Norm](https://mlsanity.com/paper/1804.03728/) (2018)
- [Exact tensor completion using t-SVD](https://mlsanity.com/paper/1502.04689/) (2015)
- [Hyperspectral Image Restoration via Total Variation Regularized Low-rank Tensor Decomposition](https://mlsanity.com/paper/1707.02477/) (2017)
- [Hyperspectral Image Denoising Employing a Spatial-Spectral Deep Residual Convolutional Neural Network](https://mlsanity.com/paper/1806.00183/) (2018)
- [3D Quasi-Recurrent Neural Network for Hyperspectral Image Denoising](https://mlsanity.com/paper/2003.04547/) (2020)
- [Fast Hyperspectral Image Denoising and Inpainting Based on Low-Rank and Sparse Representations](https://mlsanity.com/paper/2103.06842/) (2021)
- [Square Deal: Lower Bounds and Improved Relaxations for Tensor Recovery](https://mlsanity.com/paper/1307.5870/) (2013)
- [Framelet Representation of Tensor Nuclear Norm for Third-Order Tensor Completion](https://mlsanity.com/paper/1909.06982/) (2019)
- [Multi-dimensional imaging data recovery via minimizing the partial sum of tubal nuclear norm](https://mlsanity.com/paper/1712.05870/) (2017)
- [Tensor N-tubal rank and its convex relaxation for low-rank tensor recovery](https://mlsanity.com/paper/1812.00688/) (2018)
- [Dictionary Learning with Low-rank Coding Coefficients for Tensor Completion](https://mlsanity.com/paper/2009.12507/) (2020)
- [Fast L1-L2 minimization via a proximal operator](https://mlsanity.com/paper/1609.09530/) (2016)
- [Self-Supervised Nonlinear Transform-Based Tensor Nuclear Norm for Multi-Dimensional Image Recovery](https://mlsanity.com/paper/2105.14320/) (2021)
- [Hyperspectral Denoising Using Unsupervised Disentangled Spatio-Spectral Deep Priors](https://mlsanity.com/paper/2102.12310/) (2021)
- [Hyperspectral Image Denoising via Global Spatial-Spectral Total Variation Regularized Nonconvex Local Low-Rank Tensor Approximation](https://mlsanity.com/paper/2006.00235/) (2020)
- [A Fast Algorithm for Cosine Transform Based Tensor Singular Value Decomposition](https://mlsanity.com/paper/1902.03070/) (2019)
- [Frequency-Weighted Robust Tensor Principal Component Analysis](https://mlsanity.com/paper/2004.10068/) (2020)

## Abstract (arXiv)

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.