# Hyperspectral Image Denoising Using Non-convex Local Low-rank and Sparse Separation with Spatial-Spectral Total Variation Regularization

arXiv: https://arxiv.org/abs/2201.02812 · HTML: https://mlsanity.com/paper/2201.02812/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 72 references that are in the map.
- First posted on arXiv 8 Jan 2022.

## Builds on (most cited first, 6 of 6)

- [Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration](https://mlsanity.com/paper/1508.02848/) (2015)
- [Hyperspectral pansharpening: a review](https://mlsanity.com/paper/1504.04531/) (2015)
- [Fast Hyperspectral Image Denoising and Inpainting Based on Low-Rank and Sparse Representations](https://mlsanity.com/paper/2103.06842/) (2021)
- [Robust PCA via Nonconvex Rank Approximation](https://mlsanity.com/paper/1511.05261/) (2015)
- [Kernel Two-Dimensional Ridge Regression for Subspace Clustering](https://mlsanity.com/paper/2011.01477/) (2020)
- [Nonnegative Matrix Factorization with Local Similarity Learning](https://mlsanity.com/paper/1907.04150/) (2019)

## Built on by (most cited first, 5 of 5)

- [A Comprehensive Survey for Hyperspectral Image Classification: The Evolution from Conventional to Transformers and Mamba Models](https://mlsanity.com/paper/2404.14955/) (2024)
- [Pan-denoising: Guided Hyperspectral Image Denoising via Weighted Represent Coefficient Total Variation](https://mlsanity.com/paper/2407.06064/) (2024)
- [Haar Nuclear Norms with Applications to Remote Sensing Imagery Restoration](https://mlsanity.com/paper/2407.08509/) (2024)
- [Low-Rank Tensor Recovery via Variational Schatten-p Quasi-Norm and Jacobian Regularization](https://mlsanity.com/paper/2506.22134/) (2025)
- [A TRPCA-Inspired Deep Unfolding Network for Hyperspectral Image Denoising via Thresholded t-SVD and Top-K Sparse Transformer](https://mlsanity.com/paper/2506.02364/) (2025)

## Abstract (arXiv)

In this paper, we propose a novel nonconvex approach to robust principal component analysis for HSI denoising, which focuses on simultaneously developing more accurate approximations to both rank and column-wise sparsity for the low-rank and sparse components, respectively. In particular, the new method adopts the log-determinant rank approximation and a novel ℓ2,log norm, to restrict the local low-rank or column-wisely sparse properties for the component matrices, respectively. For the ℓ2,log-regularized shrinkage problem, we develop an efficient, closed-form solution, which is named ℓ2,log-shrinkage operator. The new regularization and the corresponding operator can be generally used in other problems that require column-wise sparsity. Moreover, we impose the spatial-spectral total variation regularization in the log-based nonconvex RPCA model, which enhances the global piece-wise smoothness and spectral consistency from the spatial and spectral views in the recovered HSI. Extensive experiments on both simulated and real HSIs demonstrate the effectiveness of the proposed method in denoising HSIs.