# Hyperspectral Image Restoration via Total Variation Regularized Low-rank Tensor Decomposition

arXiv: https://arxiv.org/abs/1707.02477 · HTML: https://mlsanity.com/paper/1707.02477/

## Key facts

- Cited by 61 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jul 2017.

## Built on by (most cited first, 30 of 61)

- [SpectralFormer: Rethinking Hyperspectral Image Classification with Transformers](https://mlsanity.com/paper/2107.02988/) (2021)
- [Low-Rank Tensor Function Representation for Multi-Dimensional Data Recovery](https://mlsanity.com/paper/2212.00262/) (2022)
- [Guaranteed Tensor Recovery Fused Low-rankness and Smoothness](https://mlsanity.com/paper/2302.02155/) (2023)
- [HIR-Diff: Unsupervised Hyperspectral Image Restoration Via Improved Diffusion Models](https://mlsanity.com/paper/2402.15865/) (2024)
- [DDS2M: Self-Supervised Denoising Diffusion Spatio-Spectral Model for Hyperspectral Image Restoration](https://mlsanity.com/paper/2303.06682/) (2023)
- [Deep Plug-and-Play Prior for Hyperspectral Image Restoration](https://mlsanity.com/paper/2209.08240/) (2022)
- [Exact Decomposition of Joint Low Rankness and Local Smoothness Plus Sparse Matrices](https://mlsanity.com/paper/2201.12592/) (2022)
- [A Comprehensive Survey for Hyperspectral Image Classification: The Evolution from Conventional to Transformers and Mamba Models](https://mlsanity.com/paper/2404.14955/) (2024)
- [Hybrid Spectral Denoising Transformer with Guided Attention](https://mlsanity.com/paper/2303.09040/) (2023)
- [DeepTensor: Low-Rank Tensor Decomposition with Deep Network Priors](https://mlsanity.com/paper/2204.03145/) (2022)
- [Fast Noise Removal in Hyperspectral Images via Representative Coefficient Total Variation](https://mlsanity.com/paper/2211.01825/) (2022)
- [Revisiting Nonlocal Self-Similarity from Continuous Representation](https://mlsanity.com/paper/2401.00708/) (2024)
- [Noisy Tensor Completion via Low-rank Tensor Ring](https://mlsanity.com/paper/2203.08857/) (2022)
- [Hyperspectral Denoising Using Unsupervised Disentangled Spatio-Spectral Deep Priors](https://mlsanity.com/paper/2102.12310/) (2021)
- [Tensor Decompositions for Hyperspectral Data Processing in Remote Sensing: A Comprehensive Review](https://mlsanity.com/paper/2205.06407/) (2022)
- [Mixed Attention Network for Hyperspectral Image Denoising](https://mlsanity.com/paper/2301.11525/) (2023)
- [Hyperspectral Image Denoising and Anomaly Detection Based on Low-rank and Sparse Representations](https://mlsanity.com/paper/2103.07437/) (2021)
- [ATD: Augmenting CP Tensor Decomposition by Self Supervision](https://mlsanity.com/paper/2106.07900/) (2021)
- [HSIDMamba: Exploring Bidirectional State-Space Models for Hyperspectral Denoising](https://mlsanity.com/paper/2404.09697/) (2024)
- [NeurTV: Total Variation on the Neural Domain](https://mlsanity.com/paper/2405.17241/) (2024)
- [Smooth Robust Tensor Completion for Background/Foreground Separation with Missing Pixels: Novel Algorithm with Convergence Guarantee](https://mlsanity.com/paper/2203.16328/) (2022)
- [Robust Implementation of Foreground Extraction and Vessel Segmentation for X-ray Coronary Angiography Image Sequence](https://mlsanity.com/paper/2209.07237/) (2022)
- [Deep Diversity-Enhanced Feature Representation of Hyperspectral Images](https://mlsanity.com/paper/2301.06132/) (2023)
- [Hyperspectral Image Super-Resolution via Dual-domain Network Based on Hybrid Convolution](https://mlsanity.com/paper/2304.04589/) (2023)
- [Degradation-Noise-Aware Deep Unfolding Transformer for Hyperspectral Image Denoising](https://mlsanity.com/paper/2305.04047/) (2023)
- [Pan-denoising: Guided Hyperspectral Image Denoising via Weighted Represent Coefficient Total Variation](https://mlsanity.com/paper/2407.06064/) (2024)
- [Non-Convex Tensor Low-Rank Approximation for Infrared Small Target Detection](https://mlsanity.com/paper/2105.14974/) (2021)
- [Connections between Deep Equilibrium and Sparse Representation Models with Application to Hyperspectral Image Denoising](https://mlsanity.com/paper/2203.15901/) (2022)
- [Hipandas: Hyperspectral Image Joint Denoising and Super-Resolution by Image Fusion with the Panchromatic Image](https://mlsanity.com/paper/2412.04201/) (2024)
- [H2TF for Hyperspectral Image Denoising: Where Hierarchical Nonlinear Transform Meets Hierarchical Matrix Factorization](https://mlsanity.com/paper/2304.11141/) (2023)

## Abstract (arXiv)

Hyperspectral images (HSIs) are often corrupted by a mixture of several types of noise during the acquisition process, e.g., Gaussian noise, impulse noise, dead lines, stripes, and many others. Such complex noise could degrade the quality of the acquired HSIs, limiting the precision of the subsequent processing. In this paper, we present a novel tensor-based HSI restoration approach by fully identifying the intrinsic structures of the clean HSI part and the mixed noise part respectively. Specifically, for the clean HSI part, we use tensor Tucker decomposition to describe the global correlation among all bands, and an anisotropic spatial-spectral total variation (SSTV) regularization to characterize the piecewise smooth structure in both spatial and spectral domains. For the mixed noise part, we adopt the ℓ1 norm regularization to detect the sparse noise, including stripes, impulse noise, and dead pixels. Despite that TV regulariztion has the ability of removing Gaussian noise, the Frobenius norm term is further used to model heavy Gaussian noise for some real-world scenarios. Then, we develop an efficient algorithm for solving the resulting optimization problem by using the augmented Lagrange multiplier (ALM) method. Finally, extensive experiments on simulated and real-world noise HSIs are carried out to demonstrate the superiority of the proposed method over the existing state-of-the-art ones.