# Weighted Low-rank Tensor Recovery for Hyperspectral Image Restoration

arXiv: https://arxiv.org/abs/1709.00192 · HTML: https://mlsanity.com/paper/1709.00192/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Sep 2017.

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

- [Vision-Language Gradient Descent-driven All-in-One Deep Unfolding Networks](https://mlsanity.com/paper/2503.16930/) (2025)
- [Spectral Enhanced Rectangle Transformer for Hyperspectral Image Denoising](https://mlsanity.com/paper/2304.00844/) (2023)
- [Spatial-Spectral Transformer for Hyperspectral Image Denoising](https://mlsanity.com/paper/2211.14090/) (2022)
- [Deep Plug-and-Play Prior for Hyperspectral Image Restoration](https://mlsanity.com/paper/2209.08240/) (2022)
- [Hybrid Spectral Denoising Transformer with Guided Attention](https://mlsanity.com/paper/2303.09040/) (2023)
- [Hyperspectral Image Super Resolution with Real Unaligned RGB Guidance](https://mlsanity.com/paper/2302.06298/) (2023)
- [Hyperspectral Denoising Using Unsupervised Disentangled Spatio-Spectral Deep Priors](https://mlsanity.com/paper/2102.12310/) (2021)
- [RPCANet++: Deep Interpretable Robust PCA for Sparse Object Segmentation](https://mlsanity.com/paper/2508.04190/) (2025)
- [Tensor Decompositions for Hyperspectral Data Processing in Remote Sensing: A Comprehensive Review](https://mlsanity.com/paper/2205.06407/) (2022)
- [Effective Tensor Completion via Element-wise Weighted Low-rank Tensor Train with Overlapping Ket Augmentation](https://mlsanity.com/paper/2109.05736/) (2021)
- [Mixed Attention Network for Hyperspectral Image Denoising](https://mlsanity.com/paper/2301.11525/) (2023)
- [Deep Amended Gradient Descent for Efficient Spectral Reconstruction from Single RGB Images](https://mlsanity.com/paper/2108.05547/) (2021)
- [Degradation-Noise-Aware Deep Unfolding Transformer for Hyperspectral Image Denoising](https://mlsanity.com/paper/2305.04047/) (2023)
- [Tuning-free Plug-and-Play Hyperspectral Image Deconvolution with Deep Priors](https://mlsanity.com/paper/2211.15307/) (2022)
- [Low-Rank Tensor Completion via Novel Sparsity-Inducing Regularizers](https://mlsanity.com/paper/2310.06233/) (2023)
- [Hyperspectral Image Super-Resolution in Arbitrary Input-Output Band Settings](https://mlsanity.com/paper/2103.10614/) (2021)
- [Low-rank Meets Sparseness: An Integrated Spatial-Spectral Total Variation Approach to Hyperspectral Denoising](https://mlsanity.com/paper/2204.12879/) (2022)
- [A Deep Unrolling Model with Hybrid Optimization Structure for Hyperspectral Image Deconvolution](https://mlsanity.com/paper/2306.06378/) (2023)
- [Hyperspectral Mixed Noise Removal via Subspace Representation and Weighted Low-rank Tensor Regularization](https://mlsanity.com/paper/2111.07044/) (2021)
- [Improved Quasi-Recurrent Neural Network for Hyperspectral Image Denoising](https://mlsanity.com/paper/2211.14811/) (2022)
- [Guided Deep Generative Model-based Spatial Regularization for Multiband Imaging Inverse Problems](https://mlsanity.com/paper/2306.17197/) (2023)
- [Variational Bayesian Inference for Tensor Robust Principal Component Analysis](https://mlsanity.com/paper/2412.18717/) (2024)
- [Equal is Not Always Fair: A New Perspective on Hyperspectral Representation Non-Uniformity](https://mlsanity.com/paper/2505.11267/) (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)
- [Normalized Iterative Hard Thresholding for Tensor Recovery](https://mlsanity.com/paper/2507.04228/) (2025)
- [Compact Multi-level-prior Tensor Representation for Hyperspectral Image Super-resolution](https://mlsanity.com/paper/2510.06098/) (2025)
- [Anisotropic Tensor Deconvolution of Hyperspectral Images](https://mlsanity.com/paper/2601.11694/) (2026)
- [Spatial-Spectral Adaptive Fidelity and Noise Prior Reduction Guided Hyperspectral Image Denoising](https://mlsanity.com/paper/2604.12600/) (2026)
- [Robust Low-Tubal-Rank Tensor Completion under Cross-Concentrated Sampling](https://mlsanity.com/paper/2608.03928/) (2026)
- [Registration-Free Hyperspectral Reconstruction from RGB via a Permutation-Invariant Gram-Matrix Principle](https://mlsanity.com/paper/2608.14994/) (2026)

## Abstract (arXiv)

Hyperspectral imaging, providing abundant spatial and spectral information simultaneously, has attracted a lot of interest in recent years. Unfortunately, due to the hardware limitations, the hyperspectral image (HSI) is vulnerable to various degradations, such noises (random noise, HSI denoising), blurs (Gaussian and uniform blur, HSI deblurring), and down-sampled (both spectral and spatial downsample, HSI super-resolution). Previous HSI restoration methods are designed for one specific task only. Besides, most of them start from the 1-D vector or 2-D matrix models and cannot fully exploit the structurally spectral-spatial correlation in 3-D HSI. To overcome these limitations, in this work, we propose a unified low-rank tensor recovery model for comprehensive HSI restoration tasks, in which non-local similarity between spectral-spatial cubic and spectral correlation are simultaneously captured by 3-order tensors. Further, to improve the capability and flexibility, we formulate it as a weighted low-rank tensor recovery (WLRTR) model by treating the singular values differently, and study its analytical solution. We also consider the exclusive stripe noise in HSI as the gross error by extending WLRTR to robust principal component analysis (WLRTR-RPCA). Extensive experiments demonstrate the proposed WLRTR models consistently outperform state-of-the-arts in typical low level vision HSI tasks, including denoising, destriping, deblurring and super-resolution.