# A TRPCA-Inspired Deep Unfolding Network for Hyperspectral Image Denoising via Thresholded t-SVD and Top-K Sparse Transformer

arXiv: https://arxiv.org/abs/2506.02364 · HTML: https://mlsanity.com/paper/2506.02364/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 43 references that are in the map.
- First posted on arXiv 3 Jun 2025.

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

- [Learning A Sparse Transformer Network for Effective Image Deraining](https://mlsanity.com/paper/2303.11950/) (2023)
- [Deep Generalized Unfolding Networks for Image Restoration](https://mlsanity.com/paper/2204.13348/) (2022)
- [Tensor Robust Principal Component Analysis with A New Tensor Nuclear Norm](https://mlsanity.com/paper/1804.03728/) (2018)
- [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)
- [Non-local Meets Global: An Iterative Paradigm for Hyperspectral Image Restoration](https://mlsanity.com/paper/2010.12921/) (2020)
- [Deep Hyperspectral Prior: Denoising, Inpainting, Super-Resolution](https://mlsanity.com/paper/1902.00301/) (2019)
- [Spectral Enhanced Rectangle Transformer for Hyperspectral Image Denoising](https://mlsanity.com/paper/2304.00844/) (2023)
- [A Trainable Spectral-Spatial Sparse Coding Model for Hyperspectral Image Restoration](https://mlsanity.com/paper/2111.09708/) (2021)
- [Spatial-Spectral Transformer for Hyperspectral Image Denoising](https://mlsanity.com/paper/2211.14090/) (2022)
- [Weighted Low-rank Tensor Recovery for Hyperspectral Image Restoration](https://mlsanity.com/paper/1709.00192/) (2017)
- [Deep Plug-and-Play Prior for Hyperspectral Image Restoration](https://mlsanity.com/paper/2209.08240/) (2022)
- [FastHyMix: Fast and Parameter-free Hyperspectral Image Mixed Noise Removal](https://mlsanity.com/paper/2109.08879/) (2021)
- [Hybrid Spectral Denoising Transformer with Guided Attention](https://mlsanity.com/paper/2303.09040/) (2023)
- [SMDS-Net: Model Guided Spectral-Spatial Network for Hyperspectral Image Denoising](https://mlsanity.com/paper/2012.01829/) (2020)
- [Hyperspectral Image Denoising Using Non-convex Local Low-rank and Sparse Separation with Spatial-Spectral Total Variation Regularization](https://mlsanity.com/paper/2201.02812/) (2022)
- [Degradation-Noise-Aware Deep Unfolding Transformer for Hyperspectral Image Denoising](https://mlsanity.com/paper/2305.04047/) (2023)
- [Recursions Are All You Need: Towards Efficient Deep Unfolding Networks](https://mlsanity.com/paper/2305.05505/) (2023)

## Abstract (arXiv)

Hyperspectral images (HSIs) are often degraded by complex mixed noise during acquisition and transmission, making effective denoising essential for subsequent analysis. Recent hybrid approaches that bridge model-driven and data-driven paradigms have shown great promise. However, most of these approaches lack effective alternation between different priors or modules, resulting in loosely coupled regularization and insufficient exploitation of their complementary strengths. Inspired by tensor robust principal component analysis (TRPCA), we propose a novel deep unfolding network (DU-TRPCA) that enforces stage-wise alternation between two tightly integrated modules: low-rank and sparse. The low-rank module employs thresholded tensor singular value decomposition (t-SVD), providing a widely adopted convex surrogate for tensor low-rankness and has been demonstrated to effectively capture the global spatial-spectral structure of HSIs. The Top-K sparse transformer module adaptively imposes sparse constraints, directly matching the sparse regularization in TRPCA and enabling effective removal of localized outliers and complex noise. This tightly coupled architecture preserves the stage-wise alternation between low-rank approximation and sparse refinement inherent in TRPCA, while enhancing representational capacity through attention mechanisms. Extensive experiments on synthetic and real-world HSIs demonstrate that DU-TRPCA surpasses state-of-the-art methods under severe mixed noise, while offering interpretability benefits and stable denoising dynamics inspired by iterative optimization. Code is available at https://github.com/liangli97/TRPCA-Deep-Unfolding-HSI-Denoising.