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

2025-06-03

AI Summary

Hyperspectral images are often corrupted by complex mixed noise, and existing denoising methods struggle to effectively integrate model-based priors with data-driven learning. To address this, we propose an end-to-end interpretable deep unfolding network featuring a novel TRPCA-inspired staged alternating architecture: it alternately applies thresholded t-SVD (to capture global low-rank structure) and Top-K sparse Transformer (to suppress local outliers), tightly coupling model-driven and data-driven paradigms within a unified framework. This is the first work to jointly embed both principles in a single architecture, achieving balanced structural fidelity and outlier robustness. Extensive experiments on diverse synthetic and real-world datasets demonstrate significant improvements over state-of-the-art methods—achieving over 2.5 dB PSNR gain under severe mixed noise—while ensuring stable convergence, physical interpretability, and strong generalization capability.

Technology Category

• Computer Vision: Other Foundations of Computer Vision
• Machine Learning: Multi-instance/Multi-view Learning
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Security and Privacy: Data transparency and provenance

Abstract

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.

Problem

• Denoising hyperspectral images degraded by complex mixed noise
• Bridging model-driven and data-driven paradigms for effective denoising
• Enhancing low-rank and sparse module integration for better noise removal

Innovation

• Deep unfolding network with TRPCA inspiration
• Thresholded t-SVD for low-rank HSI denoising
• Top-K sparse transformer for adaptive noise removal