Deep Equilibrium Convolutional Sparse Coding for Hyperspectral Image Denoising

2025-08-21

AI Summary

To address the challenge of hyperspectral image (HSI) denoising under complex, mixed noise while preserving physical consistency, this paper proposes a Deep Equilibrium Convolutional Sparse Coding (DE-CSC) framework. The method innovatively embeds convolutional sparse coding (CSC) via proximal gradient descent into a deep equilibrium model, enabling infinite-depth optimization through fixed-point iteration and jointly modeling local spatial-spectral correlations, non-local self-similarity, and global spatial consistency. The architecture integrates shared 2D and unshared 3D convolutional sparse representations, a Transformer module for long-range dependency modeling, and a detail-enhancement module. Extensive experiments on both synthetic and real-world noisy HSIs demonstrate that DE-CSC significantly outperforms state-of-the-art methods, achieving breakthrough improvements in denoising accuracy and faithful preservation of spectral fidelity and fine spatial structures.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Machine Learning: Deep Generative Models & Autoencoders
• Search and Optimization: Non-convex Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Data transparency and provenance
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Hyperspectral images (HSIs) play a crucial role in remote sensing but are often degraded by complex noise patterns. Ensuring the physical property of the denoised HSIs is vital for robust HSI denoising, giving the rise of deep unfolding-based methods. However, these methods map the optimization of a physical model to a learnable network with a predefined depth, which lacks convergence guarantees. In contrast, Deep Equilibrium (DEQ) models treat the hidden layers of deep networks as the solution to a fixed-point problem and models them as infinite-depth networks, naturally consistent with the optimization. Under the framework of DEQ, we propose a Deep Equilibrium Convolutional Sparse Coding (DECSC) framework that unifies local spatial-spectral correlations, nonlocal spatial self-similarities, and global spatial consistency for robust HSI denoising. Within the convolutional sparse coding (CSC) framework, we enforce shared 2D convolutional sparse representation to ensure global spatial consistency across bands, while unshared 3D convolutional sparse representation captures local spatial-spectral details. To further exploit nonlocal self-similarities, a transformer block is embedded after the 2D CSC. Additionally, a detail enhancement module is integrated with the 3D CSC to promote image detail preservation. We formulate the proximal gradient descent of the CSC model as a fixed-point problem and transform the iterative updates into a learnable network architecture within the framework of DEQ. Experimental results demonstrate that our DECSC method achieves superior denoising performance compared to state-of-the-art methods.

Problem

• Denoising hyperspectral images degraded by complex noise
• Ensuring physical properties in denoised hyperspectral imagery
• Lack of convergence guarantees in deep unfolding methods

Innovation

• Deep Equilibrium Convolutional Sparse Coding framework
• Combines 2D and 3D convolutional sparse representations
• Integrates transformer block for nonlocal self-similarities