# Deep Equilibrium Convolutional Sparse Coding for Hyperspectral Image Denoising

arXiv: https://arxiv.org/abs/2508.15553 · HTML: https://mlsanity.com/paper/2508.15553/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 72 references that are in the map.
- First posted on arXiv 21 Aug 2025.

## Builds on (most cited first, 30 of 31)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [VMamba: Visual State Space Model](https://mlsanity.com/paper/2401.10166/) (2024)
- [Universal Transformers](https://mlsanity.com/paper/1807.03819/) (2018)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Searching Central Difference Convolutional Networks for Face Anti-Spoofing](https://mlsanity.com/paper/2003.04092/) (2020)
- [Multiscale Deep Equilibrium Models](https://mlsanity.com/paper/2006.08656/) (2020)
- [Deep Equilibrium Architectures for Inverse Problems in Imaging](https://mlsanity.com/paper/2102.07944/) (2021)
- [Monotone operator equilibrium networks](https://mlsanity.com/paper/2006.08591/) (2020)
- [On Training Implicit Models](https://mlsanity.com/paper/2111.05177/) (2021)
- [Stabilizing Equilibrium Models by Jacobian Regularization](https://mlsanity.com/paper/2106.14342/) (2021)
- [Hyperspectral Image Restoration via Total Variation Regularized Low-rank Tensor Decomposition](https://mlsanity.com/paper/1707.02477/) (2017)
- [One-Step Diffusion Distillation via Deep Equilibrium Models](https://mlsanity.com/paper/2401.08639/) (2023)
- [Trellis Networks for Sequence Modeling](https://mlsanity.com/paper/1810.06682/) (2018)
- [Hyperspectral Image Denoising Employing a Spatial-Spectral Deep Residual Convolutional Neural Network](https://mlsanity.com/paper/1806.00183/) (2018)
- [MambaHSI: Spatial-Spectral Mamba for Hyperspectral Image Classification](https://mlsanity.com/paper/2501.04944/) (2025)
- [Non-local Meets Global: An Iterative Paradigm for Hyperspectral Image Restoration](https://mlsanity.com/paper/2010.12921/) (2020)
- [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)
- [Pixel Adaptive Deep Unfolding Transformer for Hyperspectral Image Reconstruction](https://mlsanity.com/paper/2308.10820/) (2023)
- [SSUMamba: Spatial-Spectral Selective State Space Model for Hyperspectral Image Denoising](https://mlsanity.com/paper/2405.01726/) (2024)
- [Convolutional Sparse Coding for Compressed Sensing CT Reconstruction](https://mlsanity.com/paper/1903.08549/) (2019)
- [Hybrid Noise Removal in Hyperspectral Imagery With a Spatial-Spectral Gradient Network](https://mlsanity.com/paper/1810.00495/) (2018)
- [SMDS-Net: Model Guided Spectral-Spatial Network for Hyperspectral Image Denoising](https://mlsanity.com/paper/2012.01829/) (2020)
- [Hyperspectral Image Denoising and Anomaly Detection Based on Low-rank and Sparse Representations](https://mlsanity.com/paper/2103.07437/) (2021)
- [Degradation-Noise-Aware Deep Unfolding Transformer for Hyperspectral Image Denoising](https://mlsanity.com/paper/2305.04047/) (2023)
- [Connections between Deep Equilibrium and Sparse Representation Models with Application to Hyperspectral Image Denoising](https://mlsanity.com/paper/2203.15901/) (2022)
- [Wavelet-Inspired Multiscale Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2401.06040/) (2024)

## Abstract (arXiv)

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.