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.
Abstract (translated)
高光谱图像（HSI）在遥感领域中扮演着重要角色，但通常会受到复杂噪声模式的影响。确保去噪后的HSI保持其物理特性对于稳健的HSI去噪至关重要，这促使了基于深度展开的方法的发展。然而，这些方法将一个物理模型的优化映射到具有预定义深度的学习网络上，缺乏收敛保证。相比之下，Deep Equilibrium (DEQ) 模型将深层网络中的隐藏层视为固定点问题的解，并将其建模为无限深度的网络，自然地与优化保持一致。 在DEQ框架下，我们提出了一种名为Deep Equilibrium Convolutional Sparse Coding（DECSC）的框架，该框架统一了局部空间-光谱相关性、非局部的空间自相似性和全局的空间一致性，以实现稳健的HSI去噪。在卷积稀疏编码(CSC)框架内，我们在所有频带之间强制执行共享2D卷积稀疏表示，以确保跨频带的全球空间一致性，同时利用非共享3D卷积稀疏表示来捕捉局部空间-光谱细节。为了进一步挖掘非本地自相似性，在2D CSC之后嵌入了一个变压器块。此外，还集成了一个细节增强模块，与3D CSC结合使用以促进图像细节保留。 我们把CSC模型的近似梯度下降公式化为固定点问题，并将其迭代更新转化为DEQ框架内的可学习网络架构。实验结果表明，我们的DECSC方法在去噪性能上优于现有最先进的方法。
URL
https://arxiv.org/abs/2508.15553
