发表机构
School of Mathematics, Harbin Institute of Technology; Department of Mathematics, University of Bologna（哈尔滨工业大学数学学院; 博洛尼亚大学数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种基于几何先验的DEQ图像复原框架，用定制镜像下降算法优化，性能优于模型基方法、接近先进DEQ，且参数更少。
AI 中文摘要
我们提出了一种深度学习框架，用于从受乘性伽马噪声和模糊共同退化的图像中复原图像。与依赖隐式神经正则化的传统深度均衡（DEQ）模型不同，所提方法学习由与表面积和平均曲率相关的几何先验参数化的显式且可解释的正则化项。为最小化所得变分模型，我们开发了一种针对常用伽马噪声保真项定制的镜像下降算法。利用o-极小结构中定义的函数的Kurdyka-Lojasiewicz性质，我们证明了生成迭代序列全局收敛到一个临界点。在灰度和彩色图像复原上的实验结果表明，所提方法在性能上始终优于代表性的基于模型的方法，同时达到了基于隐式正则化的最先进DEQ模型的可比性能，尽管所需的可训练参数显著更少。
英文摘要
We propose a deep learning framework for image restoration from images degraded by both multiplicative Gamma noise and blur. Unlike conventional deep equilibrium (DEQ) models that rely on implicit neural regularization, the proposed method learns an explicit and interpretable regularizer parameterized by geometric priors associated with surface area and mean curvature. To minimize the resulting variational model, we develop a mirror descent algorithm tailored to the commonly used Gamma-noise fidelity terms. Leveraging the Kurdyka-Lojasiewicz property for functions defined in $o$-minimal structures, we establish the global convergence of the generated iterates to a critical point. Experimental results on both grayscale and color image restoration demonstrate that the proposed method consistently outperforms representative model-based approaches while achieving performance comparable to state-of-the-art DEQ models based on implicit regularization, despite requiring substantially fewer trainable parameters.
