用几何先验构建可解释的图像去噪模型，有效处理伽马噪声与模糊。
A geometry-based deep equilibrium model for image restoration under multiplicative Gamma noise
- 基于表面面积和平均曲率设计显式正则项，提升可解释性。
- 在灰度与彩色图像上均优于传统模型，参数量更少。
- 适合追求高效、可解释性图像恢复的研究者使用。
我们提出一种深度学习框架，用于去除同时受乘性伽马噪声和模糊影响的图像。不同于依赖隐式神经正则化的传统深度均衡（DEQ）模型，该方法通过与曲面面积和平均曲率相关的几何先验，学习一个显式且可解释的正则化项。为最小化所得变分模型，我们设计了一种针对常用伽马噪声保真项的镜像下降算法。借助定义在o-极小结构上的Kurdyka-Łojasiewicz性质，证明了迭代序列全局收敛至临界点。在灰度与彩色图像恢复任务上的实验表明，该方法持续优于代表性模型基方法，性能接近基于隐式正则化的最先进DEQ模型，且所需可训练参数显著更少。
原文摘要 · Abstract (English)
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.
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