A geometry-based deep equilibrium model for image restoration under multiplicative Gamma noise

2026-08-05

AI Summary

This work addresses the problem of image restoration under multiplicative Gamma noise and blur degradation by proposing a deep equilibrium model that integrates explicit geometric priors. Instead of implicit neural regularization, the method incorporates surface area and mean curvature as explicit geometric regularizers within a variational framework, which is solved via a mirror descent algorithm. Leveraging Kurdyka–Łojasiewicz property analysis, the approach guarantees global convergence of the iterative sequence. Experimental results demonstrate that the proposed model significantly outperforms conventional model-based methods on both grayscale and color image restoration tasks, achieving performance comparable to larger implicit deep equilibrium models while offering enhanced interpretability and computational efficiency.

Abstract

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.

Problem

• image restoration
• multiplicative Gamma noise
• blur
• deep equilibrium model

Innovation

• deep equilibrium model
• geometric priors
• multiplicative Gamma noise
• mirror descent
• variational image restoration