FiRe: Fixed-points of Restoration Priors for Solving Inverse Problems

2024-11-28

arXiv.org

AI Summary

In imaging inverse problems, effectively leveraging restoration models as priors to compensate for information loss in measurements remains a fundamental challenge. This paper proposes FiRe (Fixed-point-based Recovery prior), a novel framework that formally defines natural images as fixed points of the composition of degradation and restoration operators—yielding an analytically tractable and differentiable implicit prior. FiRe explicitly integrates general-purpose, pre-trained restoration networks (e.g., for deblurring or super-resolution) into Plug-and-Play (PnP) optimization, enabling multi-model ensembling and joint acquisition-aware optimization. Extensive experiments on computed tomography (CT) reconstruction and phase retrieval demonstrate that FiRe consistently outperforms conventional denoising-based PnP methods. These results validate restoration models as effective, generalizable, and theoretically consistent generalized image priors—bridging the gap between learned models and principled optimization.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

Selecting an appropriate prior to compensate for information loss due to the measurement operator is a fundamental challenge in imaging inverse problems. Implicit priors based on denoising neural networks have become central to widely-used frameworks such as Plug-and-Play (PnP) algorithms. In this work, we introduce Fixed-points of Restoration (FiRe) priors as a new framework for expanding the notion of priors in PnP to general restoration models beyond traditional denoising models. The key insight behind FiRe is that natural images emerge as fixed points of the composition of a degradation operator with the corresponding restoration model. This enables us to derive an explicit formula for our implicit prior by quantifying invariance of images under this composite operation. Adopting this fixed-point perspective, we show how various restoration networks can effectively serve as priors for solving inverse problems. The FiRe framework further enables ensemble-like combinations of multiple restoration models as well as acquisition-informed restoration networks, all within a unified optimization approach. Experimental results validate the effectiveness of FiRe across various inverse problems, establishing a new paradigm for incorporating pretrained restoration models into PnP-like algorithms.

Problem

• Expanding priors in Plug-and-Play beyond denoising models
• Deriving explicit formula for implicit priors via fixed-points
• Enabling ensemble combinations of restoration models

Innovation

• Fixed-points of Restoration (FiRe) priors framework
• Expands priors beyond traditional denoising models
• Unified optimization with ensemble restoration models