Learning Gradually Non-convex Image Priors Using Score Matching

TL;DR

This paper introduces a unified framework for denoising score-based models using graduated non-convex energy minimization, enabling robust image prior learning and improved inverse problem solving.

Contribution

It presents a novel framework connecting score-based models with graduated non-convexity, and applies it to learn generalized Fields of Experts image priors.

Findings

Energy becomes convex at high noise variance

Priors facilitate fast, robust inverse problem solutions

Framework unifies denoising and non-convex optimization

Abstract

In this paper, we propose a unified framework of denoising score-based models in the context of graduated non-convex energy minimization. We show that for sufficiently large noise variance, the associated negative log density -- the energy -- becomes convex. Consequently, denoising score-based models essentially follow a graduated non-convexity heuristic. We apply this framework to learning generalized Fields of Experts image priors that approximate the joint density of noisy images and their associated variances. These priors can be easily incorporated into existing optimization algorithms for solving inverse problems and naturally implement a fast and robust graduated non-convexity mechanism.