Learning Gradually Non-convex Image Priors Using Score Matching
This work addresses the challenge of non-convex optimization in image processing for researchers and practitioners, though it appears incremental as it builds on existing denoising score-based models and graduated non-convexity heuristics.
The paper tackles the problem of learning image priors for inverse problems by proposing a unified framework that links denoising score-based models to graduated non-convex energy minimization, showing that the energy becomes convex for large noise variance. The result is a method that enables fast and robust graduated non-convexity, applicable to existing optimization algorithms.
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.