Regularizing Inverse Problems with Generative Models
Martin Zach, Technische Universität Graz

Meeting • 2024-03-04

Abstract
From a Bayesian point of view, the optimization problems encountered in regularized inverse problems can be interpreted as maximizing a posterior distribution comprised of a likelihood and a prior distribution. Generative models, which aim to learn a reference distribution from samples, have recently made remarkable advances. In this talk, we show how we can utilize the prior information encoded in these models to solve inverse problems. In particular, we focus on energy-based and diffusion models and show applications to computed tomography and magnetic resonance imaging. Further, we present a novel learning paradigm for diffusion models, which utilizes models that obey the heat diffusion equation exactly. Due to the construction, we can use one learned model for noise estimation and blind heteroscedastic denoising. Quantitative denoising results are promising while the networks remain small and interpretable. Finally, we discuss open research questions.