Bayesian Inversion for Nonlinear Imaging Models using Deep Generative Priors

Abstract

Most modern imaging systems involve a computational reconstruction pipeline to infer the image of interest from acquired measurements. The Bayesian reconstruction framework relies on the characterization of the posterior distribution, which depends on a model of the imaging system and prior knowledge on the image, for solving such inverse problems. Here, the choice of the prior distribution is critical for obtaining highquality estimates. In this work, we use deep generative models to represent the prior distribution. We develop a posterior sampling scheme for the class of nonlinear inverse problems where the forward model has a neural-network-like structure. This class includes most existing imaging modalities. We introduce the notion of augmented generative models in order to suitably handle quantitative image recovery. We illustrate the advantages of our framework by applying it to two nonlinear imaging modalities-phase retrieval and optical diffraction tomography.

Phase Retrieval: From Computational Imaging to Machine Learning: A tutorial

“…With this point of view, one can not only produce a point estimate of the unknown signal but also perform a Bayesian sampling of the posterior distribution. This enables the computation of statistical estimates, such as the spatial distribution of the variance of the final image [43].…”