Bayesian Inversion for Nonlinear Imaging Models using Deep Generative Priors

Most modern imaging systems incorporate a computational pipeline to infer the image of interest from acquired measurements. The Bayesian approach for solving such ill-posed inverse problems involves the characterization of the posterior distribution of the image. This depends on the model of the imaging system and prior knowledge on the image of interest. In this work, we present a Bayesian reconstruction framework for nonlinear imaging models, where the prior knowledge on the image is specified by a deep generative model. We develop a tractable posterior sampling scheme based on the Metropolis-adjusted Langevin algorithm (MALA) for the class of nonlinear inverse problems where the forward model has a neural-network-like structure. This class includes most practical imaging modalities. We introduce the notion of augmented deep generative priors 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.