  Most modern imaging systems incorporate a computational pipeline to infer the
image of interest from acquired measurements. The Bayesian approach to solve
such ill-posed inverse problems involves the characterization of the posterior
distribution of the image. It depends on the model of the imaging system and on
prior knowledge on the image of interest. In this work, we present a Bayesian
reconstruction framework for nonlinear imaging models where we specify the
prior knowledge on the image through a deep generative model. We develop a
tractable posterior-sampling scheme based on the Metropolis-adjusted Langevin
algorithm 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 the recovery of quantitative images.We illustrate the
advantages of our framework by applying it to two nonlinear imaging
modalities-phase retrieval and optical diffraction tomography.
