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Most modern imaging systems incorporate a computational pipeline to infer theimage of interest from acquired measurements. The Bayesian approach to solvesuch ill-posed inverse problems involves the characterization of the posteriordistribution of the image. It depends on the model of the imaging system and onprior knowledge on the image of interest. In this work, we present a Bayesianreconstruction framework for nonlinear imaging models where we specify theprior knowledge on the image through a deep generative model. We develop atractable posterior-sampling scheme based on the Metropolis-adjusted Langevinalgorithm for the class of nonlinear inverse problems where the forward modelhas a neural-network-like structure. This class includes most practical imagingmodalities. We introduce the notion of augmented deep generative priors inorder to suitably handle the recovery of quantitative images.We illustrate theadvantages of our framework by applying it to two nonlinear imagingmodalities-phase retrieval and optical diffraction tomography.

Bayesian Inversion for Nonlinear Imaging Models using Deep Generative Priors