Bayesian Inversion for Nonlinear Imaging Models Using Deep Generative Priors

Abstract

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 Metropolisadjusted 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.

Bayesian Inverse Problems Are Usually Well-Posed

“…Especially in Bayesian image reconstruction, the use of neural-network-based, data-driven prior measures has become popular in recent years. The well-posedness of such approaches has been discussed by [10,39,58]. The well-posedness of Bayesian inverse acoustic scattering was studied by [83] in Hellinger and Wasserstein distance, as well as in the Kullback--Leibler divergence.…”