Bayesian Inversion for Nonlinear Imaging Models using Deep Generative Priors
This work addresses the challenge of solving ill-posed inverse problems in imaging for applications like medical or scientific imaging, though it is incremental as it builds on existing deep generative and sampling methods.
The authors tackled the problem of Bayesian inversion for nonlinear imaging models by developing a posterior-sampling scheme using deep generative priors, achieving improved reconstruction results in phase retrieval and optical diffraction tomography.
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.