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 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...

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Bibliographic Details
Published in:IEEE transactions on computational imaging 2022-01, Vol.8, p.1-15
Main Authors: Bohra, Pakshal, Pham, Thanh-an, Dong, Jonathan, Unser, Michael
Format: Article
Language:English
Subjects:
Algorithms
Bayes methods
Bayesian analysis
Bayesian inference
Computational modeling
deep learning
generative adversarial networks
generative models
Image acquisition
Image reconstruction
Imaging
Inverse problems
Neural networks
nonlinear inverse problems
Optical diffraction
optical diffraction tomography
Phase retrieval
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Summary: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.
ISSN:2573-0436
2333-9403
DOI:10.1109/TCI.2023.3236155