Empirical Bayesian Imaging with Large-Scale Push-Forward Generative Priors

S. Melidonis, M. Holden, Y. Altmann, M. Pereyra, K. C. Zygalakis

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Abstract

We propose a new methodology for leveraging deep generative priors for Bayesian inference in imaging inverse problems. Modern Bayesian imaging often relies on score-based diffusion generative priors, which deliver remarkable point estimates but significantly underestimate uncertainty. Push-forward models such as variational auto-encoders and generative adversarial networks provide a robust alternative, leading to Bayesian models that are provably well-posed and which produce accurate uncertainty quantification results for small problems. However, push-forward models scale poorly to large problems because of issues related to bias, mode collapse and multimodality. We propose to address this difficulty by embedding a conditional deep generative prior within an empirical Bayesian framework. We consider generative priors with a super-resolution architecture, and perform inference by using a Bayesian computation strategy that simultaneously computes the maximum marginal likelihood estimate (MMLE) of the low-resolution image of interest, and draws Monte Carlo samples from the posterior distribution of the high-resolution image, conditionally to the observed data and the MMLE. The methodology is demonstrated with an image deblurring experiment and comparisons with the state-of-the-art.

Original languageEnglish
Pages (from-to)631-635
Number of pages5
JournalIEEE Signal Processing Letters
Volume31
Early online date2 Feb 2024
DOIs
Publication statusPublished - 2024

Keywords

  • Bayes methods
  • Bayesian inference
  • computational imaging
  • deep generative models
  • Estimation
  • Imaging
  • inverse problems
  • Markov chain Monte Carlo
  • Monte Carlo methods
  • Optimization
  • stochastic optimisation
  • Superresolution
  • Uncertainty
  • uncertainty quantification

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering
  • Applied Mathematics

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