Fast Bayesian Model Selection in Imaging Inverse Problems Using Residuals

Ana Fernandez Vidal, Marcelo Pereyra, Alain Durmus, Jean-Francois Giovannelli

Research output: Chapter in Book/Report/Conference proceedingConference contribution


This paper presents a fast heuristic for comparing Bayesian models to solve inverse problems related to signal processing. We focus on problems that are convex w.r.t. the unknown signal and where no ground truth is available. The proposed heuristic is very computationally efficient and does not require the estimation of the model evidence. Instead, the model evidence is used indirectly to set the regularisation parameters that define each competing model by maximum marginal likelihood estimation, followed by a simple likelihood-based or residual-based comparison of the models based on their empirical Bayesian maximum-a-posteriori solutions. The proposed methodology is illustrated with a total-variation image deblurring experiment, where it performs remarkably well.

Original languageEnglish
Title of host publication2021 IEEE Statistical Signal Processing Workshop (SSP)
Number of pages5
ISBN (Electronic)9781728157672
Publication statusPublished - 19 Aug 2021
Event21st IEEE Statistical Signal Processing Workshop 2021 - Virtual, Rio de Janeiro, Brazil
Duration: 11 Jul 202114 Jul 2021


Conference21st IEEE Statistical Signal Processing Workshop 2021
Abbreviated titleSSP 2021
CityVirtual, Rio de Janeiro


  • empirical Bayes
  • image processing
  • inverse problems
  • Markov chain Monte Carlo methods
  • Model selection
  • proximal algorithms
  • stochastic optimisation

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Applied Mathematics
  • Signal Processing
  • Computer Science Applications


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