Non-convex image reconstruction via Expectation Propagation

Abstract

Tomographic image reconstruction can be mapped to a problem of finding solutions to a large system of linear equations which maximize a function that includes \textit{a priori} knowledge regarding features of typical images such as smoothness or sharpness. This maximization can be performed with standard local optimization tools when the function is concave, but it is generally intractable for realistic priors, which are non-concave. We introduce a new method to reconstruct images obtained from Radon projections by using Expectation Propagation, which allows us to reframe the problem from an Bayesian inference perspective. We show, by means of extensive simulations, that, compared to state-of-the-art algorithms for this task, Expectation Propagation paired with very simple but non log-concave priors, is often able to reconstruct images up to a smaller error while using a lower amount of information per pixel. We provide estimates for the critical rate of information per pixel above which recovery is error-free by means of simulations on ensembles of phantom and real images.

arXiv comment12 pages, 6 figures

References in corpus (7)

• Spike and slab variable selection: Frequentist and Bayesian strategies
• Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT
• Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence (2001)
• Cluster Variation Method in Statistical Physics and Probabilistic Graphical Models
• How to Compute Loop Corrections to Bethe Approximation
• Loop expansion around the Bethe-Peierls approximation for lattice models
• Belief Propagation Reconstruction for Discrete Tomography

Cited by in corpus (2)

• Fast Scalable Image Restoration using Total Variation Priors and Expectation Propagation
• Compressed sensing reconstruction using Expectation Propagation