Non-convex image reconstruction via Expectation Propagation

TL;DR

This paper presents a novel Expectation Propagation method for non-convex image reconstruction from Radon projections, outperforming existing algorithms in accuracy and efficiency by leveraging Bayesian inference with simple priors.

Contribution

Introduces a new Expectation Propagation approach for non-convex image reconstruction, enabling better accuracy with less information compared to state-of-the-art methods.

Findings

EP achieves lower reconstruction error than existing algorithms.

Reconstruction quality improves with less information per pixel.

Critical information rate for error-free recovery is estimated.

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.