  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.
