I mentioned their work a while back when they were presenting how a BP algorithm (or AMP) could be leveraged into devising a reconstruction for CT. Here is the paper and the attendant implementation: Belief Propagation Reconstruction for Discrete Tomography by Emmanuelle Gouillart, Florent Krzakala, Marc Mezard, Lenka Zdeborová. The abstract reads:

We consider the reconstruction of a two-dimensional discrete image from a set of tomographic measurements corresponding to the Radon projection. Assuming that the image has a structure where neighbouring pixels have a larger probability to take the same value, we follow a Bayesian approach and introduce a fast message-passing reconstruction algorithm based on belief propagation. For numerical results, we specialize to the case of binary tomography. We test the algorithm on binary synthetic images with different length scales and compare our results against a more usual convex optimization approach. We investigate the reconstruction error as a function of the number of tomographic measurements, corresponding to the number of projection angles. The belief propagation algorithm turns out to be more efficient than the convex-optimization algorithm, both in terms of recovery bounds for noise-free projections, and in terms of reconstruction quality when Gaussian noise is added to the projections.

I note from the paper:

Note that this algorithm is of the embarrassingly parallel type, since each line µ can be handled separately when computing line 7 in the above pseudo-code. This could be used to speed up the algorithm by solving each line separately on diﬀerent cores

An implementation of this algorithm is available on Github here. Three weeks ago, this group advertized for two postdocs.

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