Denoising Message Passing for X-ray Computed Tomography Reconstruction

X-ray Computed Tomography (CT) reconstruction from sparse number of views is becoming a powerful way to reduce either the radiation dose or the acquisition time in CT systems but still requires a huge computational time. This paper introduces an approximate Bayesian inference framework for CT reconstruction based on a family of denoising approximate message passing (DCT-AMP) algorithms able to improve both the convergence speed and the reconstruction quality. Approximate Message Passing for Compressed Sensing has been extensively analysed for random linear measurements but there are still not clear solutions on how AMP should be modified and how it performs with real world problems. In particular to overcome the convergence issues of DCT-AMP with structured measurement matrices, we propose a disjoint preconditioned version of the algorithm tailored for both the geometric system model and the noise model. In addition the Bayesian DCT-AMP formulation allows to measure how the current estimate is close to the prediction by analysing the state evolution. This work aims to provide a proof of concept to demonstrate that approximate Bayesian reconstruction algorithms can be tailored for ill conditioned, underdetermined real problems such CT imaging. Experiments with simulated and real CT baggage scans confirm that the performance of the proposed algorithms are comparable and can even outperform traditional statistical X-ray CT reconstruction optimization solvers.