  X-ray Computed Tomography (CT) reconstruction from a sparse number of views
is a useful way to reduce either the radiation dose or the acquisition time,
for example in fixed-gantry CT systems, however this results in an ill-posed
inverse problem whose solution is typically computationally demanding.
Approximate Message Passing (AMP) techniques represent the state of the art for
solving under-sampling Compressed Sensing problems with random linear
measurements but there are still not clear solutions on how AMP should be
modified and how it performs with real world problems. This paper investigates
the question of whether we can employ an AMP framework for real sparse view CT
imaging? The proposed algorithm for approximate inference in tomographic
reconstruction incorporates a number of advances from within the AMP community,
resulting in the Denoising Generalized Approximate Message Passing CT algorithm
(D-GAMP-CT). Specifically, this exploits the use of sophisticated image
denoisers to regularize the reconstruction. While in order to reduce the
probability of divergence the (Radon) system and Poisson non-linear noise model
are treated separately, exploiting the existence of efficient preconditioners
for the former and the generalized noise modelling in GAMP for the latter.
Experiments with simulated and real CT baggage scans confirm that the
performance of the proposed algorithm outperforms statistical CT optimization
solvers.
