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X-ray Computed Tomography (CT) reconstruction from a sparse number of viewsis 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-posedinverse problem whose solution is typically computationally demanding.Approximate Message Passing (AMP) techniques represent the state of the art forsolving under-sampling Compressed Sensing problems with random linearmeasurements but there are still not clear solutions on how AMP should bemodified and how it performs with real world problems. This paper investigatesthe question of whether we can employ an AMP framework for real sparse view CTimaging? The proposed algorithm for approximate inference in tomographicreconstruction 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 imagedenoisers to regularize the reconstruction. While in order to reduce theprobability of divergence the (Radon) system and Poisson non-linear noise modelare treated separately, exploiting the existence of efficient preconditionersfor the former and the generalized noise modelling in GAMP for the latter.Experiments with simulated and real CT baggage scans confirm that theperformance of the proposed algorithm outperforms statistical CT optimizationsolvers.

Compressive Computed Tomography Reconstruction through Denoising Approximate Message Passing