Compressive Computed Tomography Reconstruction through Denoising Approximate Message Passing

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 undersampling 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 Generalised Approximate Message Passing CT algorithm (D-GAMP-CT). Specifically, this exploits the use of sophisticated image denoisers to regularise the reconstruction. While in order to reduce the probability of divergence the (Radon) system and Poission non-linear noise model are treated separately, exploiting the existence of efficient preconditioners for the former and the generalised 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 optimisation solvers.