Compressive Computed Tomography Reconstruction through Denoising Approximate Message Passing

Alessandro Perelli, Michael Lexa, Ali Can, Mike E. Davies

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Abstract

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 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 the Poisson nonlinear noise model are treated separately, exploiting the existence of efficient preconditioners for the former and the generalized noise modeling 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.
Original languageEnglish
JournalSIAM Journal on Imaging Sciences
Volume13
Issue number4
Pages (from-to)1860-1897
ISSN1936-4954
DOIs
Publication statusPublished - 2020

Keywords

  • X-ray Computed Tomography
  • Compressed Sensing
  • Approximate Message Passing
  • Image denoising
  • Preconditioning
  • Iterative algorithms

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