A joint row and column action method for cone-beam computed tomography

Abstract

The inversion of linear systems is fundamental in Computed Tomography (CT) reconstruction. Computational challenges arise when trying to invert large linear systems, as limited computing resources mean that only part of the system can be kept in computer memory at any one time. In linear tomographic inversion problems such as x-ray tomography, even a standard scan can produce millions of individual measurements and the reconstruction of x-ray attenuation profiles typically requires the estimation of a million attenuation coefficients. To deal with the large data sets encountered in real applications and to efficiently utilise modern graphics processing unit (GPU) based computing architectures, combinations of iterative reconstruction algorithms and parallel computing schemes are increasingly applied. Whilst different parallel methods have been proposed, individual computations currently need to access either the entire set of observations or estimated x-ray absorptions, which can be prohibitive in many realistic applications. We present a fully parallelizable CT image reconstruction algorithm where each computation node works on arbitrary partial subsets of the data and the reconstructed volume. We further develop a non-homogeneously randomised selection criteria which guarantees that sub-matrices of the system matrix are selected more frequently if they are dense, thus maximising information flow through the algorithm. We compare our algorithm with block alternating direction method of multipliers (block ADMM) and show that our method is significantly faster for CT reconstruction.

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Identifiers

ORCID for Thomas Blumensath: orcid.org/0000-0002-7489-265X

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