Combining ordered subsets and momentum for accelerated x ray ct image reconstruction

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COMBINING ORDERED SUBSETS AND MOMENTUM FOR ACCELERATED X-RAY
CT IMAGE RECONSTRUCTION
ABSTRACT
Statistical X-ray computed tomography (CT) reconstructioncan improve image quality
from reduced dose scans,but requires very long computation time. Ordered subsets (OS)methods
have been widely used for research in X-ray CT statisticalimage reconstruction (and are used in
clinical PET and SPECTreconstruction). In particular, OS methods based on separablequadratic
surrogates (OS-SQS) are massively parallelizable andare well suited tomodern computing
architectures, but the numberof iterations required for convergence should be reduced for
betterpractical use. This paper introduces OS-SQS-momentum algorithms that combine
Nesterov’s momentum techniques with OS-SQS methods, greatly improving convergence speed
in earlyiterations. If the number of subsets is too large, the OS-SQS-momentummethods can be
unstable, so we propose diminishing stepsizes that stabilize the method while preserving the very
fast convergencebehavior. Experiments with simulated and real 3D CTscan data illustrate the
performance of the proposed algorithms.

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