Accelerated image reconstruction using ordered subsets of projection data

TLDR

Ordered subsets EM builds on block‑Kaczmarz, SIRT, and MART methods, providing a positivity‑preserving reconstruction linked to EM. The study defines ordered subset processing to accelerate image restoration from projection data using standard algorithms such as EM. The method groups projection data into ordered subsets, iteratively applying EM to each subset in sequence, and is applicable to SPECT and PET. Simulations show OS‑EM accelerates SPECT reconstruction by an order of magnitude while preserving image quality.

Abstract

The authors define ordered subset processing for standard algorithms (such as expectation maximization, EM) for image restoration from projections. Ordered subsets methods group projection data into an ordered sequence of subsets (or blocks). An iteration of ordered subsets EM is defined as a single pass through all the subsets, in each subset using the current estimate to initialize application of EM with that data subset. This approach is similar in concept to block-Kaczmarz methods introduced by Eggermont et al. (1981) for iterative reconstruction. Simultaneous iterative reconstruction (SIRT) and multiplicative algebraic reconstruction (MART) techniques are well known special cases. Ordered subsets EM (OS-EM) provides a restoration imposing a natural positivity condition and with close links to the EM algorithm. OS-EM is applicable in both single photon (SPECT) and positron emission tomography (PET). In simulation studies in SPECT, the OS-EM algorithm provides an order-of-magnitude acceleration over EM, with restoration quality maintained.