Comparison of the convergence properties of the It-W and OS-EM algorithms in SPECT

Rapid convergence of iterative algorithms is a prerequisite for their clinical use in single-photon emission computed-tomography (SPECT). The rate of convergence of two accelerated methods, It-W (JNM, vol. 34, p. 1793, 1993) and ordered-subset expectation-maximization (OS-EM, IEEE-TMI, vol. 13, p. 601, 1994) were compared using a resolution phantom containing objects of sizes ranging from 1.0 to 2.5 cm. Object contrast was used as a measure of convergence. Attenuation and depth-dependent blur were modeled in the 90-angle projections and during reconstruction. For both methods, convergence was most rapid at the periphery and slowest in the center, with larger (lower frequency) objects converging most rapidly. When assessed under noise-free conditions, It-W converged 8-fold faster than 6-subset OS-EM, and 4-fold faster than 15-subset OS-EM. In an ensemble of 25 noisy images both methods gave essentially identical reconstructions when compared at equivalent noise levels using kernel-sieve regularization, but It-W converged 5 times faster than 15-subset OS-EM. Thus, the It-W method has a significant speed advantage for clinical application of iterative algorithms in SPECT, while retaining the favorable noise properties of the slower OS-FM and ML-EM reconstructions.