Evaluation of OS-EM vs ML-EM for 1D, 2D and fully 3D SPECT reconstruction

For SPECT reconstruction, iterative Maximum Likelihood Expectation Maximization (ML-EM) estimation has a huge computational burden. The objective of this paper is to compare images obtained by ML-EM and an EM algorithm acting on Ordered Subsets of projections (OS-EM). Two digital phantoms, a cylinder with two cold spots and an ellipsoid with several hot spots and one cold spot were reconstructed from 120 simulated noisy projections. 1D (delta-like point source response), 2D (single slice response) and fully 3D reconstruction were investigated. Three quantities were calculated for the evaluation, viz. contrast, normalized standard deviation and mean squared error. In the case of fully 3D reconstruction, OS-EM 60 reconstructions (i.e., using 60 ordered subsets) were very close to ML-EM reconstructions. This shows that the OS-EM algorithm is an extremely fast and efficient method to accelerate iterative SPECT reconstruction with speed-up factors of close to half the number of projections.