Convergence and resolution recovery of block-iterative EM algorithms modeling 3D detector response in SPECT

We evaluate fast reconstruction algorithms including ordered subsets- EM (OS-EM) and Rescaled Block Iterative EM (RBI-EM) in fully 3D SPECT applications on the basis of their convergence and resolution recovery properties as iterations proceed. Using a 3D computer-simulated phantom consisting of 3D Gaussian objects, we simulated projection data that includes only the effects of sampling and detector response of a parallel-hole collimator. Reconstructions were performed using each of the three algorithms (ML-EM, OS-EM, and RBI-EM) modeling the 3D detector response in the projection function. Resolution recovery was evaluated by fitting Gaussians to each of the four objects in the iterated image estimates at selected intervals. Results show that OS-EM and RBI-EM behave identically in this case; their resolution recovery results are virtually indistinguishable. Their resolution behavior appears to be very similar to that of ML-EM, but accelerated by a factor of twenty. For all three algorithms, smaller objects take more iterations to converge. Next, we consider the effect noise has on convergence. For both noise-free and noisy data, we evaluate the log likelihood function at each subiteration of OS-EM and RBI-EM, and at each iteration of ML-EM. With noisy data, both OS-EM and RBI-EM give results for which the log-likelihood function oscillates. Especially for 180-degree acquisitions, RBI-EM oscillates less than OS-EM. Both OS-EM and RBI-EM appear to converge to solutions, but not to the ML solution. We conclude that both OS-EM and RBI-EM can be effective algorithms for fully 3D SPECT reconstruction. Both recover resolution similarly to ML-EM, only more quickly.