Mean-variance analysis of block-iterative reconstruction algorithms modeling 3D detector response in SPECT

The authors study the statistical convergence properties of two fast iterative reconstruction algorithms, the rescaled block-iterative (RBI) and ordered subset (OS) EM algorithms, in the context of cardiac SPECT with 3D detector response modeling. The Monte Carlo method was used to generate nearly noise-free projection data modeling the effects of attenuation, detector response, and scatter from the MCAT phantom. One thousand noise realizations were generated with an average count level approximating a typical Tl-201 cardiac study. Each noise realization was reconstructed using the RBI and OS algorithms for cases with and without detector response modeling. For each iteration up to twenty, the authors generated mean and variance images, as well as covariance images for six specific locations. Both OS and RBI converged in the mean to results that were not significantly different from the noise-free ML-EM result using the same projection model. When detector response was not modeled in the reconstruction, RBI exhibited considerably lower noise variance than OS for the same resolution. When 3D detector response was modeled, the two algorithms provided the same noise variance to resolution recovery tradeoff, while OS required about half the number of iterations of RBI to reach the same point. The authors conclude that OS is faster than RBI, but may be sensitive to errors in the projection model. Both OS-EM and RBI-EM are effective alternatives to the ML-EM algorithm, but noise level and speed of convergence depend on the projection model used