Noise characterization of block-iterative reconstruction algorithms: I. Theory

Researchers have shown increasing interest in block-iterative image reconst ruction algorithms due to the computational and modeling advantages they pr ovide. Although their convergence properties have been well documented, lit tle is known about how they behave in the presence of noise. In this work, we fully characterize the ensemble statistical properties of the rescaled b lock-iterative expectation-maximization (RBI-EM) reconstruction algorithm a nd the rescaled block-iterative simultaneous multiplicative algebraic recon struction technique (RBI-SMART). Also included in the analysis are the spec ial cases of RBI-EM, maximum-likelihood EM (ML-EM) and ordered-subset EM (O S-EM), and the special case of RBI-SMART, SMART, A theoretical formulation strategy similar to that previously outlined for ML-EM is followed for the RBI methods. The theoretical formulations in this paper rely on one approxi mation, namely, that the noise in the reconstructed image is small compared to the mean image. In a second paper, the approximation will be justified through Monte Carlo simulations covering a range of noise levels, iteration points, and subset orderings. The ensemble statistical parameters could th en be used to evaluate objective measures of image quality.