In a previous report we presented a novel ART technique with the projections arranged and accessed in a multilevel scheme (MLS) for efficient algebraic image reconstruction, but whether the scheme is still superior in real situations where the data are noisy is unknown. In this paper, we make a detailed comparison between MLS and the other two conventional projection access orderings in ART: the random permutation scheme (RPS) and the sequential access scheme (SAS). By simulating reconstructions of a human head using different sizes of detector, taking different numbers of projections, each measurement under a different number of photons, a full mapping of the reconstruction accuracy measured by correlation coefficient for the three schemes has been made. Test results demonstrate that one-iteration MLS produces the best reconstruction in many situations. It outperforms one-iteration RPS when the noise level is low. SAS in many cases can never attain the image quality of one-iteration MLS, even with many more iterations. A convergence test using different initial guesses also demonstrates that MLS has less initial dependence. In the Fourier domain, it also represents an efficient and fast implementation of the Fourier slice theorem.
