Methods of least squares and SIRT in reconstruction

Abstract

In this paper we show that a particular version of the Simultaneous Iterative Reconstruction Technique (SIRT) proposed by Gilbert in 1972 strongly resembles the Richardson least-squares algorithm. By adopting the adjustable parameters of the general Richardson algorithm, we have been able to produce generalized SIRT algorithms with improved convergence. A particular generalization of the SIRT algorithm, GSIRT, has an adjustable parameter σ and the starting picture ρ 0 as input. A value 1 2 for σ and a weighted back-projection for ρ 0 produce a stable algorithm. We call the SIRT-like algorithms for the solution of the weighted leastsquares problems LSIRT and present two such algorithms, LSIRT1 and LSIRT2, which have definite computational advantages over SIRT and GSIRT. We have tested these methods on mathematically simulated phantoms and find that the new SIRT methods converge faster than Gilbert's SIRT but are more sensitive to noise present in the data. However, the faster convergence rates allow termination before the noise contribution degrades the reconstructed image excessively.