A generalization of Green´s one-step-late algorithm for penalized ML reconstruction of PET images

Green´s one-step-late (OSL) algorithm is gaining importance as an algorithm for the motion-compensated reconstruction of cardiac images. However, the original OSL algorithm does not converge, so various modifications have been made to mitigate this problem. In this paper we propose and test a modification of the OSL algorithm. The algorithm includes a new line search method which (unlike a previous method), results in a convergent sequence of positive iterates without any conditions on the size of the penalty parameter. Our simulations indicate that algorithm used to determine the step size in the line search has a significant effect on the speed of convergence of the new algorithm. Two line search algorithms are tested: an exact line search based on the bisection algorithm and an inexact search using Armijo´s rule. Our simulations showed that the OSL algorithm using the Armijo line search method converged in 25% of the time required for the algorithm based on the bisection method.