Convergence analysis of an accelerated expectation‐maximization algorithm for ill‐posed integral equations

Abstract

The maximum-likelihood expectation-maximization (EM) algorithm has attracted considerable interest in single-photon emission computed tomography, because it produces superior images in addition to be being flexible, simple, and allowing a physical interpretation. However, it often needs a large number of calculations because of the algorithm's slow rate of convergence. Therefore, there is a large body of literature concerning the EM algorithm's acceleration. One of the accelerated means is increasing an overrelaxation parameter, whereas we have not found any analysis in this method that would provide an immediate answer to the questions of the convergence. In this paper, our main focus is on the continuous version of an accelerated EM algorithm based on Lewitt and Muehllenner. We extend their conclusions to the infinitedimensional space and interpret and analyze the convergence of the accelerated EM algorithm. We also obtain some new properties of the modified algorithm.

On inversion and Sobolev estimate results about the weighted Radon transform

“…Nowadays, the SPECT algorithms can be divided into analytical methods [4][5][6] and iterative techniques. [7][8][9][10][11] On one hand, the latter can exactly reconstruct the object-function image depending on nonuniform projection data, but the calculation is so huge and takes much longer time. Therefore, there is something defective in iterative techniques.…”