### An Efficient Implementation of the Iterative ML-EM Image Reconstruction Algorithm for PET on a Pentium PC Platform

#### Abstract

The EM (Expectation-Maximization) algorithm is becoming more and more popular as a solution to the image reconstruction problem in Positron Emission Tomography (PET). However, as an iterative method, it shows high computational cost in terms of the time required to complete the reconstruction procedure and the computer memory needed (main memory and disk space) for the storage of the weight coefficients (probability matrix). These were the main problems, which impeded the practical application of this promising method in the modern PET units. In principle, the conventional filtered backprojection algorithms are still in use, although the EM algorithm and the other maximum likelihood estimation (MLE) techniques of the same kind have been known and extensively studied during the past 15 years. An efficient implementation of the ML-EM algorithm is presented here, for a low-cost PC Pentium platform running Windows NT, which can be applied to any PET system configuration, without major modifications. For the first time an iterative reconstruction algorithm for emission tomography is brought down to the PC level. A detailed description of the implementation of the algorithm is given here. Emphasis is given on the calculation of the transition (probability) matrix and its efficient implementation using sparse matrix techniques. A practically feasible implementation of the EM algorithm is the final result of this work, with optimal performance on the common PC systems available today and producing tomographic reconstruction in clinically meaningful times. The implementation of the various methods proposed to further improve the results obtained by the EM algorithm, such as acceleration methods (i.e., ordered-subsets EM), and other Bayesian, maximum entropy, etc., reconstruction techniques can be also developed and performed following the same principles described here.

#### Keywords

Positron Emission Tomography, Image Reconstruction, Maximum Likelihood Estimation, Expectation Maximization (EM) Algorithm, Sparse Matrix, PC Pentium

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