NOISE PROPERTIES OF THE EM ALGORITHM .2. MONTE-CARLO SIMULATIONS

In an earlier paper we derived a theoretical formulation for estimatin g the statistical properties of images reconstructed using the iterati ve ML-EM algorithm. To gain insight into this complex problem, two lev els of approximation were considered in the theory. These techniques r evealed the dependence of the variance and covariance of the reconstru cted image noise on the source distribution, imaging system transfer f unction, and iteration number. In this paper a Monte Carlo approach wa s taken to study the noise properties of the ML-EM algorithm and to te st the predictions of the theory. The study also served to evaluate th e approximations used in the theory. Simulated data from phantoms were used in the Monte Carlo experiments. The ML-EM statistical properties were calculated from sample averages of a large number of images with different noise realizations. The agreement between the more exact fo rm of the theoretical formulation and the Monte Carlo formulation was better than 10% in most cases examined, and for many situations the ag reement was within the expected error of the Monte Carlo experiments. Results from the studies provide valuable information about the noise characteristics of ML-EM reconstructed images. Furthermore, the studie s demonstrate the power of the theoretical and Monte Carlo approaches for investigating noise properties of statistical reconstruction algor ithms.