Title :
Noise characterization of block-iterative reconstruction algorithms: II. Monte Carlo simulations
Author :
Soares, Edward J. ; Glick, Stephen J. ; Hoppin, John W.
Author_Institution :
Univ. of Massachusetts Med. Sch., Worcester, MA, USA
Abstract :
In Soares et al. (2000), the ensemble statistical properties of the rescaled block-iterative expectation-maximization (RBI-EM) reconstruction algorithm and rescaled block-iterative simultaneous multiplicative algebraic reconstruction technique (RBI-SMART) were derived. Included in this analysis were the special cases of RBI-EM, maximum-likelihood EM (ML-EM) and ordered-subset EM (OS-EM), and the special case of RBI-SMART, SMART. Explicit expressions were found for the ensemble mean, covariance matrix, and probability density function of RBI reconstructed images, as a function of iteration number. The theoretical formulations relied on one approximation, namely that the noise in the reconstructed image was small compared to the mean image. We evaluate the predictions of the theory by using Monte Carlo methods to calculate the sample statistical properties of each algorithm and then compare the results with the theoretical formulations. In addition, the validity of the approximation will be justified.
Keywords :
Monte Carlo methods; covariance matrices; image reconstruction; maximum likelihood estimation; medical image processing; Monte Carlo simulations; covariance matrix; maximum-likelihood expectation-maximum; noise characterization; ordered-subset expectation-maximum; probability density function; rescaled block-iterative expectation-maximization reconstruction; rescaled block-iterative simultaneous multiplicative algebraic reconstruction; Blood; Cancer; Computer science; Covariance matrix; Heart; Image reconstruction; Lungs; Mathematics; Probability density function; Reconstruction algorithms; Covariance matrix; maximum-likelihood expectation-maximization; noise characterization; ordered subsets; rescaled block-iterative image reconstruction; simultaneous multiplicative algebraic reconstruction technique; Algorithms; Artificial Intelligence; Computer Simulation; Image Enhancement; Image Interpretation, Computer-Assisted; Information Storage and Retrieval; Models, Biological; Models, Statistical; Reproducibility of Results; Sensitivity and Specificity; Stochastic Processes;
Journal_Title :
Medical Imaging, IEEE Transactions on
DOI :
10.1109/TMI.2004.836876
