Noise analysis of MAP - EM algorithms for emission tomography

• Published in: Physics in medicine & biology Vol. 42; no. 11; pp. 2215 - 2232
• Main Authors: Wang, Wenli, Gindi, Gene
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01.11.1997; Institute of Physics
• Subjects: Algorithms; Biological and medical sciences; Gamma Rays; Image Processing, Computer-Assisted - methods; Investigative techniques, diagnostic techniques (general aspects); Likelihood Functions; Medical sciences; Miscellaneous. Technology; Models, Theoretical; Monte Carlo Method; Radionuclide investigations; Reproducibility of Results; Signal Processing, Computer-Assisted; Tomography, Emission-Computed - methods; Radionuclide study; Image quality; Monte Carlo method; Theoretical model; Propagation; Photon noise; Bias; Technique; Algorithm analysis; Comparative study; Image reconstruction; Emission tomography
• ISSN: 0031-9155; 1361-6560
• DOI: 10.1088/0031-9155/42/11/015

The ability to theoretically model the propagation of photon noise through PET and SPECT tomographic reconstruction algorithms is crucial in evaluating the reconstructed image quality as a function of parameters of the algorithm. In a previous approach for the important case of the iterative ML-EM (maximum-likelihood-expectation-maximization) algorithm, judicious linearizations were used to model theoretically the propagation of a mean image and a covariance matrix from one iteration to the next. Our analysis extends this approach to the case of MAP (maximum a posteriori)-EM algorithms, where the EM approach incorporates prior terms. We analyse in detail two cases: a MAP-EM algorithm incorporating an independent gamma prior, and a one-step-late (OSL) version of a MAP-EM algorithm incorporating a multivariate Gaussian prior, for which familiar smoothing priors are special cases. To validate our theoretical analyses, we use a Monte Carlo methodology to compare, at each iteration, theoretical estimates of mean and covariance with sample estimates, and show that the theory works well in practical situations where the noise and bias in the reconstructed images do not assume extreme values.