Globally convergent algorithms for maximum a posteriori transmission tomography

Author

Lange, Kenneth ; Fessler, Jeffrey A.

Author_Institution

Dept. of Biostat., Michigan Univ., Ann Arbor, MI, USA

Volume

4

Issue

10

fYear

1995

fDate

10/1/1995 12:00:00 AM

Firstpage

1430

Lastpage

1438

Abstract

This paper reviews and compares three maximum likelihood algorithms for transmission tomography. One of these algorithms is the EM algorithm, one is based on a convexity argument devised by De Pierro (see IEEE Trans. Med. Imaging, vol.12, p.328-333, 1993) in the context of emission tomography, and one is an ad hoc gradient algorithm. The algorithms enjoy desirable local and global convergence properties and combine gracefully with Bayesian smoothing priors. Preliminary numerical testing of the algorithms on simulated data suggest that the convex algorithm and the ad hoc gradient algorithm are computationally superior to the EM algorithm. This superiority stems from the larger number of exponentiations required by the EM algorithm. The convex and gradient algorithms are well adapted to parallel computing

Keywords

Bayes methods; convergence of numerical methods; emission tomography; image reconstruction; maximum likelihood estimation; medical image processing; smoothing methods; Bayesian smoothing priors; EM algorithm; convex algorithm; convexity argument; emission tomography; exponentiations; global convergence; globally convergent algorithms; gradient algorithm; image reconstruction; local convergence; maximum a posteriori transmission tomography; maximum likelihood algorithms; numerical testing; parallel computing; simulated data; Attenuation; Bayesian methods; Convergence; Image reconstruction; Maximum likelihood estimation; Object detection; Smoothing methods; Stochastic processes; Testing; Tomography;

fLanguage

English

Journal_Title

Image Processing, IEEE Transactions on

Publisher

ieee

ISSN

1057-7149

Type

jour

DOI

10.1109/83.465107

Filename

465107