The ML-EM Algorithm is Not Optimal for Poisson Noise

The ML-EM (maximum likelihood expectation maximization) algorithm is the most popular image reconstruction method when the measurement noise is Poisson distributed. This short paper considers the problem that for a given noisy projection data set, whether the ML-EM algorithm is able to provide an ap...

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Bibliographic Details
Published in:IEEE transactions on nuclear science Vol. 62; no. 5; pp. 2096 - 2101
Main Author: Zeng, Gengsheng L.
Format: Journal Article
Language:English
Published: New York IEEE 01.10.2015
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Approximation algorithms
Bayesian analysis
Computed tomography
Estimating techniques
expectation maximization (EM)
Image reconstruction
iterative reconstruction
maximum likelihood (ML)
Noise
Noise level
Noise measurement
noise weighted image reconstruction
Phantoms
Poisson noise
Positron emission tomography
positron emission tomography (PET)
single photon emission computed tomography (SPECT)
ISSN:0018-9499, 1558-1578
Online Access:Get full text
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Summary:The ML-EM (maximum likelihood expectation maximization) algorithm is the most popular image reconstruction method when the measurement noise is Poisson distributed. This short paper considers the problem that for a given noisy projection data set, whether the ML-EM algorithm is able to provide an approximate solution that is close to the true solution. It is well-known that the ML-EM algorithm at early iterations converges towards the true solution and then in later iterations diverges away from the true solution. Therefore a potential good approximate solution can only be obtained by early termination. This short paper argues that the ML-EM algorithm is not optimal in providing such an approximate solution. In order to show that the ML-EM algorithm is not optimal, it is only necessary to provide a different algorithm that performs better. An alternative algorithm is suggested in this paper and this alternative algorithm is able to outperform the ML-EM algorithm.
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ISSN:0018-9499
1558-1578
DOI:10.1109/TNS.2015.2475128