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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Veröffentlicht in:IEEE transactions on nuclear science Jg. 62; H. 5; S. 2096 - 2101
1. Verfasser: Zeng, Gengsheng L.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York IEEE 01.10.2015
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
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
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Abstract 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.
AbstractList 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.
Author Zeng, Gengsheng L.
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CitedBy_id crossref_primary_10_1007_s40314_016_0313_0
crossref_primary_10_1016_j_compbiomed_2016_08_006
crossref_primary_10_1016_j_compeleceng_2017_02_014
crossref_primary_10_1093_rpd_ncz095
Cites_doi 10.1109/TMI.1982.4307558
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References langer (ref1) 1984; 8
ref2
zeng (ref3) 2009
References_xml – year: 2009
  ident: ref3
  publication-title: Medical Imaging Reconstruction A Tutorial
– volume: 8
  start-page: 302
  year: 1984
  ident: ref1
  article-title: EM reconstruction algorithms for emission and transmission tomography
  publication-title: J Comp Assist Tomogr
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  doi: 10.1109/TMI.1982.4307558
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Snippet The ML-EM (maximum likelihood expectation maximization) algorithm is the most popular image reconstruction method when the measurement noise is Poisson...
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SubjectTerms 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)
Title The ML-EM Algorithm is Not Optimal for Poisson Noise
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