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...

Full description

Saved in:
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
Tags: Add Tag
No Tags, Be the first to tag this record!
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.
Author_xml – sequence: 1
  givenname: Gengsheng L.
  surname: Zeng
  fullname: Zeng, Gengsheng L.
  email: larryzeng@weber.edu
  organization: Department of Engineering, Weber State University, Ogden, UT, USA
BookMark eNp9kE1LAzEQhoNUsFbvgpcFz1szySa7OZZSP6AfgvUcttmJTWk3NUkP_nu3tHjw4GmY4X1mhuea9FrfIiF3QIcAVD0u5-9DRkEMWVEKYNUF6YMQVQ6irHqkTylUuSqUuiLXMW66thBU9EmxXGM2m-aTWTbafvrg0nqXuZjNfcoW--R29TazPmRv3sXo227uIt6QS1tvI96e64B8PE2W45d8unh-HY-mueESUq6woFJVylg0dVNxbgViYzk2DYKQ5QpqzktLAWqLlCNjhhaNKaSybCUM5QPycNq7D_7rgDHpjT-EtjupoWSKlRK46lL0lDLBxxjQ6n3o_g7fGqg-utGdG310o89uOkT-QYxLdXK-TaF22__A-xPoEPH3TskqWUnFfwBpIXFq
CODEN IETNAE
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
ContentType Journal Article
Copyright Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2015
Copyright_xml – notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2015
DBID 97E
RIA
RIE
AAYXX
CITATION
7QF
7QL
7QQ
7SC
7SE
7SP
7SR
7T7
7TA
7TB
7U5
7U9
8BQ
8FD
C1K
F28
FR3
H8D
H94
JG9
JQ2
KR7
L7M
L~C
L~D
M7N
P64
DOI 10.1109/TNS.2015.2475128
DatabaseName IEEE Xplore (IEEE)
IEEE All-Society Periodicals Package (ASPP) 1998–Present
IEEE Electronic Library (IEL)
CrossRef
Aluminium Industry Abstracts
Bacteriology Abstracts (Microbiology B)
Ceramic Abstracts
Computer and Information Systems Abstracts
Corrosion Abstracts
Electronics & Communications Abstracts
Engineered Materials Abstracts
Industrial and Applied Microbiology Abstracts (Microbiology A)
Materials Business File
Mechanical & Transportation Engineering Abstracts
Solid State and Superconductivity Abstracts
Virology and AIDS Abstracts
METADEX
Technology Research Database
Environmental Sciences and Pollution Management
ANTE: Abstracts in New Technology & Engineering
Engineering Research Database
Aerospace Database
AIDS and Cancer Research Abstracts
Materials Research Database
ProQuest Computer Science Collection
Civil Engineering Abstracts
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts – Academic
Computer and Information Systems Abstracts Professional
Algology Mycology and Protozoology Abstracts (Microbiology C)
Biotechnology and BioEngineering Abstracts
DatabaseTitle CrossRef
Materials Research Database
Technology Research Database
Computer and Information Systems Abstracts – Academic
Mechanical & Transportation Engineering Abstracts
ProQuest Computer Science Collection
Computer and Information Systems Abstracts
Materials Business File
Environmental Sciences and Pollution Management
Aerospace Database
Engineered Materials Abstracts
Bacteriology Abstracts (Microbiology B)
Algology Mycology and Protozoology Abstracts (Microbiology C)
AIDS and Cancer Research Abstracts
Industrial and Applied Microbiology Abstracts (Microbiology A)
Advanced Technologies Database with Aerospace
ANTE: Abstracts in New Technology & Engineering
Civil Engineering Abstracts
Aluminium Industry Abstracts
Virology and AIDS Abstracts
Electronics & Communications Abstracts
Ceramic Abstracts
METADEX
Biotechnology and BioEngineering Abstracts
Computer and Information Systems Abstracts Professional
Solid State and Superconductivity Abstracts
Engineering Research Database
Corrosion Abstracts
DatabaseTitleList
Materials Research Database
Database_xml – sequence: 1
  dbid: RIE
  name: IEEE Electronic Library (IEL)
  url: https://ieeexplore.ieee.org/
  sourceTypes: Publisher
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
EISSN 1558-1578
EndPage 2101
ExternalDocumentID 3855727321
10_1109_TNS_2015_2475128
7286869
Genre orig-research
GroupedDBID .DC
.GJ
0R~
29I
3O-
4.4
53G
5GY
5RE
5VS
6IK
8WZ
97E
A6W
AAJGR
AARMG
AASAJ
AAWTH
ABAZT
ABQJQ
ABVLG
ACGFO
ACGFS
ACIWK
ACNCT
ACPRK
AENEX
AETEA
AETIX
AFRAH
AGQYO
AGSQL
AHBIQ
AI.
AIBXA
AKJIK
AKQYR
ALLEH
ALMA_UNASSIGNED_HOLDINGS
ASUFR
ATWAV
BEFXN
BFFAM
BGNUA
BKEBE
BPEOZ
CS3
DU5
EBS
EJD
F5P
HZ~
H~9
IAAWW
IBMZZ
ICLAB
IDIHD
IFIPE
IFJZH
IPLJI
JAVBF
LAI
M43
MS~
O9-
OCL
P2P
RIA
RIE
RNS
TAE
TN5
VH1
VOH
AAYXX
CITATION
7QF
7QL
7QQ
7SC
7SE
7SP
7SR
7T7
7TA
7TB
7U5
7U9
8BQ
8FD
C1K
F28
FR3
H8D
H94
JG9
JQ2
KR7
L7M
L~C
L~D
M7N
P64
RIG
ID FETCH-LOGICAL-c361t-9e406989cfecad833f5eedf3edde1567b1a337f011afe03e22c04dc469f2b5c03
IEDL.DBID RIE
ISICitedReferencesCount 3
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000363242200022&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0018-9499
IngestDate Mon Jun 30 08:31:29 EDT 2025
Tue Nov 18 22:11:21 EST 2025
Sat Nov 29 05:53:18 EST 2025
Wed Aug 27 02:43:08 EDT 2025
IsPeerReviewed true
IsScholarly true
Issue 5
Language English
License https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c361t-9e406989cfecad833f5eedf3edde1567b1a337f011afe03e22c04dc469f2b5c03
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
PQID 1729276139
PQPubID 85457
PageCount 6
ParticipantIDs proquest_journals_1729276139
crossref_citationtrail_10_1109_TNS_2015_2475128
crossref_primary_10_1109_TNS_2015_2475128
ieee_primary_7286869
PublicationCentury 2000
PublicationDate 2015-Oct.
2015-10-00
20151001
PublicationDateYYYYMMDD 2015-10-01
PublicationDate_xml – month: 10
  year: 2015
  text: 2015-Oct.
PublicationDecade 2010
PublicationPlace New York
PublicationPlace_xml – name: New York
PublicationTitle IEEE transactions on nuclear science
PublicationTitleAbbrev TNS
PublicationYear 2015
Publisher IEEE
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher_xml – name: IEEE
– name: The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
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
– ident: ref2
  doi: 10.1109/TMI.1982.4307558
SSID ssj0014505
Score 2.1511037
Snippet The ML-EM (maximum likelihood expectation maximization) algorithm is the most popular image reconstruction method when the measurement noise is Poisson...
SourceID proquest
crossref
ieee
SourceType Aggregation Database
Enrichment Source
Index Database
Publisher
StartPage 2096
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
URI https://ieeexplore.ieee.org/document/7286869
https://www.proquest.com/docview/1729276139
Volume 62
WOSCitedRecordID wos000363242200022&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVIEE
  databaseName: IEEE Electronic Library (IEL)
  customDbUrl:
  eissn: 1558-1578
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0014505
  issn: 0018-9499
  databaseCode: RIE
  dateStart: 19630101
  isFulltext: true
  titleUrlDefault: https://ieeexplore.ieee.org/
  providerName: IEEE
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LT8JAEJ4A8aAHX2hE0fTgxcRC2912t0diMB4ASUTDrWm3s0oC1EDx9ztbCtFoTLw1zc6m-XYe33RndwCuTZYs_ZTbUgtlc8a1HXN07Vi7OkmRqaAo-X_picFAjsfhsAK327MwiFgUn2HLPBZ7-WmmVuZXWVt4MpBBWIWqEMH6rNZ2x4D7TtmtgAyYaPxmS9IJ26PBk6nh8lseFxTf5LcQVPRU-eGIi-hyf_C_7zqE_ZJFWp31sh9BBefHsPflbsE6cFIAq9-zu32rM33NFpP8bWZNltYgy61H8hMzkifCag0zgj6b0_vJEk_g-b47unuwyxYJtmKBm9shmpOrMlQaVZxKxrRPQU8zJK9FmZlI3JgxocmIY40OQ89TDk8V5cTaS3zlsFOozbM5noFFPEYkGBOfSSTX3JcpBm4q49RXktTNbUB7g1qkyvvDTRuLaVTkEU4YEc6RwTkqcW7AzVbifX13xh9j6wbX7bgS0gY0NwsTlca1jIhzhZ4gHhKe_y51Abtm7nXNXRNq-WKFl7CjPvLJcnFV6M0nose-_A
linkProvider IEEE
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LS8NAEB58gXrwVcX6zMGLYNoku0k2xyItFdsoWMVbSDazWtBGmujvdzZNg6II3kLYYcO38_gmO7sDcKazZOGm3BTKlyZnXJkxR9uMla2SFJn0ypL_h4EfhuLxMbhdgIv6LAwilsVn2NKP5V5-msl3_aus7TvCE16wCMu6c1Z1WqveM-CuVfUrIBMmIj_flLSC9ii801VcbsvhPkU48S0IlV1VfrjiMr70Nv_3ZVuwUfFIozNb-G1YwMkOrH-5XbABnFTAGA7M7tDovDxl03Hx_GqMcyPMCuOGPMUryRNlNW4zAj-b0Ptxjrtw3-uOLvtm1STBlMyzCzNAfXZVBFKhjFPBmHIp7CmG5LcoN_MTO2bMV2TGsUKLoeNIi6eSsmLlJK602B4sTbIJ7oNBTMZPMCZGkwiuuCtS9OxUxKkrBSmc3YT2HLVIVjeI60YWL1GZSVhBRDhHGueowrkJ57XE2-z2jD_GNjSu9bgK0iYczRcmqswrj4h1BY5PTCQ4-F3qFFb7o-EgGlyF14ewpueZVeAdwVIxfcdjWJEfxTifnpQ69AnFCMJF
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=The+ML-EM+Algorithm+is+Not+Optimal+for+Poisson+Noise&rft.jtitle=IEEE+transactions+on+nuclear+science&rft.au=Zeng%2C+Gengsheng+L.&rft.date=2015-10-01&rft.pub=IEEE&rft.issn=0018-9499&rft.volume=62&rft.issue=5&rft.spage=2096&rft.epage=2101&rft_id=info:doi/10.1109%2FTNS.2015.2475128&rft.externalDocID=7286869
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0018-9499&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0018-9499&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0018-9499&client=summon