Poisson intensity estimation for tomographic data using a wavelet shrinkage approach

We consider a two-dimensional (2-D) problem of positron-emission tomography (PET) where the random mechanism of the generation of the tomographic data is modeled by Poisson processes. The goal is to estimate the intensity function which corresponds to emission density. Using the wavelet-vaguelette d...

Full description

Saved in:
Bibliographic Details
Published inIEEE transactions on information theory Vol. 48; no. 10; pp. 2794 - 2802
Main Authors Cavalier, L., Ja-Yong Koo
Format Journal Article
LanguageEnglish
Published New York IEEE 01.10.2002
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Adaptive estimation
Adaptive systems
Convergence
Convergence of numerical methods
Data reduction
Density
Emission
Estimating techniques
Estimators
Inverse problems
Linear programming
Mathematical models
Minimax methods
Minimax technique
Nonlinear programming
Optimal systems
Optimization
Poisson distribution
Positron emission tomography
Random processes
Stochastic processes
Tomography
Wavelet transforms
Online AccessGet full text
ISSN0018-9448
1557-9654
DOI10.1109/TIT.2002.802632

Cover

Abstract We consider a two-dimensional (2-D) problem of positron-emission tomography (PET) where the random mechanism of the generation of the tomographic data is modeled by Poisson processes. The goal is to estimate the intensity function which corresponds to emission density. Using the wavelet-vaguelette decomposition (WVD), we propose an estimator based on thresholding of empirical vaguelette coefficients which attains the minimax rates of convergence on Besov function classes. Furthermore, we construct an adaptive estimator which attains the optimal rate of convergence up to a logarithmic term.
AbstractList We consider a two-dimensional (2-D) problem of positron-emission tomography (PET) where the random mechanism of the generation of the tomographic data is modeled by Poisson processes. The goal is to estimate the intensity function which corresponds to emission density. Using the wavelet-vaguelette decomposition (WVD), we propose an estimator based on thresholding of empirical vaguelette coefficients which attains the minimax rates of convergence on Besov function classes. Furthermore, we construct an adaptive estimator which attains the optimal rate of convergence up to a logarithmic term.
We consider a two-dimensional (2-D) problem of positron-emission tomography (PET) where the random mechanism of the generation of the tomographic data is modeled by Poisson processes. The goal is to estimate the intensity function which corresponds to emission density. Using the wavelet-vaguelette decompositiom (WVD), we propose an estimator based on thresholding of empirical vaguelette coefficients which attains the minimax rates of convergence on Besov function classes. Furthermore, we construct an adaptive estimator which attains the optimal rate of convergence up to a logarithmic term.
Author Cavalier, L.
Ja-Yong Koo
Author_xml – sequence: 1
  givenname: L.
  surname: Cavalier
  fullname: Cavalier, L.
  organization: Centre de Mathematiques et Informatique, Univ. Aix-Marseille, Marseille, France
– sequence: 2
  surname: Ja-Yong Koo
  fullname: Ja-Yong Koo
BookMark eNqNkTtPBCEURonRxPVRW9gQC61mBYY7MKUxvhITLdaaIMPsorOwAqvZfy-6FsZCrQhwvgv3nh206YO3CB1QMqaUtKeTm8mYEcLGkrCmZhtoRAFE1TbAN9GIECqrlnO5jXZSeipbDpSN0OQ-uJSCx85n65PLK2xTdnOdXTnsQ8Q5zMM06sXMGdzprPEyOT_FGr_pVzvYjNMsOv-spxbrxSIGbWZ7aKvXQ7L7X-sueri8mJxfV7d3VzfnZ7eV4ZTmSj52jWytlsaInoGFFoBIbcCUNggR0HHdy04KxoD1urGcm64B1knyKMHU9S46Wdctz74sy7_V3CVjh0F7G5ZJtUS0XAgmCnn8K8kkQA2M_w1SILSu_1GxDFxwTgt49AN8Csvoy1wUbaE0JwgrEKwhE0NK0fbKuPzpIEftBkWJ-pCsimT1IVmtJZfc6Y_cIhZ5cfVL4nCdcNbab3QNtNy-A3wlsvE
CODEN IETTAW
CitedBy_id crossref_primary_10_1088_0266_5611_24_2_025001
crossref_primary_10_3150_bj_1155735930
crossref_primary_10_1080_17415977_2020_1864348
crossref_primary_10_1016_j_jmva_2010_01_009
crossref_primary_10_1198_106186004X2615
crossref_primary_10_1109_TIT_2006_871053
crossref_primary_10_1088_0266_5611_32_6_065003
crossref_primary_10_1109_TIP_2008_2008223
crossref_primary_10_1111_rssb_12128
crossref_primary_10_1214_08_EJS319
crossref_primary_10_1109_TSP_2007_893754
crossref_primary_10_1109_TIP_2010_2053941
crossref_primary_10_1088_0029_5515_52_1_013005
crossref_primary_10_1214_13_EJS794
crossref_primary_10_1214_009053606000000687
crossref_primary_10_1109_42_963822
crossref_primary_10_1007_s00184_019_00716_7
crossref_primary_10_1051_ps_2008017
crossref_primary_10_1088_0266_5611_21_4_010
crossref_primary_10_1080_10485252_2019_1599376
crossref_primary_10_1088_0266_5611_29_9_095010
crossref_primary_10_1016_j_amc_2013_07_090
crossref_primary_10_1088_0266_5611_28_10_104004
crossref_primary_10_1146_annurev_statistics_010814_020343
crossref_primary_10_1016_j_nima_2010_12_073
crossref_primary_10_1088_0266_5611_32_9_093001
crossref_primary_10_1214_21_EJS1835
Cites_doi 10.1097/00004728-198106000-00015
10.1007/BF00972983
10.1007/978-1-4612-2222-4
10.1017/cbo9780511623820
10.1007/978-1-4612-1880-7_12
10.1080/02664768900000016
10.1109/42.959298
10.1109/18.857797
10.1214/aos/1176349138
10.1109/18.986021
10.1006/jmva.1998.1772
10.1111/j.2517-6161.1990.tb01788.x
10.1214/aos/1016218233
10.1063/1.4823127
10.1214/aos/1032894449
10.1007/978-3-663-01409-6
10.1109/18.857789
10.1214/aos/1176347500
10.1214/aos/1032894451
10.2307/3318602
10.1093/biomet/85.1.115
10.1006/acha.1995.1008
10.2307/2291727
10.1214/aos/1176324709
10.2307/2288030
10.1007/BF00532480
10.1093/biomet/81.3.425
10.1109/TNS.1985.4334521
10.1007/978-1-4613-9308-5
10.1214/aos/1176348665
10.1214/aos/1030563989
10.1109/42.293921
10.1109/78.134477
10.1007/s004400100169
10.1109/42.963822
10.1109/42.75614
ContentType Journal Article
Copyright Copyright Institute of Electrical and Electronics Engineers, Inc. (IEEE) Oct 2002
Copyright_xml – notice: Copyright Institute of Electrical and Electronics Engineers, Inc. (IEEE) Oct 2002
DBID RIA
RIE
AAYXX
CITATION
7SC
7SP
8FD
JQ2
L7M
L~C
L~D
7QO
FR3
P64
F28
DOI 10.1109/TIT.2002.802632
DatabaseName IEEE All-Society Periodicals Package (ASPP) 1998–Present
IEEE Electronic Library (IEL)
CrossRef
Computer and Information Systems Abstracts
Electronics & Communications Abstracts
Technology Research Database
ProQuest Computer Science Collection
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts – Academic
Computer and Information Systems Abstracts Professional
Biotechnology Research Abstracts
Engineering Research Database
Biotechnology and BioEngineering Abstracts
ANTE: Abstracts in New Technology & Engineering
DatabaseTitle CrossRef
Technology Research Database
Computer and Information Systems Abstracts – Academic
Electronics & Communications Abstracts
ProQuest Computer Science Collection
Computer and Information Systems Abstracts
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts Professional
Engineering Research Database
Biotechnology Research Abstracts
Biotechnology and BioEngineering Abstracts
ANTE: Abstracts in New Technology & Engineering
DatabaseTitleList
Engineering Research Database
Technology Research Database

Technology Research Database
Computer and Information Systems Abstracts
Database_xml – sequence: 1
  dbid: RIE
  name: IEEE Electronic Library (IEL)
  url: https://proxy.k.utb.cz/login?url=https://ieeexplore.ieee.org/
  sourceTypes: Publisher
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
Computer Science
EISSN 1557-9654
EndPage 2802
ExternalDocumentID 639754
195658801
10_1109_TIT_2002_802632
1035132
Genre Feature
GroupedDBID -~X
.DC
0R~
29I
3EH
4.4
5GY
5VS
6IK
97E
AAJGR
AARMG
AASAJ
AAWTH
ABAZT
ABFSI
ABQJQ
ABVLG
ACGFO
ACGFS
ACGOD
ACIWK
AENEX
AETEA
AETIX
AGQYO
AGSQL
AHBIQ
AI.
AIBXA
AKJIK
AKQYR
ALLEH
ALMA_UNASSIGNED_HOLDINGS
ASUFR
ATWAV
BEFXN
BFFAM
BGNUA
BKEBE
BPEOZ
CS3
DU5
E.L
EBS
EJD
F5P
HZ~
H~9
IAAWW
IBMZZ
ICLAB
IDIHD
IFIPE
IFJZH
IPLJI
JAVBF
LAI
M43
MS~
O9-
OCL
P2P
PQQKQ
RIA
RIE
RNS
RXW
TAE
TN5
VH1
VJK
AAYXX
CITATION
7SC
7SP
8FD
JQ2
L7M
L~C
L~D
RIG
7QO
FR3
P64
F28
ID FETCH-LOGICAL-c411t-8bd689ea8cc7f25e595508ac5c0020075d4af8d872252fa6e44cd652d80b85c33
IEDL.DBID RIE
ISSN 0018-9448
IngestDate Sat Sep 27 18:15:10 EDT 2025
Sun Sep 28 11:41:35 EDT 2025
Sun Sep 28 10:21:08 EDT 2025
Wed Oct 01 14:32:33 EDT 2025
Fri Jul 25 07:03:29 EDT 2025
Thu Apr 24 23:04:29 EDT 2025
Wed Oct 01 06:33:53 EDT 2025
Tue Aug 26 21:00:35 EDT 2025
IsPeerReviewed true
IsScholarly true
Issue 10
Language English
License https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c411t-8bd689ea8cc7f25e595508ac5c0020075d4af8d872252fa6e44cd652d80b85c33
Notes SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ObjectType-Article-2
content type line 23
PQID 195872702
PQPubID 23462
PageCount 9
ParticipantIDs proquest_miscellaneous_907947727
proquest_miscellaneous_28553524
proquest_miscellaneous_21501337
crossref_primary_10_1109_TIT_2002_802632
ieee_primary_1035132
crossref_citationtrail_10_1109_TIT_2002_802632
proquest_miscellaneous_20187441
proquest_journals_195872702
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate 2002-10-01
PublicationDateYYYYMMDD 2002-10-01
PublicationDate_xml – month: 10
  year: 2002
  text: 2002-10-01
  day: 01
PublicationDecade 2000
PublicationPlace New York
PublicationPlace_xml – name: New York
PublicationTitle IEEE transactions on information theory
PublicationTitleAbbrev TIT
PublicationYear 2002
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 ref13
ref35
Feller (ref41) 1971; 2
ref12
ref15
ref37
ref14
ref36
ref31
ref30
ref11
ref33
ref10
ref32
ref2
ref1
ref17
ref16
ref38
ref19
ref18
Härdle (ref34) 1998
ref24
ref23
Kingman (ref39) 1993
ref25
ref42
ref22
Deans (ref27) 1983
Johnstone (ref21) 1999; 9
ref28
ref29
ref8
ref7
ref9
ref4
ref3
ref6
ref5
Korostelev (ref26) 1991; 27
ref40
Geman (ref20); 52
References_xml – volume: 2
  volume-title: An Introduction to Probability Theory and Its Applications
  year: 1971
  ident: ref41
– ident: ref29
  doi: 10.1097/00004728-198106000-00015
– ident: ref42
  doi: 10.1007/BF00972983
– volume: 27
  start-page: 73
  year: 1991
  ident: ref26
  article-title: Optimal rates of convergence of estimators in a probabilistic setup of tomography problem
  publication-title: Probl. Inform. Transm.
– volume-title: Wavelets, Approximation and Statistical Applications
  year: 1998
  ident: ref34
  doi: 10.1007/978-1-4612-2222-4
– ident: ref35
  doi: 10.1017/cbo9780511623820
– ident: ref3
  doi: 10.1007/978-1-4612-1880-7_12
– ident: ref22
  doi: 10.1080/02664768900000016
– ident: ref30
  doi: 10.1109/42.959298
– ident: ref36
  doi: 10.1109/18.857797
– ident: ref37
  doi: 10.1214/aos/1176349138
– ident: ref6
  doi: 10.1109/18.986021
– ident: ref24
  doi: 10.1006/jmva.1998.1772
– ident: ref11
  doi: 10.1111/j.2517-6161.1990.tb01788.x
– ident: ref16
  doi: 10.1214/aos/1016218233
– ident: ref33
  doi: 10.1063/1.4823127
– ident: ref8
  doi: 10.1214/aos/1032894449
– volume-title: The Radon Transform and Some of Its Applications
  year: 1983
  ident: ref27
– ident: ref28
  doi: 10.1007/978-3-663-01409-6
– ident: ref15
  doi: 10.1109/18.857789
– ident: ref23
  doi: 10.1214/aos/1176347500
– ident: ref2
  doi: 10.1214/aos/1032894451
– ident: ref17
  doi: 10.2307/3318602
– ident: ref5
  doi: 10.1093/biomet/85.1.115
– volume-title: Poisson Processes
  year: 1993
  ident: ref39
– ident: ref4
  doi: 10.1006/acha.1995.1008
– ident: ref7
  doi: 10.2307/2291727
– ident: ref9
  doi: 10.1214/aos/1176324709
– ident: ref13
  doi: 10.2307/2288030
– ident: ref38
  doi: 10.1007/BF00532480
– ident: ref1
  doi: 10.1093/biomet/81.3.425
– ident: ref12
  doi: 10.1109/TNS.1985.4334521
– volume: 52
  start-page: 5
  volume-title: Proc. 46 Sect. ISI, Bull. ISI
  ident: ref20
  article-title: Statistical methods for tomographic image reconstruction
– ident: ref40
  doi: 10.1007/978-1-4613-9308-5
– ident: ref19
  doi: 10.1214/aos/1176348665
– ident: ref25
  doi: 10.1214/aos/1030563989
– ident: ref14
  doi: 10.1109/42.293921
– volume: 9
  start-page: 51
  year: 1999
  ident: ref21
  article-title: Wavelet shrinkage for correlated data and inverse problems: Adaptivity results
  publication-title: Statist. Sinica
– ident: ref31
  doi: 10.1109/78.134477
– ident: ref18
  doi: 10.1007/s004400100169
– ident: ref32
  doi: 10.1109/42.963822
– ident: ref10
  doi: 10.1109/42.75614
SSID ssj0014512
Score 1.8509561
Snippet We consider a two-dimensional (2-D) problem of positron-emission tomography (PET) where the random mechanism of the generation of the tomographic data is...
SourceID proquest
crossref
ieee
SourceType Aggregation Database
Enrichment Source
Index Database
Publisher
StartPage 2794
SubjectTerms Adaptive estimation
Adaptive systems
Convergence
Convergence of numerical methods
Data reduction
Density
Emission
Estimating techniques
Estimators
Inverse problems
Linear programming
Mathematical models
Minimax methods
Minimax technique
Nonlinear programming
Optimal systems
Optimization
Poisson distribution
Positron emission tomography
Random processes
Stochastic processes
Tomography
Wavelet transforms
Title Poisson intensity estimation for tomographic data using a wavelet shrinkage approach
URI https://ieeexplore.ieee.org/document/1035132
https://www.proquest.com/docview/195872702
https://www.proquest.com/docview/20187441
https://www.proquest.com/docview/21501337
https://www.proquest.com/docview/28553524
https://www.proquest.com/docview/907947727
Volume 48
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVIEE
  databaseName: IEEE Electronic Library (IEL)
  customDbUrl:
  eissn: 1557-9654
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0014512
  issn: 0018-9448
  databaseCode: RIE
  dateStart: 19630101
  isFulltext: true
  titleUrlDefault: https://ieeexplore.ieee.org/
  providerName: IEEE
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV3LTt0wEB0Bq7Io5VE1pYAXXXTRpHnYsbOsKhBFouriIrGL_EqLgAT15grRr-9MnFzR8lA3UaRMLEuTGc_Ex-cAvNeNlxiAOuYKUyBeeKyL0sY-z4jgyTrrqVE8_VYen_GTc3G-Ah-XZ2G89wP4zCd0O-zlu84u6FcZRnghsHtahVWpynBWa7ljwEUWmMEzDGDsOUYanyytPs2-zgYsQqJSYif_awUaJFUe5OFhcTnagNNpWgFTcpksepPY3_8wNv7vvF_By7HKZJ_DZ7EJK77dgo1JwYGNAb0F6_foCLdh9r1DN3Qtuwi49v6OEQdHONzIsLplfXcdKK4vLCNsKSPY_A-m2a0mAYuezX_iUJeYo9hEVr4DZ0eHsy_H8ai6EFueZX2sjCtV5bWyVja58KLCJkZpKyyVllhhOK4b5ZTETJA3uvScW1eK3KnUKGGL4jWstV3r3wBritwRY6HmpeLWuEoak5pcVoYwbo2IIJk8UduRkpyUMa7qoTVJqxpdR0KZeR1cF8GH5Qs3gY3jadNtcsQ9s8EHEexOrq7HaJ3XRLgj6WBeBAfLpxhmtHeiW98t5jgyiRfy7BkLLK2x4ZfPWChBZDo8AvaERZViesR-R759fPa78CKo0RCY8B2s9b8Wfg-Lot7sD9HwBx3oCfQ
linkProvider IEEE
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV3PT9VAEJ4gHtSDKGisIOyBAwdb-2O33R4NkTyQRzyUhFuzv6oEbY2vL0b_eme67QuoEC5Nk043m0xndqb77fcB7KvGFRiAKuQSUyBeeKiy3IQuTYjgyVjjqFGcn-Wzc35yIS7W4O3qLIxzbgCfuYhuh71825kl_SrDCM8Edk8P4KHgnAt_Wmu1Z8BF4rnBEwxh7DpGIp8kLt9Vx9WARohkTPzkN9agQVTln0w8LC9HGzCfJuZRJVfRsteR-f0XZ-N9Z_4Mno51JnvvP4znsObaTdiYNBzYGNKb8OQaIeEWVJ86dETXskuPbO9_MWLh8McbGda3rO--eZLrS8MIXcoIOP-ZKfZTkYRFzxZfcKgrzFJsoit_AedHH6rDWTjqLoSGJ0kfSm1zWToljSmaVDhRYhsjlRGGikusMSxXjbSywFyQNip3nBubi9TKWEthsuwlrLdd614Ba7LUEmeh4rnkRtuy0DrWaVFqQrk1IoBo8kRtRlJy0sb4Wg_NSVzW6DqSykxr77oADlYvfPd8HLebbpEjrpkNPghge3J1PcbroibKnYKO5gWwt3qKgUa7J6p13XKBI5N8IU_usMDiGlv-4g4LKYhOhwfAbrEoY0yQ2PEUr_8_-z14NKvmp_Xp8dnHbXjstWkIWrgD6_2PpXuDJVKvd4fI-AMlQw1B
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=Poisson+intensity+estimation+for+tomographic+data+using+a+wavelet+shrinkage+approach&rft.jtitle=IEEE+transactions+on+information+theory&rft.au=Cavalier%2C+L&rft.au=Koo%2C+Ja-Yong&rft.date=2002-10-01&rft.issn=0018-9448&rft.volume=48&rft.issue=10&rft.spage=2794&rft.epage=2802&rft_id=info:doi/10.1109%2FTIT.2002.802632&rft.externalDBID=NO_FULL_TEXT
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0018-9448&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0018-9448&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0018-9448&client=summon