On a simple derivation of the complementary matching pursuit

Sparse approximation in a redundant basis has attracted considerable attention in recent years because of many practical applications. The problem basically involves solving an under-determined system of linear equations under some sparsity constraint. In this paper, we present a simple interpretati...

Full description

Saved in:

Bibliographic Details
Published in	Signal processing Vol. 90; no. 2; pp. 702 - 706
Main Authors	Rath, Gagan, Guillemot, Christine
Format	Journal Article
Language	English
Published	Amsterdam Elsevier B.V 01.02.2010 Elsevier
Subjects	Algorithms Applied sciences Approximation Chemical-mechanical polishing Complementary matching pursuit Derivation Error analysis Exact sciences and technology Greedy algorithms Information, signal and communications theory Matching Matching pursuit Mathematical analysis Miscellaneous Orthogonal matching pursuit Signal processing Sparse approximation Telecommunications and information theory Vectors (mathematics) Orthogonal matching pursuit Greedy algorithms Sparse approximation Complementary matching pursuit Matching pursuit Performance evaluation Linear equation Greedy algorithm Signal processing Iterative method Sparse representation
Online Access	Get full text
ISSN	0165-1684 1872-7557
DOI	10.1016/j.sigpro.2009.07.030

Cover

Abstract	Sparse approximation in a redundant basis has attracted considerable attention in recent years because of many practical applications. The problem basically involves solving an under-determined system of linear equations under some sparsity constraint. In this paper, we present a simple interpretation of the recently proposed complementary matching pursuit (CMP) algorithm. The interpretation shows that the CMP, unlike the classical MP, selects an atom and determines its weight based on a certain sparsity measure of the resulting residual error. Based on this interpretation, we also derive another simple algorithm which is seen to outperform CMP at low sparsity levels for noisy measurement vectors.
AbstractList	Sparse approximation in a redundant basis has attracted considerable attention in recent years because of many practical applications. The problem basically involves solving an under-determined system of linear equations under some sparsity constraint. In this paper, we present a simple interpretation of the recently proposed complementary matching pursuit (CMP) algorithm. The interpretation shows that the CMP, unlike the classical MP, selects an atom and determines its weight based on a certain sparsity measure of the resulting residual error. Based on this interpretation, we also derive another simple algorithm which is seen to outperform CMP at low sparsity levels for noisy measurement vectors.
Author	Guillemot, Christine Rath, Gagan
Author_xml	– sequence: 1 givenname: Gagan surname: Rath fullname: Rath, Gagan email: grath@irisa.fr – sequence: 2 givenname: Christine surname: Guillemot fullname: Guillemot, Christine
BackLink	http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=22602210$$DView record in Pascal Francis
BookMark	eNqFkM9LwzAYhoNMcJv-Bx56EU-tX5o2bUUEGf6CwS56Dln6dcto05lkA_97MzsvHvQU-PK8L7zPhIxMb5CQSwoJBcpvNonTq63tkxSgSqBIgMEJGdOySOMiz4sRGQcsjykvszMycW4DAJRxGJO7hYlk5HS3bTGq0eq99Lo3Ud9Efo2R6g8fHRov7WfUSa_W2qyi7c66nfbn5LSRrcOL4zsl70-Pb7OXeL54fp09zGPFeOnjHLNlVeaSqaJGCciLvC4pk1SFUwXLihXAa15BzRBzWdWUL2WTI6WZZCHLpuR66A0bP3bovOi0U9i20mC_c6IK60qWpjSQV0dSOiXbxkqjtBNbq7swQKQph4BB4G4HTtneOYuNUNp_L_dW6lZQEAezYiMGs-JgVkAhgtkQzn6Ff_r_id0PMQyq9hqtcEqjUVhri8qLutd_F3wBPEGXQg
CODEN	SPRODR
CitedBy_id	crossref_primary_10_1016_j_compeleceng_2012_10_001 crossref_primary_10_1179_1743131X15Y_0000000004 crossref_primary_10_1145_3447958
Cites_doi	10.1007/s10208-008-9031-3 10.1109/TIT.2005.855614 10.1109/TIT.2007.909108 10.1016/j.acha.2008.07.002 10.1137/S1064827596304010 10.1109/TIT.2009.2016006 10.1109/78.258082 10.1109/TSP.2007.911494 10.1002/cpa.20132 10.1109/TSP.2007.916124
ContentType	Journal Article
Copyright	2009 Elsevier B.V. 2015 INIST-CNRS
Copyright_xml	– notice: 2009 Elsevier B.V. – notice: 2015 INIST-CNRS
DBID	AAYXX CITATION IQODW 7SC 7SP 8FD JQ2 L7M L~C L~D
DOI	10.1016/j.sigpro.2009.07.030
DatabaseName	CrossRef Pascal-Francis 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
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
DatabaseTitleList	Technology Research Database
DeliveryMethod	fulltext_linktorsrc
Discipline	Engineering Applied Sciences
EISSN	1872-7557
EndPage	706
ExternalDocumentID	22602210 10_1016_j_sigpro_2009_07_030 S0165168409003442
GroupedDBID	--K --M -~X .DC .~1 0R~ 123 1B1 1~. 1~5 4.4 457 4G. 53G 5VS 7-5 71M 8P~ 9JN AABNK AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO AAYFN ABBOA ABFNM ABFRF ABMAC ABXDB ABYKQ ACDAQ ACGFO ACGFS ACNNM ACRLP ACZNC ADBBV ADEZE ADJOM ADMUD ADTZH AEBSH AECPX AEFWE AEKER AENEX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHJVU AHZHX AIALX AIEXJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ AOUOD ASPBG AVWKF AXJTR AZFZN BJAXD BKOJK BLXMC CS3 DU5 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 F0J F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-Q G8K GBLVA GBOLZ HLZ HVGLF HZ~ IHE J1W JJJVA KOM LG9 M41 MO0 N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. Q38 R2- RIG ROL RPZ SBC SDF SDG SDP SES SEW SPC SPCBC SST SSV SSZ T5K TAE TN5 WUQ XPP ZMT ~02 ~G- AATTM AAXKI AAYWO AAYXX ABDPE ABJNI ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD AFXIZ AGCQF AGRNS BNPGV IQODW SSH 7SC 7SP 8FD JQ2 L7M L~C L~D
ID	FETCH-LOGICAL-c368t-5e4b985a3c7dea0e675d813a1ca3c90b93706d690d3ee5a9d16baf5e114a3e4b3
IEDL.DBID	AIKHN
ISSN	0165-1684
IngestDate	Mon Sep 29 06:09:10 EDT 2025 Mon Jul 21 09:12:03 EDT 2025 Wed Oct 01 02:46:22 EDT 2025 Thu Apr 24 23:01:06 EDT 2025 Fri Feb 23 02:28:12 EST 2024
IsPeerReviewed	true
IsScholarly	true
Issue	2
Keywords	Orthogonal matching pursuit Greedy algorithms Sparse approximation Complementary matching pursuit Matching pursuit Performance evaluation Linear equation Greedy algorithm Signal processing Iterative method Sparse representation
Language	English
License	https://www.elsevier.com/tdm/userlicense/1.0 CC BY 4.0
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c368t-5e4b985a3c7dea0e675d813a1ca3c90b93706d690d3ee5a9d16baf5e114a3e4b3
Notes	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
PQID	901683221
PQPubID	23500
PageCount	5
ParticipantIDs	proquest_miscellaneous_901683221 pascalfrancis_primary_22602210 crossref_citationtrail_10_1016_j_sigpro_2009_07_030 crossref_primary_10_1016_j_sigpro_2009_07_030 elsevier_sciencedirect_doi_10_1016_j_sigpro_2009_07_030
ProviderPackageCode	CITATION AAYXX
PublicationCentury	2000
PublicationDate	2010-02-01
PublicationDateYYYYMMDD	2010-02-01
PublicationDate_xml	– month: 02 year: 2010 text: 2010-02-01 day: 01
PublicationDecade	2010
PublicationPlace	Amsterdam
PublicationPlace_xml	– name: Amsterdam
PublicationTitle	Signal processing
PublicationYear	2010
Publisher	Elsevier B.V Elsevier
Publisher_xml	– name: Elsevier B.V – name: Elsevier
References	Fuchs (bib5) 2005; 51 Blumensath, Davies (bib10) June 2008; 56 Donoho (bib4) 2006; 59 Y.C. Pati, R. Rezaiifar, P.S. Krishnaprasad, Orthogonal matching pursuit: recursive function approximation with applications to wavelet decompositions, in: Proceedings of the 27th Asilomar Conference on Signals, Systems and Computers, 1993. Schnass, Vandergheynst (bib12) May 2008; 56 W. Dai, O. Milenkovic, Subspace pursuit for compressive sensing signal reconstruction, Preprint, January 2009. Tropp, Gilbert (bib9) December 2007; 53 G. Rath, C. Guillemot, Complementary matching pursuit algorithms for sparse approximation, IEEE Trans. SP (April 2008), submitted for publication. D. Needell, R. Vershynin, Signal recovery from inaccurate and incomplete measurements via regularized orthogonal matching pursuit, Preprint, December 2007. Chen, Donoho, Saunders (bib3) 1988; 20 Mallat, Zhang (bib1) 1993; 41 D. Needell, J.A. Tropp, CoSaMP: iterative signal recovery from incomplete and inaccurate samples, Appl. Comput. Harm. Anal., DOI: 10.1016/j.acha.2008.07.002. 10.1016/j.sigpro.2009.07.030_bib11 Schnass (10.1016/j.sigpro.2009.07.030_bib12) 2008; 56 10.1016/j.sigpro.2009.07.030_bib2 Fuchs (10.1016/j.sigpro.2009.07.030_bib5) 2005; 51 Chen (10.1016/j.sigpro.2009.07.030_bib3) 1988; 20 10.1016/j.sigpro.2009.07.030_bib6 10.1016/j.sigpro.2009.07.030_bib7 10.1016/j.sigpro.2009.07.030_bib8 Mallat (10.1016/j.sigpro.2009.07.030_bib1) 1993; 41 Tropp (10.1016/j.sigpro.2009.07.030_bib9) 2007; 53 Donoho (10.1016/j.sigpro.2009.07.030_bib4) 2006; 59 Blumensath (10.1016/j.sigpro.2009.07.030_bib10) 2008; 56
References_xml	– volume: 59 start-page: 797 year: 2006 end-page: 829 ident: bib4 article-title: For most large underdetermined systems of linear equations the minimal publication-title: Comm. Pure Appl. Math. – volume: 53 start-page: 4655 year: December 2007 end-page: 4666 ident: bib9 article-title: Signal recovery from random measurements via orthogonal matching pursuit publication-title: IEEE Trans. Inform. Theory – volume: 56 start-page: 2370 year: June 2008 end-page: 2382 ident: bib10 article-title: Gradient pursuits publication-title: IEEE Trans. Signal Process. – reference: D. Needell, R. Vershynin, Signal recovery from inaccurate and incomplete measurements via regularized orthogonal matching pursuit, Preprint, December 2007. – volume: 41 start-page: 3397 year: 1993 end-page: 3415 ident: bib1 article-title: Matching pursuit in a time-frequency dictionary publication-title: IEEE Trans. SP – reference: Y.C. Pati, R. Rezaiifar, P.S. Krishnaprasad, Orthogonal matching pursuit: recursive function approximation with applications to wavelet decompositions, in: Proceedings of the 27th Asilomar Conference on Signals, Systems and Computers, 1993. – reference: W. Dai, O. Milenkovic, Subspace pursuit for compressive sensing signal reconstruction, Preprint, January 2009. – volume: 51 start-page: 3601 year: 2005 end-page: 3608 ident: bib5 article-title: Recovery of exact sparse representations in the presence of bounded noise publication-title: IEEE Trans. Inform. Theory – volume: 20 start-page: 33 year: 1988 end-page: 61 ident: bib3 article-title: Atomic decomposition by basis pursuit publication-title: SIAM J. Sci. Comput. – reference: D. Needell, J.A. Tropp, CoSaMP: iterative signal recovery from incomplete and inaccurate samples, Appl. Comput. Harm. Anal., DOI: 10.1016/j.acha.2008.07.002. – volume: 56 start-page: 1994 year: May 2008 end-page: 2002 ident: bib12 article-title: Dictionary preconditioning for greedy algorithms publication-title: IEEE Trans. SP – reference: G. Rath, C. Guillemot, Complementary matching pursuit algorithms for sparse approximation, IEEE Trans. SP (April 2008), submitted for publication. – ident: 10.1016/j.sigpro.2009.07.030_bib2 – ident: 10.1016/j.sigpro.2009.07.030_bib6 doi: 10.1007/s10208-008-9031-3 – volume: 51 start-page: 3601 issue: 10 year: 2005 ident: 10.1016/j.sigpro.2009.07.030_bib5 article-title: Recovery of exact sparse representations in the presence of bounded noise publication-title: IEEE Trans. Inform. Theory doi: 10.1109/TIT.2005.855614 – volume: 53 start-page: 4655 issue: 12 year: 2007 ident: 10.1016/j.sigpro.2009.07.030_bib9 article-title: Signal recovery from random measurements via orthogonal matching pursuit publication-title: IEEE Trans. Inform. Theory doi: 10.1109/TIT.2007.909108 – ident: 10.1016/j.sigpro.2009.07.030_bib7 doi: 10.1016/j.acha.2008.07.002 – volume: 20 start-page: 33 issue: 1 year: 1988 ident: 10.1016/j.sigpro.2009.07.030_bib3 article-title: Atomic decomposition by basis pursuit publication-title: SIAM J. Sci. Comput. doi: 10.1137/S1064827596304010 – ident: 10.1016/j.sigpro.2009.07.030_bib8 doi: 10.1109/TIT.2009.2016006 – ident: 10.1016/j.sigpro.2009.07.030_bib11 – volume: 41 start-page: 3397 issue: 12 year: 1993 ident: 10.1016/j.sigpro.2009.07.030_bib1 article-title: Matching pursuit in a time-frequency dictionary publication-title: IEEE Trans. SP doi: 10.1109/78.258082 – volume: 56 start-page: 1994 issue: 5 year: 2008 ident: 10.1016/j.sigpro.2009.07.030_bib12 article-title: Dictionary preconditioning for greedy algorithms publication-title: IEEE Trans. SP doi: 10.1109/TSP.2007.911494 – volume: 59 start-page: 797 issue: 6 year: 2006 ident: 10.1016/j.sigpro.2009.07.030_bib4 article-title: For most large underdetermined systems of linear equations the minimal l1-norm solution is also the sparsest solution publication-title: Comm. Pure Appl. Math. doi: 10.1002/cpa.20132 – volume: 56 start-page: 2370 issue: 6 year: 2008 ident: 10.1016/j.sigpro.2009.07.030_bib10 article-title: Gradient pursuits publication-title: IEEE Trans. Signal Process. doi: 10.1109/TSP.2007.916124
SSID	ssj0001360
Score	1.9358457
Snippet	Sparse approximation in a redundant basis has attracted considerable attention in recent years because of many practical applications. The problem basically...
SourceID	proquest pascalfrancis crossref elsevier
SourceType	Aggregation Database Index Database Enrichment Source Publisher
StartPage	702
SubjectTerms	Algorithms Applied sciences Approximation Chemical-mechanical polishing Complementary matching pursuit Derivation Error analysis Exact sciences and technology Greedy algorithms Information, signal and communications theory Matching Matching pursuit Mathematical analysis Miscellaneous Orthogonal matching pursuit Signal processing Sparse approximation Telecommunications and information theory Vectors (mathematics)
Title	On a simple derivation of the complementary matching pursuit
URI	https://dx.doi.org/10.1016/j.sigpro.2009.07.030 https://www.proquest.com/docview/901683221
Volume	90
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVESC databaseName: Elsevier SD Complete Freedom Collection [SCCMFC] customDbUrl: eissn: 1872-7557 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0001360 issn: 0165-1684 databaseCode: ACRLP dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier – providerCode: PRVESC databaseName: ScienceDirect (Elsevier) customDbUrl: eissn: 1872-7557 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0001360 issn: 0165-1684 databaseCode: .~1 dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier – providerCode: PRVESC databaseName: ScienceDirect Freedom Collection Journals customDbUrl: eissn: 1872-7557 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0001360 issn: 0165-1684 databaseCode: AIKHN dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier – providerCode: PRVLSH databaseName: Elsevier Journals customDbUrl: mediaType: online eissn: 1872-7557 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0001360 issn: 0165-1684 databaseCode: AKRWK dateStart: 19930101 isFulltext: true providerName: Library Specific Holdings
link	http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3NS8MwFA9zuygifuL8GDl47dYsTZuAlzEcU3EedLBbSNtUKtKVtT148W_3pR_DoTDwGvJIeU1--b32995D6IaHzKWeIyzim5ScIdOWopRYYsiGtrYdzYYmwflp5k7nzsOCLVpo3OTCGFlljf0VppdoXY8Mam8O0jgevJhEHGJqlYiybh3gcAfuH87bqDO6f5zO1oBMaJksbOZbxqDJoCtlXln8BlBVF670-qUc-u8baj9VGfgtqhpe_MLu8kKaHKKDmkniUfWwR6ilk2O096O-4Am6fU6wwllsKgDjEAar7694GWHgfbiUk1fq8dUnBupa6ipxWqyyIs5P0Xxy9zqeWnW7BCugLs8tph1fcKZo4IVa2RpCgZATqkgAQ8L2gYjYbgjRcEi1ZkqExPVVxDRERIqCLT1D7WSZ6HOEaQSBo81DmyrXAdKnuG-Otw_BJveEL7qINi6SQV1L3LS0-JCNaOxdVo41bS6FtD0Jju0ia22VVrU0tsz3Gu_LjT0hAe63WPY2XtZ6OSCbQFoITMDN25NwnsxPEpXoZZFJ4EeuQTly8e_VL9FupTEwopcr1M5Xhb4G6pL7PbTT_yK9eoN-A4jW7Nk
linkProvider	Elsevier
linkToHtml	http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3PS8MwFA5jHlRE_Inzx8zBa7emadoGvMhwTN3mwQ12C2mbSUW6sm4HL_7tvqTtdCgMvIYXUl6TL99rv_ceQjdBzDzqu9wioU7JcZiyJKXE4g5zbGW7ijk6wXkw9Hpj93HCJjXUqXJhtKyyxP4C0w1alyPt0pvtLEnaLzoRh-haJdzUrQMc3nKZ4-sIrPX5rfMg1KQKa2tLm1f5c0bklSevAFRl2Uq_ZcTQf99Pe5nMwWvTot3FL-Q211H3AO2XPBLfFY96iGoqPUK7P6oLHqPb5xRLnCe6_i-OYbD4-opnUwysDxsxeaEdn39gIK5GVYmz5TxfJosTNO7ejzo9q2yWYEXUCxYWU27IAyZp5MdK2goCgTggVJIIhrgdAg2xvRhi4ZgqxSSPiRfKKVMQD0kKc-kpqqezVJ0hTKcQNtpBbFPpuUD5ZBDqwx1CqBn4POQNRCsXiaisJK4bWryLSjL2JgrH6iaXXNi-AMc2kLWalRWVNDbY-5X3xdqOEAD2G2Y2117WajmgmkBZCBjg6u0JOE36F4lM1WyZC2BHnsY4cv7v1a_Rdm806Iv-w_DpAu0UagMtf7lE9cV8qa6AxCzCptmkX4Gc7aE
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=On+a+simple+derivation+of+the+complementary+matching+pursuit&rft.jtitle=Signal+processing&rft.au=RATH%2C+Gagan&rft.au=GUILLEMOT%2C+Christine&rft.date=2010-02-01&rft.pub=Elsevier&rft.issn=0165-1684&rft.volume=90&rft.issue=2&rft.spage=702&rft.epage=706&rft_id=info:doi/10.1016%2Fj.sigpro.2009.07.030&rft.externalDBID=n%2Fa&rft.externalDocID=22602210
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0165-1684&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0165-1684&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0165-1684&client=summon