{"id":"https://openalex.org/W1507723351","doi":"https://doi.org/10.1109/icip.2003.1246891","title":"Sparse decompositions in \"incoherent\" dictionaries","display_name":"Sparse decompositions in \"incoherent\" dictionaries","publication_year":2004,"publication_date":"2004-06-21","ids":{"openalex":"https://openalex.org/W1507723351","doi":"https://doi.org/10.1109/icip.2003.1246891","mag":"1507723351"},"language":"en","primary_location":{"id":"doi:10.1109/icip.2003.1246891","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icip.2003.1246891","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://inria.hal.science/inria-00570099","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041230403","display_name":"R\u00e9mi Gribonval","orcid":"https://orcid.org/0000-0002-9450-8125"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I2802519937","display_name":"Institut de Recherche en Informatique et Syst\u00e8mes Al\u00e9atoires","ror":"https://ror.org/00myn0z94","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I205703379","https://openalex.org/I2802204017","https://openalex.org/I2802519937","https://openalex.org/I28221208","https://openalex.org/I4210127572","https://openalex.org/I4210159245","https://openalex.org/I56067802"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"R. Gribonval","raw_affiliation_strings":["Campus de Beaulieu, IKlSA (INRIA and CNRS UMK 6074), Rennes, France","IRISA, Rennes, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Campus de Beaulieu, IKlSA (INRIA and CNRS UMK 6074), Rennes, France","institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"IRISA, Rennes, France","institution_ids":["https://openalex.org/I2802519937"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031288563","display_name":"Morten Nielsen","orcid":"https://orcid.org/0000-0002-9078-0594"},"institutions":[{"id":"https://openalex.org/I891191580","display_name":"Aalborg University","ror":"https://ror.org/04m5j1k67","country_code":"DK","type":"education","lineage":["https://openalex.org/I891191580"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"M. Nielsen","raw_affiliation_strings":["Department of Mathematical Science, University of Aalborg, Denmark","Department of Mathematical Sciences [Aalborg]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Science, University of Aalborg, Denmark","institution_ids":["https://openalex.org/I891191580"]},{"raw_affiliation_string":"Department of Mathematical Sciences [Aalborg]","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8907,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.71401033,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"1","issue":null,"first_page":"I","last_page":"33"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/orthonormal-basis","display_name":"Orthonormal basis","score":0.9321179389953613},{"id":"https://openalex.org/keywords/sparse-approximation","display_name":"Sparse approximation","score":0.7309128642082214},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6478134393692017},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6087909936904907},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5549166202545166},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.5061494708061218},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.45090100169181824},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3718133270740509},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3466804027557373},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.300712913274765},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.19886291027069092},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.12574756145477295}],"concepts":[{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.9321179389953613},{"id":"https://openalex.org/C124066611","wikidata":"https://www.wikidata.org/wiki/Q28684319","display_name":"Sparse approximation","level":2,"score":0.7309128642082214},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6478134393692017},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6087909936904907},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5549166202545166},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.5061494708061218},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.45090100169181824},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3718133270740509},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3466804027557373},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.300712913274765},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.19886291027069092},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12574756145477295},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/icip.2003.1246891","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icip.2003.1246891","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429)","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.535.5343","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.535.5343","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://people.math.aau.dk/~mnielsen/reprints/icip02.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:inria-00570099v1","is_oa":true,"landing_page_url":"https://inria.hal.science/inria-00570099","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Proc. IEEE Intl. Conf. Image Proc. (ICIP'03), Sep 2003, Barcelona, Spain. pp.I-33 -- I-36, ⟨10.1109/ICIP.2003.1246891⟩","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"pmh:oai:pure.atira.dk:publications/84ad9c30-0043-11da-b4d5-000ea68e967b","is_oa":false,"landing_page_url":"https://vbn.aau.dk/da/publications/84ad9c30-0043-11da-b4d5-000ea68e967b","pdf_url":null,"source":{"id":"https://openalex.org/S4306401731","display_name":"VBN Forskningsportal (Aalborg Universitet)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I891191580","host_organization_name":"Aalborg University","host_organization_lineage":["https://openalex.org/I891191580"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Gribonval , R & Nielsen , M 2003 , Sparse decompositions in 'incoherent' dictionaries . in Proceedings of the 2003 International Conference on Image Processing . vol. 1 , Kluwer Academic Publishers , pp. 33-36 , 2003 International Conference on Image Processing , 14/09/2003 . https://doi.org/10.1109/ICIP.2003.1246891","raw_type":"contributionToPeriodical"}],"best_oa_location":{"id":"pmh:oai:HAL:inria-00570099v1","is_oa":true,"landing_page_url":"https://inria.hal.science/inria-00570099","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Proc. IEEE Intl. Conf. Image Proc. (ICIP'03), Sep 2003, Barcelona, Spain. pp.I-33 -- I-36, ⟨10.1109/ICIP.2003.1246891⟩","raw_type":"info:eu-repo/semantics/conferenceObject"},"sustainable_development_goals":[{"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4","score":0.7300000190734863}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W121085262","https://openalex.org/W1986931325","https://openalex.org/W1987842033","https://openalex.org/W2017399882","https://openalex.org/W2021302824","https://openalex.org/W2076866563","https://openalex.org/W2079556846","https://openalex.org/W2086869478","https://openalex.org/W2099641086","https://openalex.org/W2133866430","https://openalex.org/W2145889472","https://openalex.org/W2146842127","https://openalex.org/W2151693816","https://openalex.org/W2154332973","https://openalex.org/W2157969180","https://openalex.org/W2161219071","https://openalex.org/W2167839759","https://openalex.org/W2169013483","https://openalex.org/W4231428347","https://openalex.org/W4242704675","https://openalex.org/W4251405722","https://openalex.org/W6669955640","https://openalex.org/W6683039091","https://openalex.org/W6685347855","https://openalex.org/W6813223041"],"related_works":["https://openalex.org/W2370850565","https://openalex.org/W2381894435","https://openalex.org/W2296214397","https://openalex.org/W2951195293","https://openalex.org/W2029951831","https://openalex.org/W3141309046","https://openalex.org/W2497125423","https://openalex.org/W2032552241","https://openalex.org/W4296643228","https://openalex.org/W2984862312"],"abstract_inverted_index":{"The":[0,93],"purpose":[1],"of":[2,19,24,61,68,104],"this":[3],"paper":[4],"is":[5,56,99,108],"to":[6],"generalize":[7],"a":[8,22,41,45,51,69,74,102],"result":[9,60],"by":[10,101],"Donoho,":[11],"Huo,":[12,64],"Elad":[13],"and":[14,36,63,113],"Bruckstein":[15],"on":[16,40],"sparse":[17,47,81],"representations":[18],"signals/images":[20],"in":[21,33,49,110],"union":[23,103],"two":[25],"orthonormal":[26,106],"bases.":[27],"We":[28],"consider":[29],"general":[30],"(redundant)":[31],"dictionaries":[32,87],"finite":[34],"dimension,":[35],"derive":[37],"sufficient":[38],"conditions":[39],"signal/image":[42],"for":[43,80,86],"having":[44],"unique":[46],"representation":[48],"such":[50],"dictionary.":[52],"In":[53],"particular,":[54],"it":[55],"proved":[57],"that":[58,88],"the":[59,66,97],"Donoho":[62],"concerning":[65],"replacement":[67],"combinatorial":[70],"optimization":[71],"problem":[72,77],"with":[73],"linear":[75],"programming":[76],"when":[78],"searching":[79],"representations,":[82],"has":[83],"an":[84],"analog":[85],"may":[89],"be":[90],"highly":[91],"redundant.":[92],"special":[94],"case":[95],"where":[96],"dictionary":[98],"given":[100],"several":[105],"bases":[107],"studied":[109],"more":[111],"detail":[112],"some":[114],"examples":[115],"are":[116],"given.":[117]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}