{"id":"https://openalex.org/W1980929117","doi":"https://doi.org/10.1137/120874990","title":"Clustered Sparsity and Separation of Cartoon and Texture","display_name":"Clustered Sparsity and Separation of Cartoon and Texture","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1980929117","doi":"https://doi.org/10.1137/120874990","mag":"1980929117"},"language":"en","primary_location":{"id":"doi:10.1137/120874990","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120874990","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Imaging Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090767423","display_name":"Gitta Kutyniok","orcid":"https://orcid.org/0000-0001-9738-2487"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Gitta Kutyniok","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5090767423"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.488,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.9029091,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"6","issue":"2","first_page":"848","last_page":"874"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9991999864578247,"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"}},{"id":"https://openalex.org/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9976000189781189,"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"}},{"id":"https://openalex.org/T10824","display_name":"Image Retrieval and Classification Techniques","score":0.9919999837875366,"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/curvelet","display_name":"Curvelet","score":0.8035039901733398},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5671955347061157},{"id":"https://openalex.org/keywords/texture","display_name":"Texture (cosmology)","score":0.551703691482544},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5321084260940552},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5214211940765381},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.49377474188804626},{"id":"https://openalex.org/keywords/energy-minimization","display_name":"Energy minimization","score":0.47456198930740356},{"id":"https://openalex.org/keywords/gabor-wavelet","display_name":"Gabor wavelet","score":0.45801085233688354},{"id":"https://openalex.org/keywords/discontinuity","display_name":"Discontinuity (linguistics)","score":0.45647722482681274},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.44554227590560913},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42741888761520386},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3830713927745819},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.3604692816734314},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15415167808532715},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.14117392897605896}],"concepts":[{"id":"https://openalex.org/C131720326","wikidata":"https://www.wikidata.org/wiki/Q5196075","display_name":"Curvelet","level":4,"score":0.8035039901733398},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5671955347061157},{"id":"https://openalex.org/C2781195486","wikidata":"https://www.wikidata.org/wiki/Q289436","display_name":"Texture (cosmology)","level":3,"score":0.551703691482544},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5321084260940552},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5214211940765381},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.49377474188804626},{"id":"https://openalex.org/C14961307","wikidata":"https://www.wikidata.org/wiki/Q5377176","display_name":"Energy minimization","level":2,"score":0.47456198930740356},{"id":"https://openalex.org/C136902061","wikidata":"https://www.wikidata.org/wiki/Q16981559","display_name":"Gabor wavelet","level":5,"score":0.45801085233688354},{"id":"https://openalex.org/C2777042112","wikidata":"https://www.wikidata.org/wiki/Q5281658","display_name":"Discontinuity (linguistics)","level":2,"score":0.45647722482681274},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.44554227590560913},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42741888761520386},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3830713927745819},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.3604692816734314},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15415167808532715},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.14117392897605896},{"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/C147597530","wikidata":"https://www.wikidata.org/wiki/Q369472","display_name":"Computational chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.0},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/120874990","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120874990","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Imaging Sciences","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1440672848","display_name":null,"funder_award_id":"various","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G2160137948","display_name":null,"funder_award_id":"KU 1446/14","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G2300626487","display_name":null,"funder_award_id":"Matheon","funder_id":"https://openalex.org/F4320323688","funder_display_name":"Einstein Stiftung Berlin"},{"id":"https://openalex.org/G3127212197","display_name":null,"funder_award_id":"SPP-1324","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G4946944115","display_name":null,"funder_award_id":"Matheon","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5106512922","display_name":null,"funder_award_id":"Deutsche Forschungsgemeinschaft (DFG","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6024419964","display_name":null,"funder_award_id":"Deutsche Forschungsgemeinschaft (DFG)","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6052429835","display_name":null,"funder_award_id":"(DFG)","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6537435729","display_name":null,"funder_award_id":"Heisenberg","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8965197529","display_name":null,"funder_award_id":"SPP-1324 KU 1446/13","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320308380","display_name":"Yale University","ror":"https://ror.org/03v76x132"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320323688","display_name":"Einstein Stiftung Berlin","ror":"https://ror.org/03s0fv852"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":60,"referenced_works":["https://openalex.org/W1488881187","https://openalex.org/W1532154335","https://openalex.org/W1552686093","https://openalex.org/W1560910787","https://openalex.org/W1593431850","https://openalex.org/W1674776290","https://openalex.org/W1952959721","https://openalex.org/W1965366508","https://openalex.org/W1981337995","https://openalex.org/W1990805796","https://openalex.org/W1992950686","https://openalex.org/W1997149618","https://openalex.org/W1999905919","https://openalex.org/W2008076677","https://openalex.org/W2031200994","https://openalex.org/W2040073627","https://openalex.org/W2044628011","https://openalex.org/W2045009766","https://openalex.org/W2050834445","https://openalex.org/W2066630786","https://openalex.org/W2069912449","https://openalex.org/W2072476274","https://openalex.org/W2078204800","https://openalex.org/W2079756223","https://openalex.org/W2084115655","https://openalex.org/W2087377426","https://openalex.org/W2092231222","https://openalex.org/W2093212899","https://openalex.org/W2097323375","https://openalex.org/W2098439395","https://openalex.org/W2099641086","https://openalex.org/W2109305553","https://openalex.org/W2111730426","https://openalex.org/W2114147096","https://openalex.org/W2116148865","https://openalex.org/W2121651107","https://openalex.org/W2125455772","https://openalex.org/W2128057924","https://openalex.org/W2136235822","https://openalex.org/W2137155471","https://openalex.org/W2138923206","https://openalex.org/W2145889472","https://openalex.org/W2150920547","https://openalex.org/W2152171106","https://openalex.org/W2154332973","https://openalex.org/W2154996879","https://openalex.org/W2161219071","https://openalex.org/W2162023479","https://openalex.org/W2162547327","https://openalex.org/W2164452299","https://openalex.org/W2167839759","https://openalex.org/W2296616510","https://openalex.org/W2591953731","https://openalex.org/W2963358108","https://openalex.org/W2963851978","https://openalex.org/W2964514338","https://openalex.org/W3099751318","https://openalex.org/W4210381520","https://openalex.org/W4242359720","https://openalex.org/W4251028087"],"related_works":["https://openalex.org/W2020709293","https://openalex.org/W2033386799","https://openalex.org/W3142541301","https://openalex.org/W1585855827","https://openalex.org/W2378906974","https://openalex.org/W4242398081","https://openalex.org/W2146220314","https://openalex.org/W2170080599","https://openalex.org/W2353022594","https://openalex.org/W2047865552"],"abstract_inverted_index":{"Natural":[0],"images":[1],"are":[2,148,237],"typically":[3],"a":[4,37,69,76,84,101,106,110,167,173,182,187,198,203,241],"composition":[5],"of":[6,40,72,75,78,91,105,207,220,234],"cartoon":[7,27,79,124,170],"and":[8,29,45,55,80,109,113,130,240],"texture":[9,34,81,132,190],"structures.":[10],"One":[11],"common":[12],"task":[13],"is":[14,161,178,212],"to":[15,51],"separate":[16],"such":[17],"an":[18,214],"image":[19,99],"into":[20,126,134],"two":[21],"single":[22],"images,":[23],"one":[24],"containing":[25,32],"the":[26,30,33,73,98,115,123,127,131,135,140,143,146,208,218,221,227,231],"part":[28],"other":[31],"part.":[35],"Recently,":[36],"powerful":[38],"class":[39,90],"algorithms":[41],"using":[42,88],"sparse":[43],"approximation":[44,119],"$\\ell_1$":[46,116],"minimization":[47],"has":[48],"been":[49,62],"introduced":[50],"resolve":[52],"this":[53,65,89,164],"problem,":[54],"numerous":[56],"inspiring":[57],"empirical":[58],"results":[59],"have":[60],"already":[61],"obtained.":[63],"In":[64,224],"paper":[66],"we":[67,95,151,171,191],"provide":[68],"theoretical":[70],"study":[71],"separation":[74,160],"combination":[77],"structures":[82],"in":[83,100],"continuum":[85,228],"model":[86,168,188],"situation":[87],"algorithms.":[92],"The":[93],"methodology":[94],"consider":[96,172,192],"expands":[97],"combined":[102],"dictionary":[103],"consisting":[104],"curvelet":[107,128,222],"frame":[108,112],"Gabor":[111,136,199,209],"minimizes":[114],"norm.":[117],"Sparse":[118],"properties":[120],"then":[121],"force":[122],"components":[125,133],"coefficients":[129,147],"coefficients,":[137],"thereby":[138],"separating":[139],"image.":[141],"Utilizing":[142],"fact":[144],"that":[145,153],"clustered":[149],"geometrically,":[150],"prove":[152],"at":[154],"sufficiently":[155],"fine":[156],"scales":[157],"arbitrarily":[158],"precise":[159],"possible.":[162],"For":[163],"analysis,":[165],"as":[166],"for":[169,189],"compactly":[174],"supported":[175],"function":[176],"which":[177,211],"$C^2$":[179,183],"apart":[180],"from":[181],"discontinuity":[184],"curve.":[185],"As":[186],"locally":[193],"oscillatory":[194],"patterns":[195],"generated":[196],"by":[197],"system":[200],"associated":[201],"with":[202,226],"fixed":[204],"appropriate":[205],"size":[206],"window,":[210],"linked---satisfying":[213],"energy":[215],"matching":[216],"condition---to":[217],"scale":[219],"system.":[223],"accordance":[225],"domain":[229],"setting,":[230],"main":[232],"ingredients":[233],"our":[235],"analysis":[236],"clustered/geometric":[238],"sparsity":[239],"phase":[242],"space":[243],"viewpoint.":[244]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
