{"id":"https://openalex.org/W2043718001","doi":"https://doi.org/10.1109/ciss.2010.5464811","title":"Sobolev duals of random frames","display_name":"Sobolev duals of random frames","publication_year":2010,"publication_date":"2010-03-01","ids":{"openalex":"https://openalex.org/W2043718001","doi":"https://doi.org/10.1109/ciss.2010.5464811","mag":"2043718001"},"language":"en","primary_location":{"id":"doi:10.1109/ciss.2010.5464811","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ciss.2010.5464811","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 44th Annual Conference on Information Sciences and Systems (CISS)","raw_type":"proceedings-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/A5029375269","display_name":"C. Si\u0307nan G\u00fcnt\u00fcrk","orcid":null},"institutions":[{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]},{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"C. Sinan Gunturk","raw_affiliation_strings":["Courant Institute of Mathematical Sciences, New York University, NY, USA","Courant Institute of Mathematical Sciences, New York University USA"],"affiliations":[{"raw_affiliation_string":"Courant Institute of Mathematical Sciences, New York University, NY, USA","institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974"]},{"raw_affiliation_string":"Courant Institute of Mathematical Sciences, New York University USA","institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087721458","display_name":"Mark Lammers","orcid":"https://orcid.org/0000-0003-0969-5374"},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]},{"id":"https://openalex.org/I153901656","display_name":"University of North Carolina Wilmington","ror":"https://ror.org/02t0qr014","country_code":"US","type":"education","lineage":["https://openalex.org/I153901656"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mark Lammers","raw_affiliation_strings":["North Carolina State University, Wilmington, NC, USA","University of North Carolina , Wilmington, USA"],"affiliations":[{"raw_affiliation_string":"North Carolina State University, Wilmington, NC, USA","institution_ids":["https://openalex.org/I153901656","https://openalex.org/I137902535"]},{"raw_affiliation_string":"University of North Carolina , Wilmington, USA","institution_ids":["https://openalex.org/I153901656"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102144141","display_name":"Alex Powell","orcid":null},"institutions":[{"id":"https://openalex.org/I200719446","display_name":"Vanderbilt University","ror":"https://ror.org/02vm5rt34","country_code":"US","type":"education","lineage":["https://openalex.org/I200719446"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alex Powell","raw_affiliation_strings":["Vanderbilt University, Nashville, TN, USA","Vanderbilt University Nashville TN USA"],"affiliations":[{"raw_affiliation_string":"Vanderbilt University, Nashville, TN, USA","institution_ids":["https://openalex.org/I200719446"]},{"raw_affiliation_string":"Vanderbilt University Nashville TN USA","institution_ids":["https://openalex.org/I200719446"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055778695","display_name":"Rayan Saab","orcid":null},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Rayan Saab","raw_affiliation_strings":["University of British Columbia, Vancouver, BC, Canada","University of British Columbia  Vancouver Canada"],"affiliations":[{"raw_affiliation_string":"University of British Columbia, Vancouver, BC, Canada","institution_ids":["https://openalex.org/I141945490"]},{"raw_affiliation_string":"University of British Columbia  Vancouver Canada","institution_ids":["https://openalex.org/I141945490"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001594301","display_name":"\u00d6zg\u00fcr Y\u0131lmaz","orcid":"https://orcid.org/0000-0002-4349-3859"},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Ozgur Yilmaz","raw_affiliation_strings":["University of British Columbia, Vancouver, BC, Canada","University of British Columbia  Vancouver Canada"],"affiliations":[{"raw_affiliation_string":"University of British Columbia, Vancouver, BC, Canada","institution_ids":["https://openalex.org/I141945490"]},{"raw_affiliation_string":"University of British Columbia  Vancouver Canada","institution_ids":["https://openalex.org/I141945490"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5029375269"],"corresponding_institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974"],"apc_list":null,"apc_paid":null,"fwci":0.6465,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.70549612,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"5"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9998000264167786,"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":0.9998000264167786,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9993000030517578,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/quantization","display_name":"Quantization (signal processing)","score":0.6379134654998779},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6159158945083618},{"id":"https://openalex.org/keywords/bandlimiting","display_name":"Bandlimiting","score":0.6072742938995361},{"id":"https://openalex.org/keywords/dual-polyhedron","display_name":"Dual polyhedron","score":0.5054867267608643},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5037259459495544},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.44709721207618713},{"id":"https://openalex.org/keywords/signal-reconstruction","display_name":"Signal reconstruction","score":0.43584054708480835},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4324926435947418},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36088818311691284},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22007879614830017},{"id":"https://openalex.org/keywords/signal-processing","display_name":"Signal processing","score":0.20047909021377563},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.14403262734413147},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.12724873423576355},{"id":"https://openalex.org/keywords/digital-signal-processing","display_name":"Digital signal processing","score":0.09440189599990845}],"concepts":[{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.6379134654998779},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6159158945083618},{"id":"https://openalex.org/C129997835","wikidata":"https://www.wikidata.org/wiki/Q806263","display_name":"Bandlimiting","level":3,"score":0.6072742938995361},{"id":"https://openalex.org/C105313907","wikidata":"https://www.wikidata.org/wiki/Q1053857","display_name":"Dual polyhedron","level":2,"score":0.5054867267608643},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5037259459495544},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.44709721207618713},{"id":"https://openalex.org/C70958404","wikidata":"https://www.wikidata.org/wiki/Q7512728","display_name":"Signal reconstruction","level":4,"score":0.43584054708480835},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4324926435947418},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36088818311691284},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22007879614830017},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.20047909021377563},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.14403262734413147},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.12724873423576355},{"id":"https://openalex.org/C84462506","wikidata":"https://www.wikidata.org/wiki/Q173142","display_name":"Digital signal processing","level":2,"score":0.09440189599990845},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/ciss.2010.5464811","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ciss.2010.5464811","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 44th Annual Conference on Information Sciences and Systems (CISS)","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.168.3645","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.168.3645","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ece.ubc.ca/%7Erayans/publications/CISS_SobDuals.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320307521","display_name":"American Institute of Mathematics","ror":"https://ror.org/02a0fwv66"},{"id":"https://openalex.org/F4320329205","display_name":"Banff International Research Station for Mathematical Innovation and Discovery","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W118952169","https://openalex.org/W1527312120","https://openalex.org/W1582983303","https://openalex.org/W1989877067","https://openalex.org/W2008840379","https://openalex.org/W2014771970","https://openalex.org/W2018342351","https://openalex.org/W2020509300","https://openalex.org/W2058936451","https://openalex.org/W2122645855","https://openalex.org/W2126749541","https://openalex.org/W2163296328","https://openalex.org/W2168494960","https://openalex.org/W2340870620","https://openalex.org/W4297669117","https://openalex.org/W6604851887","https://openalex.org/W6654257567"],"related_works":["https://openalex.org/W1527312120","https://openalex.org/W2963638790","https://openalex.org/W1902265650","https://openalex.org/W4298027785","https://openalex.org/W2161136939","https://openalex.org/W2160209843","https://openalex.org/W1964786086","https://openalex.org/W3012217557","https://openalex.org/W3003347734","https://openalex.org/W2111403872"],"abstract_inverted_index":{"Sobolev":[0,48,71],"dual":[1,26,49,72],"frames":[2,73,120],"have":[3],"recently":[4],"been":[5],"proposed":[6],"as":[7],"optimal":[8,35],"alternative":[9],"reconstruction":[10,55,91],"operators":[11],"that":[12,92,110],"are":[13,93,133],"specifically":[14],"tailored":[15],"for":[16,36,57,117],"Sigma-Delta":[17],"(\u00bf\u00bf)":[18],"quantization":[19,40,141],"of":[20,28,42,53,60,70,88,102,127,149],"frame":[21,27,33,82],"coefficients.":[22],"While":[23],"the":[24,37,47,54,58,68,79,99,125,128,137],"canonical":[25],"a":[29],"given":[30,80],"analysis":[31,81,129],"(sampling)":[32],"is":[34],"white-noise":[38],"type":[39],"error":[41,56],"Pulse":[43],"Code":[44],"Modulation":[45],"(PCM),":[46],"offers":[50],"significant":[51],"reduction":[52],"colored-noise":[59],"\u00bf\u00bf":[61],"quantization.":[62],"However,":[63],"initial":[64],"quantitative":[65],"results":[66,132],"concerning":[67],"use":[69],"required":[74],"certain":[75],"regularity":[76,112],"assumptions":[77,113],"on":[78,90,124],"in":[83,98,136],"order":[84],"to":[85,95,146],"deduce":[86],"improvements":[87],"performance":[89],"similar":[94],"those":[96],"achieved":[97],"standard":[100],"setting":[101],"bandlimited":[103],"functions.":[104],"In":[105],"this":[106],"paper,":[107],"we":[108],"show":[109],"these":[111],"can":[114],"be":[115],"lifted":[116],"(Gaussian)":[118],"random":[119],"with":[121],"high":[122],"probability":[123],"choice":[126],"frame.":[130],"Our":[131],"immediately":[134],"applicable":[135],"traditional":[138],"oversampled":[139],"(coarse)":[140],"scenario,":[142],"but":[143],"also":[144],"extend":[145],"compressive":[147],"sampling":[148],"sparse":[150],"signals.":[151]},"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}