{"id":"https://openalex.org/W2938524150","doi":"https://doi.org/10.1109/icassp.2019.8683214","title":"Solving Continuous-domain Problems Exactly with Multiresolution B-splines","display_name":"Solving Continuous-domain Problems Exactly with Multiresolution B-splines","publication_year":2019,"publication_date":"2019-04-17","ids":{"openalex":"https://openalex.org/W2938524150","doi":"https://doi.org/10.1109/icassp.2019.8683214","mag":"2938524150"},"language":"en","primary_location":{"id":"doi:10.1109/icassp.2019.8683214","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icassp.2019.8683214","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://infoscience.epfl.ch/record/267674","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046721821","display_name":"Thomas Debarre","orcid":"https://orcid.org/0000-0002-1953-3064"},"institutions":[{"id":"https://openalex.org/I4210133377","display_name":"Centre d'Imagerie BioMedicale","ror":"https://ror.org/03fw2bn12","country_code":"CH","type":"facility","lineage":["https://openalex.org/I4210133377"]},{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Thomas Debarre","raw_affiliation_strings":["Biomedical Imaging Group, École polytechnique fédérale de Lausanne, Switzerland","Biomedical Imaging Group, \u00c9cole polytechnique f\u00e9d\u00e9rale de Lausanne, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Biomedical Imaging Group, École polytechnique fédérale de Lausanne, Switzerland","institution_ids":["https://openalex.org/I4210133377"]},{"raw_affiliation_string":"Biomedical Imaging Group, \u00c9cole polytechnique f\u00e9d\u00e9rale de Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015119381","display_name":"Julien Fageot","orcid":"https://orcid.org/0000-0002-2122-2580"},"institutions":[{"id":"https://openalex.org/I4210133377","display_name":"Centre d'Imagerie BioMedicale","ror":"https://ror.org/03fw2bn12","country_code":"CH","type":"facility","lineage":["https://openalex.org/I4210133377"]},{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Julien Fageot","raw_affiliation_strings":["Biomedical Imaging Group, École polytechnique fédérale de Lausanne, Switzerland","Biomedical Imaging Group, \u00c9cole polytechnique f\u00e9d\u00e9rale de Lausanne, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Biomedical Imaging Group, École polytechnique fédérale de Lausanne, Switzerland","institution_ids":["https://openalex.org/I4210133377"]},{"raw_affiliation_string":"Biomedical Imaging Group, \u00c9cole polytechnique f\u00e9d\u00e9rale de Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008465855","display_name":"Harshit Gupta","orcid":"https://orcid.org/0000-0002-2910-9072"},"institutions":[{"id":"https://openalex.org/I4210133377","display_name":"Centre d'Imagerie BioMedicale","ror":"https://ror.org/03fw2bn12","country_code":"CH","type":"facility","lineage":["https://openalex.org/I4210133377"]},{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Harshit Gupta","raw_affiliation_strings":["Biomedical Imaging Group, École polytechnique fédérale de Lausanne, Switzerland","Biomedical Imaging Group, \u00c9cole polytechnique f\u00e9d\u00e9rale de Lausanne, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Biomedical Imaging Group, École polytechnique fédérale de Lausanne, Switzerland","institution_ids":["https://openalex.org/I4210133377"]},{"raw_affiliation_string":"Biomedical Imaging Group, \u00c9cole polytechnique f\u00e9d\u00e9rale de Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027830035","display_name":"Micha\u00ebl Unser","orcid":"https://orcid.org/0000-0003-1248-2513"},"institutions":[{"id":"https://openalex.org/I4210133377","display_name":"Centre d'Imagerie BioMedicale","ror":"https://ror.org/03fw2bn12","country_code":"CH","type":"facility","lineage":["https://openalex.org/I4210133377"]},{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Michael Unser","raw_affiliation_strings":["Biomedical Imaging Group, École polytechnique fédérale de Lausanne, Switzerland","Biomedical Imaging Group, \u00c9cole polytechnique f\u00e9d\u00e9rale de Lausanne, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Biomedical Imaging Group, École polytechnique fédérale de Lausanne, Switzerland","institution_ids":["https://openalex.org/I4210133377"]},{"raw_affiliation_string":"Biomedical Imaging Group, \u00c9cole polytechnique f\u00e9d\u00e9rale de Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"5122","last_page":"5126"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9943000078201294,"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/T10534","display_name":"Structural Health Monitoring Techniques","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6954976320266724},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5794580578804016},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.5744957327842712},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.542323887348175},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5375914573669434},{"id":"https://openalex.org/keywords/spline","display_name":"Spline (mechanical)","score":0.534896969795227},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.5102999210357666},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4858567416667938},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.47869470715522766},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.47517627477645874},{"id":"https://openalex.org/keywords/total-variation-denoising","display_name":"Total variation denoising","score":0.44364798069000244},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4392911195755005},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4192246198654175},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3774232566356659},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3706132769584656},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18166136741638184},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09553799033164978},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08741316199302673}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6954976320266724},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5794580578804016},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.5744957327842712},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.542323887348175},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5375914573669434},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.534896969795227},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.5102999210357666},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4858567416667938},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.47869470715522766},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47517627477645874},{"id":"https://openalex.org/C207282899","wikidata":"https://www.wikidata.org/wiki/Q7828156","display_name":"Total variation denoising","level":3,"score":0.44364798069000244},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4392911195755005},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4192246198654175},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3774232566356659},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3706132769584656},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18166136741638184},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09553799033164978},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08741316199302673},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/icassp.2019.8683214","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icassp.2019.8683214","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)","raw_type":"proceedings-article"},{"id":"pmh:oai:infoscience.epfl.ch:267674","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/267674","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"conference proceedings"}],"best_oa_location":{"id":"pmh:oai:infoscience.epfl.ch:267674","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/267674","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"conference proceedings"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W143004564","https://openalex.org/W340244495","https://openalex.org/W1202875439","https://openalex.org/W1971258090","https://openalex.org/W1980300788","https://openalex.org/W2003410902","https://openalex.org/W2017718716","https://openalex.org/W2096504426","https://openalex.org/W2129638195","https://openalex.org/W2155447220","https://openalex.org/W2164278908","https://openalex.org/W2290904946","https://openalex.org/W2296616510","https://openalex.org/W2524857034","https://openalex.org/W2605215440","https://openalex.org/W2722359275","https://openalex.org/W2786494993","https://openalex.org/W2962904605","https://openalex.org/W2962925391","https://openalex.org/W2963748825","https://openalex.org/W2964325628","https://openalex.org/W3103915668","https://openalex.org/W4210426676","https://openalex.org/W4250955649","https://openalex.org/W4292363360","https://openalex.org/W4300263211","https://openalex.org/W6627877419","https://openalex.org/W6742195890"],"related_works":["https://openalex.org/W2889253769","https://openalex.org/W2588406281","https://openalex.org/W3033981387","https://openalex.org/W2068276401","https://openalex.org/W2131662362","https://openalex.org/W2922512599","https://openalex.org/W629372277","https://openalex.org/W3098958300","https://openalex.org/W2184977437","https://openalex.org/W2895901585"],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2,19,45,51,79,96],"discretization":[3],"method":[4,33],"for":[5,59],"continuous-domain":[6],"linear":[7],"inverse":[8,26,110],"problems":[9,27],"with":[10,42],"multiple-order":[11],"total-variation":[12],"(TV)":[13],"regularization.":[14],"It":[15],"is":[16,101],"based":[17],"on":[18,44],"recent":[20],"result":[21],"that":[22,24,117],"proves":[23],"such":[25],"have":[28],"sparse":[29,106],"polynomial-spline":[30],"solutions.":[31],"Our":[32,85],"consists":[34],"in":[35,50],"restricting":[36],"the":[37,65,69,92],"search":[38,61],"space":[39],"to":[40,68,78,105],"splines":[41],"knots":[43],"uniform":[46],"grid,":[47],"which":[48,72],"results":[49,116],"standard":[52],"convex":[53],"finite-dimensional":[54],"problem.":[55,111],"As":[56],"basis":[57],"functions":[58],"this":[60],"space,":[62],"we":[63,113],"use":[64],"B-splines":[66],"matched":[67],"regularization":[70],"order,":[71],"are":[73],"optimally":[74],"localized.":[75],"This":[76],"leads":[77],"well-conditioned,":[80],"computationally":[81],"feasible":[82],"optimization":[83],"task.":[84],"proposed":[86],"iterative":[87],"multiresolution":[88],"algorithm":[89],"then":[90],"refines":[91],"grid":[93],"size":[94],"until":[95],"desired":[97],"level":[98],"of":[99,108],"accuracy":[100],"met":[102],"and":[103],"converges":[104],"solutions":[107],"our":[109,119],"Finally,":[112],"present":[114],"experimental":[115],"validate":[118],"approach.":[120]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}