{"id":"https://openalex.org/W2336180720","doi":"https://doi.org/10.1109/lsp.2016.2555139","title":"An Inner-Product Calculus for Periodic Functions and Curves","display_name":"An Inner-Product Calculus for Periodic Functions and Curves","publication_year":2016,"publication_date":"2016-04-15","ids":{"openalex":"https://openalex.org/W2336180720","doi":"https://doi.org/10.1109/lsp.2016.2555139","mag":"2336180720"},"language":"en","primary_location":{"id":"doi:10.1109/lsp.2016.2555139","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2016.2555139","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Signal Processing Letters","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://infoscience.epfl.ch/record/220942","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000203590","display_name":"Ana\u00efs Badoual","orcid":"https://orcid.org/0000-0001-7303-6344"},"institutions":[{"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":true,"raw_author_name":"Anais Badoual","raw_affiliation_strings":["Biomedical Imaging Group, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), 1015 Lausanne, Switzerland"],"affiliations":[{"raw_affiliation_string":"Biomedical Imaging Group, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), 1015 Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010972561","display_name":"Daniel Schmitter","orcid":null},"institutions":[{"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":"Daniel Schmitter","raw_affiliation_strings":["Biomedical Imaging Group, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), 1015 Lausanne, Switzerland"],"affiliations":[{"raw_affiliation_string":"Biomedical Imaging Group, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), 1015 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/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, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), 1015 Lausanne, Switzerland"],"affiliations":[{"raw_affiliation_string":"Biomedical Imaging Group, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), 1015 Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5000203590"],"corresponding_institution_ids":["https://openalex.org/I5124864"],"apc_list":null,"apc_paid":null,"fwci":1.0162,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.82597325,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"23","issue":"6","first_page":"878","last_page":"882"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9995999932289124,"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":0.9995999932289124,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9987999796867371,"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/T13487","display_name":"Statistical and numerical algorithms","score":0.9764000177383423,"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/parametric-equation","display_name":"Parametric equation","score":0.6612337827682495},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5496155619621277},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4726879894733429},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.46040618419647217},{"id":"https://openalex.org/keywords/aliasing","display_name":"Aliasing","score":0.45781129598617554},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45596498250961304},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4249183237552643},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.4012182652950287},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3687444031238556},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16095668077468872},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09663504362106323}],"concepts":[{"id":"https://openalex.org/C99636146","wikidata":"https://www.wikidata.org/wiki/Q35889","display_name":"Parametric equation","level":2,"score":0.6612337827682495},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5496155619621277},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4726879894733429},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.46040618419647217},{"id":"https://openalex.org/C4069607","wikidata":"https://www.wikidata.org/wiki/Q868732","display_name":"Aliasing","level":3,"score":0.45781129598617554},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45596498250961304},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4249183237552643},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4012182652950287},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3687444031238556},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16095668077468872},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09663504362106323},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C136536468","wikidata":"https://www.wikidata.org/wiki/Q1225894","display_name":"Undersampling","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/lsp.2016.2555139","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2016.2555139","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Signal Processing Letters","raw_type":"journal-article"},{"id":"pmh:oai:infoscience.epfl.ch:220942","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/220942","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:infoscience.tind.io:220942","is_oa":true,"landing_page_url":"http://bigwww.epfl.ch/publications/badoual1601.html","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"research article"}],"best_oa_location":{"id":"pmh:oai:infoscience.epfl.ch:220942","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/220942","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1441312571","display_name":null,"funder_award_id":"00020","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G1781244499","display_name":null,"funder_award_id":"Grant 200020-162343","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G2926069366","display_name":"Spline methods for the continuous/discrete processing of images","funder_award_id":"162343","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G4836148144","display_name":"Immunologie des Typ-1 Diabetes.","funder_award_id":"20002","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G5599649393","display_name":null,"funder_award_id":"200020","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G628552264","display_name":null,"funder_award_id":"200020","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G6510213724","display_name":null,"funder_award_id":"200020-162343","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W168681803","https://openalex.org/W1028196162","https://openalex.org/W1479895638","https://openalex.org/W1814362492","https://openalex.org/W1831978873","https://openalex.org/W1982662510","https://openalex.org/W1982814196","https://openalex.org/W1984896113","https://openalex.org/W2018332268","https://openalex.org/W2029964832","https://openalex.org/W2057085895","https://openalex.org/W2062024414","https://openalex.org/W2064855647","https://openalex.org/W2065829287","https://openalex.org/W2088869937","https://openalex.org/W2103300762","https://openalex.org/W2104095591","https://openalex.org/W2113885710","https://openalex.org/W2115755118","https://openalex.org/W2115943920","https://openalex.org/W2132984323","https://openalex.org/W2142195632","https://openalex.org/W2153058280","https://openalex.org/W2159152281","https://openalex.org/W2159579975","https://openalex.org/W2161770118","https://openalex.org/W2165697862","https://openalex.org/W2166500461","https://openalex.org/W2166796177","https://openalex.org/W4255272544","https://openalex.org/W6606880008"],"related_works":["https://openalex.org/W2382174632","https://openalex.org/W2100212762","https://openalex.org/W2129959498","https://openalex.org/W2784060934","https://openalex.org/W2902714807","https://openalex.org/W2537489131","https://openalex.org/W2394084632","https://openalex.org/W2358293514","https://openalex.org/W2046633342","https://openalex.org/W2014650515"],"abstract_inverted_index":{"Our":[0],"motivation":[1],"is":[2,85,96],"the":[3,44,53,97,101],"design":[4],"of":[5,49,55,100],"efficient":[6],"algorithms":[7],"to":[8,26,87],"process":[9],"closed":[10,56],"curves":[11,60,89],"represented":[12],"by":[13],"basis":[14],"functions":[15],"or":[16],"wavelets.":[17],"To":[18,73],"that":[19,70,84],"end,":[20],"we":[21,40,77],"introduce":[22],"an":[23],"inner-product":[24],"calculus":[25],"evaluate":[27],"correlations":[28],"and":[29,46,61],"L":[30],"<sub":[31],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[32],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sub>":[33],"distances":[34],"between":[35],"such":[36],"curves.":[37],"In":[38],"particular,":[39],"present":[41],"formulas":[42],"for":[43,67],"direct":[45],"exact":[47,98],"evaluation":[48],"correlation":[50],"matrices":[51],"in":[52],"case":[54],"(i.e.,":[57],"periodic)":[58],"parametric":[59],"periodic":[62],"signals.":[63],"We":[64],"give":[65],"simplifications":[66],"practical":[68],"cases":[69],"involve":[71],"B-splines.":[72],"illustrate":[74],"this":[75],"approach,":[76],"also":[78],"propose":[79],"a":[80],"least-squares":[81],"approximation":[82],"scheme":[83],"able":[86],"resample":[88],"while":[90],"minimizing":[91],"aliasing":[92],"artifacts.":[93],"Another":[94],"application":[95],"calculation":[99],"enclosed":[102],"area.":[103]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3}],"updated_date":"2026-03-15T09:29:46.208133","created_date":"2025-10-10T00:00:00"}
