{"id":"https://openalex.org/W2039574235","doi":"https://doi.org/10.1137/140982428","title":"Interior Tomography Using 1D Generalized Total Variation. Part I: Mathematical Foundation","display_name":"Interior Tomography Using 1D Generalized Total Variation. Part I: Mathematical Foundation","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2039574235","doi":"https://doi.org/10.1137/140982428","mag":"2039574235"},"language":"en","primary_location":{"id":"doi:10.1137/140982428","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140982428","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":true,"oa_status":"green","oa_url":"http://infoscience.epfl.ch/record/208382","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038321378","display_name":"John Paul Ward","orcid":"https://orcid.org/0000-0003-0289-117X"},"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":"John Paul Ward","raw_affiliation_strings":["Biomedical Imaging Group, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), CH-1015, Lausanne, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Biomedical Imaging Group, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), CH-1015, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100747575","display_name":"Minji Lee","orcid":"https://orcid.org/0000-0003-2957-4457"},"institutions":[{"id":"https://openalex.org/I157485424","display_name":"Korea Advanced Institute of Science and Technology","ror":"https://ror.org/05apxxy63","country_code":"KR","type":"education","lineage":["https://openalex.org/I157485424"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Minji Lee","raw_affiliation_strings":["Bio Imaging and Signal Processing Lab, Department of Bio and Brain Engineering, KAIST, Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bio Imaging and Signal Processing Lab, Department of Bio and Brain Engineering, KAIST, Korea","institution_ids":["https://openalex.org/I157485424"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012644755","display_name":"Jong Chul Ye","orcid":"https://orcid.org/0000-0001-9763-9609"},"institutions":[{"id":"https://openalex.org/I157485424","display_name":"Korea Advanced Institute of Science and Technology","ror":"https://ror.org/05apxxy63","country_code":"KR","type":"education","lineage":["https://openalex.org/I157485424"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Jong Chul Ye","raw_affiliation_strings":["Bio Imaging and Signal Processing Lab, Department of Bio and Brain Engineering, KAIST, Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bio Imaging and Signal Processing Lab, Department of Bio and Brain Engineering, KAIST, Korea","institution_ids":["https://openalex.org/I157485424"]}]},{"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, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), CH-1015, Lausanne, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Biomedical Imaging Group, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), CH-1015, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.7036,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.89336661,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"8","issue":"1","first_page":"226","last_page":"247"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10522","display_name":"Medical Imaging Techniques and Applications","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},"topics":[{"id":"https://openalex.org/T10522","display_name":"Medical Imaging Techniques and Applications","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9927999973297119,"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/radon-transform","display_name":"Radon transform","score":0.7422033548355103},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7250009179115295},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6569867134094238},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5280811786651611},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5100453495979309},{"id":"https://openalex.org/keywords/variation","display_name":"Variation (astronomy)","score":0.49549710750579834},{"id":"https://openalex.org/keywords/tomography","display_name":"Tomography","score":0.42713138461112976},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3977259397506714},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3916647434234619},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35866230726242065},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21578553318977356},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11049529910087585}],"concepts":[{"id":"https://openalex.org/C197231052","wikidata":"https://www.wikidata.org/wiki/Q979829","display_name":"Radon transform","level":2,"score":0.7422033548355103},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7250009179115295},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6569867134094238},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5280811786651611},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5100453495979309},{"id":"https://openalex.org/C2778334786","wikidata":"https://www.wikidata.org/wiki/Q1586270","display_name":"Variation (astronomy)","level":2,"score":0.49549710750579834},{"id":"https://openalex.org/C163716698","wikidata":"https://www.wikidata.org/wiki/Q841267","display_name":"Tomography","level":2,"score":0.42713138461112976},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3977259397506714},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3916647434234619},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35866230726242065},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21578553318977356},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11049529910087585},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","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},{"id":"https://openalex.org/C44870925","wikidata":"https://www.wikidata.org/wiki/Q37547","display_name":"Astrophysics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/140982428","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140982428","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"},{"id":"pmh:oai:infoscience.epfl.ch:208382","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/208382","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:208382","is_oa":true,"landing_page_url":"http://bigwww.epfl.ch/publications/ward1501.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:208382","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/208382","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":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.7099999785423279}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1488877410","https://openalex.org/W1531371725","https://openalex.org/W1868782008","https://openalex.org/W1999493577","https://openalex.org/W2027631343","https://openalex.org/W2038284539","https://openalex.org/W2058583833","https://openalex.org/W2060686929","https://openalex.org/W2063476643","https://openalex.org/W2068017087","https://openalex.org/W2077236721","https://openalex.org/W2082737320","https://openalex.org/W2098426318","https://openalex.org/W2130859329","https://openalex.org/W2142224912","https://openalex.org/W2165565866","https://openalex.org/W2578992305","https://openalex.org/W2936995161","https://openalex.org/W2955491277"],"related_works":["https://openalex.org/W2386430105","https://openalex.org/W2356521405","https://openalex.org/W2384358604","https://openalex.org/W1567829292","https://openalex.org/W2038534795","https://openalex.org/W3001063351","https://openalex.org/W3196905815","https://openalex.org/W2351370765","https://openalex.org/W3181247111","https://openalex.org/W2189202338"],"abstract_inverted_index":{"Motivated":[0],"by":[1,72],"the":[2,36,46,101,117,126],"interior":[3],"tomography":[4],"problem,":[5],"we":[6,64,109,121],"propose":[7],"a":[8,14,19,39,53,74],"method":[9],"for":[10,48],"exact":[11,68],"reconstruction":[12,41,69,112],"of":[13,16,18,29,38,56,103,116,125],"region":[15],"interest":[17],"function":[20],"from":[21],"its":[22],"local":[23],"Radon":[24],"transform":[25],"in":[26],"any":[27],"number":[28],"dimensions.":[30],"Our":[31],"aim":[32],"is":[33,70,87,91],"to":[34],"verify":[35],"feasibility":[37],"one-dimensional":[40,93],"procedure":[42],"that":[43,66,88,95],"can":[44],"provide":[45],"foundation":[47],"an":[49,67],"efficient":[50],"algorithm.":[51],"For":[52],"broad":[54],"class":[55,102],"functions,":[57],"including":[58],"piecewise":[59],"polynomials":[60],"and":[61,94,120],"generalized":[62,75],"splines,":[63],"prove":[65],"possible":[71],"minimizing":[73],"total":[76],"variation":[77],"seminorm":[78],"along":[79],"lines.":[80],"The":[81],"main":[82],"difference":[83],"with":[84],"previous":[85],"works":[86],"our":[89],"approach":[90],"inherently":[92],"it":[96],"imposes":[97],"less":[98],"constraints":[99],"on":[100],"admissible":[104],"signals.":[105],"Within":[106],"this":[107],"formulation,":[108],"derive":[110],"unique":[111],"results":[113],"using":[114],"properties":[115],"Hilbert":[118],"transform,":[119],"present":[122],"numerical":[123],"examples":[124],"reconstruction.":[127]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}
