{"id":"https://openalex.org/W2051958361","doi":"https://doi.org/10.1137/050622791","title":"Limited Data X-Ray Tomography Using Nonlinear Evolution Equations","display_name":"Limited Data X-Ray Tomography Using Nonlinear Evolution Equations","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2051958361","doi":"https://doi.org/10.1137/050622791","mag":"2051958361"},"language":"en","primary_location":{"id":"doi:10.1137/050622791","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050622791","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5009260583","display_name":"Ville Kolehmainen","orcid":"https://orcid.org/0000-0002-5621-795X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ville Kolehmainen","raw_affiliation_strings":["ville.kolehmainen@uku.fi#TAB#"],"affiliations":[{"raw_affiliation_string":"ville.kolehmainen@uku.fi#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052627284","display_name":"Matti Lassas","orcid":"https://orcid.org/0000-0003-2043-3156"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Matti Lassas","raw_affiliation_strings":["matti.lassas@tkk.fi#TAB#"],"affiliations":[{"raw_affiliation_string":"matti.lassas@tkk.fi#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024895932","display_name":"Samuli Siltanen","orcid":"https://orcid.org/0000-0002-5988-5232"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Samuli Siltanen","raw_affiliation_strings":["samuli.siltanen@tut.fi#TAB#"],"affiliations":[{"raw_affiliation_string":"samuli.siltanen@tut.fi#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5009260583"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.9907,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.85898076,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"30","issue":"3","first_page":"1413","last_page":"1429"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10522","display_name":"Medical Imaging Techniques and Applications","score":0.9998999834060669,"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":0.9998999834060669,"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/T12386","display_name":"Advanced X-ray and CT Imaging","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.998199999332428,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7739746570587158},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.6776046752929688},{"id":"https://openalex.org/keywords/imaging-phantom","display_name":"Imaging phantom","score":0.6566778421401978},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6250512599945068},{"id":"https://openalex.org/keywords/algebraic-reconstruction-technique","display_name":"Algebraic Reconstruction Technique","score":0.587787389755249},{"id":"https://openalex.org/keywords/tomography","display_name":"Tomography","score":0.5108251571655273},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49996519088745117},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4842548072338104},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.48165714740753174},{"id":"https://openalex.org/keywords/iterative-reconstruction","display_name":"Iterative reconstruction","score":0.47897031903266907},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4574720859527588},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45139122009277344},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4511222243309021},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.43403160572052},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3422219753265381},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11905679106712341},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.10396566987037659},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09427332878112793},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.0815851092338562}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7739746570587158},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.6776046752929688},{"id":"https://openalex.org/C104293457","wikidata":"https://www.wikidata.org/wiki/Q28324852","display_name":"Imaging phantom","level":2,"score":0.6566778421401978},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6250512599945068},{"id":"https://openalex.org/C206654267","wikidata":"https://www.wikidata.org/wiki/Q4723986","display_name":"Algebraic Reconstruction Technique","level":3,"score":0.587787389755249},{"id":"https://openalex.org/C163716698","wikidata":"https://www.wikidata.org/wiki/Q841267","display_name":"Tomography","level":2,"score":0.5108251571655273},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49996519088745117},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4842548072338104},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.48165714740753174},{"id":"https://openalex.org/C141379421","wikidata":"https://www.wikidata.org/wiki/Q6094427","display_name":"Iterative reconstruction","level":2,"score":0.47897031903266907},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4574720859527588},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45139122009277344},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4511222243309021},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.43403160572052},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3422219753265381},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11905679106712341},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.10396566987037659},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09427332878112793},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0815851092338562},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"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/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/050622791","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050622791","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.492.8189","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.492.8189","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.siltanen-research.net/evolution_revision.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W1489222793","https://openalex.org/W1517403807","https://openalex.org/W1583839317","https://openalex.org/W1870701051","https://openalex.org/W1967581593","https://openalex.org/W1967981081","https://openalex.org/W1969899894","https://openalex.org/W1972054485","https://openalex.org/W1980617746","https://openalex.org/W1984634678","https://openalex.org/W2014746566","https://openalex.org/W2037521346","https://openalex.org/W2037775121","https://openalex.org/W2039285020","https://openalex.org/W2048005451","https://openalex.org/W2058583833","https://openalex.org/W2062383436","https://openalex.org/W2067711488","https://openalex.org/W2075254304","https://openalex.org/W2078193953","https://openalex.org/W2088787049","https://openalex.org/W2093834886","https://openalex.org/W2101455165","https://openalex.org/W2106652190","https://openalex.org/W2109188022","https://openalex.org/W2112259827","https://openalex.org/W2122184642","https://openalex.org/W2134904727","https://openalex.org/W2135691000","https://openalex.org/W2140785413","https://openalex.org/W2143320618","https://openalex.org/W2144751639","https://openalex.org/W2145096794","https://openalex.org/W2155482078","https://openalex.org/W2159451621","https://openalex.org/W2159955373","https://openalex.org/W2166327612","https://openalex.org/W2166887721","https://openalex.org/W2167061157","https://openalex.org/W2169623698","https://openalex.org/W2170399784","https://openalex.org/W2181453853","https://openalex.org/W2480404596","https://openalex.org/W2569816327","https://openalex.org/W2998023265","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W170151271","https://openalex.org/W1995230427","https://openalex.org/W2990075560","https://openalex.org/W2144778520","https://openalex.org/W2793883929","https://openalex.org/W35509000","https://openalex.org/W2348306544","https://openalex.org/W2090411925","https://openalex.org/W1972985034","https://openalex.org/W4231065235"],"abstract_inverted_index":{"A":[0],"novel":[1],"approach":[2],"to":[3,48,61,108,111],"the":[4,16,39,49,71,112],"X-ray":[5,17],"tomography":[6],"problem":[7],"with":[8,74],"sparse":[9,75],"projection":[10,68,83],"data":[11,69,84],"is":[12,20,29,36,59],"proposed.":[13],"Nonnegativity":[14],"of":[15,42,70,85],"attenuation":[18],"coefficient":[19],"enforced":[21],"by":[22,98],"modelling":[23],"it":[24],"as":[25,38],"$\\max\\{\\Phi(x),0\\}$,":[26],"where":[27],"$\\Phi$":[28,35],"a":[30,43],"smooth":[31],"function.":[32],"The":[33,56,90],"function":[34],"computed":[37],"equilibrium":[40],"solution":[41],"nonlinear":[44],"evolution":[45],"equation":[46],"analogous":[47],"equations":[50],"used":[51],"in":[52,86,104],"level":[53],"set":[54],"methods.":[55],"reconstruction":[57,114],"algorithm":[58],"applied":[60],"(a)":[62],"simulated":[63],"full":[64],"and":[65,78,102],"limited":[66,81],"angle":[67,82],"Shepp\u2013Logan":[72],"phantom":[73],"angular":[76],"sampling":[77],"(b)":[79],"measured":[80],"vitro":[87],"dental":[88],"specimens.":[89],"results":[91],"are":[92],"significantly":[93],"better":[94],"than":[95],"those":[96],"given":[97],"traditional":[99],"backprojection-based":[100],"approaches,":[101],"similar":[103],"quality":[105],"(but":[106],"faster":[107],"compute)":[109],"compared":[110],"algebraic":[113],"technique.":[115]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":5}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
