{"id":"https://openalex.org/W1981617171","doi":"https://doi.org/10.1137/130942784","title":"Series Expansions of the Reconstruction Kernel of the Radon Transform over a Cormack-Type Family of Curves with Applications in Tomography","display_name":"Series Expansions of the Reconstruction Kernel of the Radon Transform over a Cormack-Type Family of Curves with Applications in Tomography","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W1981617171","doi":"https://doi.org/10.1137/130942784","mag":"1981617171"},"language":"en","primary_location":{"id":"doi:10.1137/130942784","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130942784","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055589246","display_name":"Ga\u00ebl Rigaud","orcid":"https://orcid.org/0000-0002-5318-3846"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"G. Rigaud","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008273040","display_name":"A Lakhal","orcid":"https://orcid.org/0000-0001-7590-0474"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. Lakhal","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5028719622","display_name":"Alfred K. Louis","orcid":"https://orcid.org/0000-0001-8518-2592"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. K. Louis","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5513,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.694134,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"7","issue":"2","first_page":"924","last_page":"943"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10522","display_name":"Medical Imaging Techniques and Applications","score":1.0,"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":1.0,"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":0.9994000196456909,"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/T10844","display_name":"Radiation Dose and Imaging","score":0.9983000159263611,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/radon-transform","display_name":"Radon transform","score":0.8770810961723328},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6529642343521118},{"id":"https://openalex.org/keywords/iterative-reconstruction","display_name":"Iterative reconstruction","score":0.5881859064102173},{"id":"https://openalex.org/keywords/tomographic-reconstruction","display_name":"Tomographic reconstruction","score":0.5761316418647766},{"id":"https://openalex.org/keywords/tomography","display_name":"Tomography","score":0.5712616443634033},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.530487596988678},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45957183837890625},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4501934349536896},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.43306151032447815},{"id":"https://openalex.org/keywords/integral-transform","display_name":"Integral transform","score":0.4304819107055664},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4230571389198303},{"id":"https://openalex.org/keywords/inversion","display_name":"Inversion (geology)","score":0.4130682945251465},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20803546905517578},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.19536703824996948},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1623343527317047},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12438243627548218},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.10374683141708374}],"concepts":[{"id":"https://openalex.org/C197231052","wikidata":"https://www.wikidata.org/wiki/Q979829","display_name":"Radon transform","level":2,"score":0.8770810961723328},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6529642343521118},{"id":"https://openalex.org/C141379421","wikidata":"https://www.wikidata.org/wiki/Q6094427","display_name":"Iterative reconstruction","level":2,"score":0.5881859064102173},{"id":"https://openalex.org/C97742081","wikidata":"https://www.wikidata.org/wiki/Q7820109","display_name":"Tomographic reconstruction","level":3,"score":0.5761316418647766},{"id":"https://openalex.org/C163716698","wikidata":"https://www.wikidata.org/wiki/Q841267","display_name":"Tomography","level":2,"score":0.5712616443634033},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.530487596988678},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45957183837890625},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4501934349536896},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.43306151032447815},{"id":"https://openalex.org/C200052193","wikidata":"https://www.wikidata.org/wiki/Q877802","display_name":"Integral transform","level":2,"score":0.4304819107055664},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4230571389198303},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.4130682945251465},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20803546905517578},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.19536703824996948},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1623343527317047},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12438243627548218},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.10374683141708374},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C109007969","wikidata":"https://www.wikidata.org/wiki/Q749565","display_name":"Structural basin","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/130942784","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130942784","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1983287341","https://openalex.org/W2004655061","https://openalex.org/W2004804713","https://openalex.org/W2020510568","https://openalex.org/W2025650106","https://openalex.org/W2029886652","https://openalex.org/W2058583833","https://openalex.org/W2062682184","https://openalex.org/W2065390928","https://openalex.org/W2065457486","https://openalex.org/W2072450129","https://openalex.org/W2094863094","https://openalex.org/W2111298414","https://openalex.org/W2157005274","https://openalex.org/W2530318141","https://openalex.org/W4212794193","https://openalex.org/W4241138783"],"related_works":["https://openalex.org/W3204855225","https://openalex.org/W2079352884","https://openalex.org/W3110126359","https://openalex.org/W2016224046","https://openalex.org/W2088160757","https://openalex.org/W3011253205","https://openalex.org/W2148451986","https://openalex.org/W2026961978","https://openalex.org/W4366975566","https://openalex.org/W4377140949"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2],"concerned":[3],"with":[4,78,110,153,232],"the":[5,48,54,73,76,79,83,88,94,116,122,128,133,139,147,154,158,167,188,199,208,219,233],"Radon":[6,56,95,168,184],"transform":[7,57,96],"over":[8,186],"a":[9,32,104,111,163,176],"family":[10,22],"of":[11,23,53,75,81,85,87,118,132,138,146,157,166,180,191,201,210,213,221,226],"Cormack-type":[12],"curves":[13],"and":[14,41,203,212,228],"provides":[15],"an":[16,144],"exact":[17],"inversion":[18,125],"formula.":[19],"The":[20],"studied":[21],"curves,":[24],"called":[25],"$C_1$,":[26,187],"appeared":[27],"in":[28,39,59,97,175,198,207,224,230],"previous":[29],"works":[30],"as":[31],"suitable":[33],"manifold":[34],"for":[35,183],"modeling":[36],"imaging":[37],"concepts":[38],"conventional":[40,67],"Compton":[42],"scattering":[43],"tomography":[44,61],"(CST).":[45],"More":[46],"specifically,":[47],"straight":[49],"line,":[50],"integral":[51],"support":[52],"classical":[55],"used":[58],"computed":[60],"(CT)":[62],"belongs":[63],"to":[64,93,143,195],"$C_1$.":[65],"In":[66],"tomography,":[68],"many":[69],"reconstruction":[70,89,159],"techniques":[71],"compute":[72],"derivative":[74],"data":[77,102],"aim":[80],"reducing":[82],"order":[84],"singularity":[86,155],"kernel":[90,160],"associated":[91],"here":[92],"two":[98],"dimensions.":[99],"However,":[100],"differentiating":[101],"requires":[103],"regularization":[105],"step":[106],"(for":[107],"instance,":[108],"convolution":[109],"smooth":[112],"function)":[113],"which":[114,141],"reduces":[115],"resolution":[117],"reconstructed":[119],"images.":[120],"Here,":[121],"proposed":[123],"analytical":[124],"formula":[126],"recovers":[127],"circular":[129],"harmonic":[130],"components":[131],"sought":[134],"object":[135],"without":[136],"differentiation":[137],"data,":[140],"leads":[142],"improvement":[145],"final":[148],"resolution.":[149],"Furthermore,":[150],"we":[151],"deal":[152],"issue":[156],"by":[161],"applying":[162],"range":[164],"property":[165],"transform.":[169],"Since":[170],"theoretical":[171],"results":[172,206],"are":[173],"developed":[174],"quite":[177],"general":[178],"context":[179],"inverse":[181],"problems":[182],"transforms":[185],"potential":[189],"applications":[190],"our":[192],"algorithm":[193,223],"appear":[194],"be":[196],"numerous":[197],"field":[200],"CT":[202,211],"CST.":[204],"Numerical":[205],"framework":[209],"one":[214],"modality":[215],"on":[216],"CST":[217],"reveal":[218],"strength":[220],"this":[222],"terms":[225],"accuracy":[227],"stability":[229],"comparison":[231],"well-known":[234],"filtered":[235],"back-projection.":[236]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
