{"id":"https://openalex.org/W1976203937","doi":"https://doi.org/10.1137/130946642","title":"Variable Density Sampling with Continuous Trajectories","display_name":"Variable Density Sampling with Continuous Trajectories","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W1976203937","doi":"https://doi.org/10.1137/130946642","mag":"1976203937"},"language":"en","primary_location":{"id":"doi:10.1137/130946642","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130946642","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/A5063609912","display_name":"Nicolas Chauffert","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nicolas Chauffert","raw_affiliation_strings":["Modelling brain structure, function and variability based on high-field MRI data"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Modelling brain structure, function and variability based on high-field MRI data","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019588779","display_name":"Philippe Ciuciu","orcid":"https://orcid.org/0000-0001-5374-962X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Philippe Ciuciu","raw_affiliation_strings":["Modelling brain structure, function and variability based on high-field MRI data"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Modelling brain structure, function and variability based on high-field MRI data","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047574400","display_name":"Jonas Kahn","orcid":null},"institutions":[{"id":"https://openalex.org/I4210145948","display_name":"Laboratoire Paul Painlev\u00e9","ror":"https://ror.org/043n4fm24","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I2279609970","https://openalex.org/I4210141950","https://openalex.org/I4210145948"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jonas Kahn","raw_affiliation_strings":["Laboratoire Paul Painlev\u00e9 - UMR 8524"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire Paul Painlev\u00e9 - UMR 8524","institution_ids":["https://openalex.org/I4210145948"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101934388","display_name":"Pierre Weiss","orcid":"https://orcid.org/0000-0001-9083-214X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pierre Weiss","raw_affiliation_strings":["PRIMO (ITAV)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"PRIMO (ITAV)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.1517,"has_fulltext":false,"cited_by_count":111,"citation_normalized_percentile":{"value":0.95235119,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":100},"biblio":{"volume":"7","issue":"4","first_page":"1962","last_page":"1992"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"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":1.0,"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/T10378","display_name":"Advanced MRI 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/T11778","display_name":"Electrical and Bioimpedance Tomography","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/computer-science","display_name":"Computer science","score":0.6190876364707947},{"id":"https://openalex.org/keywords/coherence","display_name":"Coherence (philosophical gambling strategy)","score":0.5727325677871704},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.5313955545425415},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5042241811752319},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.48216599225997925},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.4660559594631195},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.4618889391422272},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45645543932914734},{"id":"https://openalex.org/keywords/compressed-sensing","display_name":"Compressed sensing","score":0.44259533286094666},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.42081528902053833},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.41782814264297485},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3800329267978668},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.33179324865341187},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.27813267707824707},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.21644791960716248},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.17540976405143738},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10855969786643982}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6190876364707947},{"id":"https://openalex.org/C2781181686","wikidata":"https://www.wikidata.org/wiki/Q4226068","display_name":"Coherence (philosophical gambling strategy)","level":2,"score":0.5727325677871704},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.5313955545425415},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5042241811752319},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.48216599225997925},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4660559594631195},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.4618889391422272},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45645543932914734},{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.44259533286094666},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.42081528902053833},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.41782814264297485},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3800329267978668},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.33179324865341187},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.27813267707824707},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.21644791960716248},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.17540976405143738},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10855969786643982},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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":1,"locations":[{"id":"doi:10.1137/130946642","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130946642","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":[{"id":"https://openalex.org/G7941337767","display_name":"Engineering and Imaging multicellular tumour spheroids to study 3D cell proliferation","funder_award_id":"ANR-12-BSV5-0008","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":66,"referenced_works":["https://openalex.org/W111191802","https://openalex.org/W135469740","https://openalex.org/W143004564","https://openalex.org/W1488435683","https://openalex.org/W1489238841","https://openalex.org/W1670160730","https://openalex.org/W1676212501","https://openalex.org/W1865368880","https://openalex.org/W1922757677","https://openalex.org/W1946620893","https://openalex.org/W1964808148","https://openalex.org/W1964849786","https://openalex.org/W1970071808","https://openalex.org/W1970230765","https://openalex.org/W1985380836","https://openalex.org/W1986194522","https://openalex.org/W1993966762","https://openalex.org/W2014068360","https://openalex.org/W2015726211","https://openalex.org/W2026653661","https://openalex.org/W2037501062","https://openalex.org/W2038688409","https://openalex.org/W2040319606","https://openalex.org/W2043694962","https://openalex.org/W2050611421","https://openalex.org/W2059201851","https://openalex.org/W2062194677","https://openalex.org/W2066211830","https://openalex.org/W2082690749","https://openalex.org/W2097256789","https://openalex.org/W2100410713","https://openalex.org/W2101675075","https://openalex.org/W2103766131","https://openalex.org/W2103920296","https://openalex.org/W2106285343","https://openalex.org/W2107411554","https://openalex.org/W2107906890","https://openalex.org/W2114202040","https://openalex.org/W2127079904","https://openalex.org/W2137198385","https://openalex.org/W2138309709","https://openalex.org/W2145096794","https://openalex.org/W2166163936","https://openalex.org/W2167233877","https://openalex.org/W2167836216","https://openalex.org/W2296616510","https://openalex.org/W2407170444","https://openalex.org/W2510711337","https://openalex.org/W2514277432","https://openalex.org/W2556237558","https://openalex.org/W2763109466","https://openalex.org/W2802739963","https://openalex.org/W2950968054","https://openalex.org/W2951629090","https://openalex.org/W2951714488","https://openalex.org/W2964340701","https://openalex.org/W2970346692","https://openalex.org/W3098045837","https://openalex.org/W3098440742","https://openalex.org/W3102723347","https://openalex.org/W3103091203","https://openalex.org/W3103791804","https://openalex.org/W3103879072","https://openalex.org/W3104501706","https://openalex.org/W4249760698","https://openalex.org/W4250955649"],"related_works":["https://openalex.org/W2158224665","https://openalex.org/W1980381208","https://openalex.org/W2379589510","https://openalex.org/W4300044672","https://openalex.org/W2810730439","https://openalex.org/W2364594919","https://openalex.org/W1881631164","https://openalex.org/W2358292267","https://openalex.org/W1861706286","https://openalex.org/W2150527492"],"abstract_inverted_index":{"Reducing":[0],"acquisition":[1,125,129,195],"time":[2],"is":[3,121,143],"a":[4,37,47,57,99,138,148,152,185,224],"crucial":[5,170],"challenge":[6],"for":[7,123],"many":[8,124],"imaging":[9,51],"techniques.":[10],"Compressed":[11],"sensing":[12],"(CS)":[13],"theory":[14],"offers":[15],"an":[16,68],"appealing":[17],"framework":[18],"to":[19,55,91,128,171,175,183,218,226],"address":[20],"this":[21,42,133],"issue":[22],"since":[23],"it":[24],"provides":[25],"theoretical":[26,206],"guarantees":[27],"on":[28,36,46,81,161,190,200],"the":[29,50,65,82,93,113,135,194,201,220],"reconstruction":[30,74],"of":[31,60,67,75,85,137,223],"sparse":[32,76,229],"signals":[33],"by":[34],"projection":[35],"low-dimensional":[38],"linear":[39],"subspace.":[40],"In":[41],"paper,":[43],"we":[44,216],"focus":[45],"setting":[48],"where":[49],"device":[52],"allows":[53],"us":[54],"sense":[56],"fixed":[58],"set":[59],"measurements.":[61,87],"We":[62,88,178],"first":[63],"discuss":[64,89],"choice":[66],"optimal":[69],"sampling":[70,105,120],"subspace":[71],"allowing":[72],"perfect":[73],"signals.":[77],"Its":[78],"design":[79],"relies":[80],"random":[83,119,191],"drawing":[84,94],"independent":[86,107,118,162],"how":[90],"select":[92],"distribution":[95],"and":[96,106,145,197,208,236],"show":[97],"that":[98],"mixed":[100],"strategy":[101],"involving":[102],"partial":[103],"deterministic":[104],"drawings":[108],"can":[109],"help":[110],"in":[111,212],"breaking":[112],"so-called":[114],"coherence":[115],"barrier.":[116],"Unfortunately,":[117],"irrelevant":[122],"devices":[126],"owing":[127],"constraints.":[130],"To":[131],"overcome":[132],"limitation,":[134],"notion":[136],"variable":[139],"density":[140],"sampler":[141],"(VDS)":[142],"introduced":[144],"defined":[146],"as":[147],"stochastic":[149],"process":[150],"with":[151],"prescribed":[153],"limit":[154,233],"empirical":[155,234],"measure.":[156],"It":[157],"encompasses":[158],"samplers":[159],"based":[160,189,199],"measurements":[163],"or":[164],"continuous":[165,186],"curves.":[166],"The":[167],"latter":[168],"are":[169],"extend":[172],"CS":[173,210],"results":[174],"actual":[176],"applications.":[177],"propose":[179],"two":[180],"original":[181],"approaches":[182],"designing":[184],"VDS,":[187],"one":[188,198],"walks":[192],"over":[193],"space":[196],"travelling":[202],"salesman":[203],"problem.":[204],"Following":[205],"considerations":[207],"retrospective":[209],"simulations":[211],"magnetic":[213],"resonance":[214],"imaging,":[215],"intend":[217],"highlight":[219],"key":[221],"properties":[222],"VDS":[225],"ensure":[227],"accurate":[228],"reconstructions,":[230],"namely":[231],"its":[232,237],"measure":[235],"mixing":[238],"time.":[239]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":52},{"year":2020,"cited_by_count":12},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2}],"updated_date":"2026-06-20T22:02:38.213706","created_date":"2025-10-10T00:00:00"}