{"id":"https://openalex.org/W2754970528","doi":"https://doi.org/10.1137/17m1147822","title":"MultiDimensional Sparse Super-Resolution","display_name":"MultiDimensional Sparse Super-Resolution","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2754970528","doi":"https://doi.org/10.1137/17m1147822","mag":"2754970528"},"language":"en","primary_location":{"id":"doi:10.1137/17m1147822","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1147822","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1709.03157","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004350216","display_name":"Clarice Poon","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Clarice Poon","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5058651667","display_name":"Gabriel Peyr\u00e9","orcid":"https://orcid.org/0000-0002-4477-0387"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gabriel Peyr\u00e9","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5183,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.56009455,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"51","issue":"1","first_page":"1","last_page":"44"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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/T12015","display_name":"Photoacoustic and Ultrasonic Imaging","score":0.9998000264167786,"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/T11996","display_name":"Random lasers and scattering media","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/3102","display_name":"Acoustics and Ultrasonics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/sparse-grid","display_name":"Sparse grid","score":0.5481371283531189},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4887213706970215},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.4876004755496979},{"id":"https://openalex.org/keywords/resolution","display_name":"Resolution (logic)","score":0.4868147075176239},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4809502959251404},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.47336265444755554},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4719991683959961},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4630368649959564},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.4520180821418762},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.44589734077453613},{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.4240190088748932},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39228320121765137},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3370569348335266},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.14791610836982727},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.13836419582366943},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1350630223751068},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.13074991106987},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11984410881996155},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11269143223762512}],"concepts":[{"id":"https://openalex.org/C156439662","wikidata":"https://www.wikidata.org/wiki/Q7573793","display_name":"Sparse grid","level":2,"score":0.5481371283531189},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4887213706970215},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.4876004755496979},{"id":"https://openalex.org/C138268822","wikidata":"https://www.wikidata.org/wiki/Q1051925","display_name":"Resolution (logic)","level":2,"score":0.4868147075176239},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4809502959251404},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.47336265444755554},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4719991683959961},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4630368649959564},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.4520180821418762},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.44589734077453613},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.4240190088748932},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39228320121765137},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3370569348335266},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.14791610836982727},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.13836419582366943},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1350630223751068},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.13074991106987},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11984410881996155},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11269143223762512},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/17m1147822","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1147822","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1709.03157","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1709.03157","pdf_url":"https://arxiv.org/pdf/1709.03157","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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:arXiv.org:1709.03157","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1709.03157","pdf_url":"https://arxiv.org/pdf/1709.03157","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2754970528","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1709.03157","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:HAL:hal-02411771v1","is_oa":false,"landing_page_url":"https://hal.science/hal-02411771","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Mathematical Analysis, 2019, 51 (1), pp.1-44. ⟨10.1137/17M1147822⟩","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1709.03157","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1709.03157","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1709.03157","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1709.03157","pdf_url":"https://arxiv.org/pdf/1709.03157","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2754970528.pdf"},"referenced_works_count":58,"referenced_works":["https://openalex.org/W905619","https://openalex.org/W129423020","https://openalex.org/W1601741115","https://openalex.org/W1937620887","https://openalex.org/W1992858116","https://openalex.org/W2016980059","https://openalex.org/W2017718716","https://openalex.org/W2018778093","https://openalex.org/W2028191993","https://openalex.org/W2038527926","https://openalex.org/W2054455698","https://openalex.org/W2057603175","https://openalex.org/W2057867606","https://openalex.org/W2064486311","https://openalex.org/W2065656021","https://openalex.org/W2069931243","https://openalex.org/W2075498078","https://openalex.org/W2075894130","https://openalex.org/W2078204800","https://openalex.org/W2089213691","https://openalex.org/W2090530235","https://openalex.org/W2103973889","https://openalex.org/W2109042903","https://openalex.org/W2111114170","https://openalex.org/W2113638573","https://openalex.org/W2114789426","https://openalex.org/W2118682956","https://openalex.org/W2119499160","https://openalex.org/W2119826715","https://openalex.org/W2120186527","https://openalex.org/W2128131274","https://openalex.org/W2135046866","https://openalex.org/W2141713516","https://openalex.org/W2142351022","https://openalex.org/W2142614231","https://openalex.org/W2145096794","https://openalex.org/W2149213383","https://openalex.org/W2151693816","https://openalex.org/W2155447220","https://openalex.org/W2162654459","https://openalex.org/W2168335598","https://openalex.org/W2296616510","https://openalex.org/W2524857034","https://openalex.org/W2585868105","https://openalex.org/W2590457536","https://openalex.org/W2605512869","https://openalex.org/W2618687184","https://openalex.org/W2642445787","https://openalex.org/W2950996929","https://openalex.org/W2962782658","https://openalex.org/W2962898451","https://openalex.org/W2963240529","https://openalex.org/W2963270586","https://openalex.org/W2963391931","https://openalex.org/W2963746586","https://openalex.org/W2963860509","https://openalex.org/W2964325628","https://openalex.org/W4250955649"],"related_works":["https://openalex.org/W2025689805","https://openalex.org/W2963224652","https://openalex.org/W2229640315","https://openalex.org/W3082361689","https://openalex.org/W2902055477","https://openalex.org/W2964910689","https://openalex.org/W2951419436","https://openalex.org/W2041139939","https://openalex.org/W2787065368","https://openalex.org/W2950688354","https://openalex.org/W3015846080","https://openalex.org/W1517766226","https://openalex.org/W2402388369","https://openalex.org/W3137906247","https://openalex.org/W2998753596","https://openalex.org/W2079526182","https://openalex.org/W2549650688","https://openalex.org/W2921780127","https://openalex.org/W2727967901","https://openalex.org/W2125240018"],"abstract_inverted_index":{"This":[0,131,185],"paper":[1],"studies":[2],"sparse":[3],"super-resolution":[4,43,175,227],"in":[5,48,70,102,177,187,228],"arbitrary":[6],"dimensions.":[7],"More":[8],"precisely,":[9],"it":[10],"develops":[11],"a":[12,100,110,167,181,189],"theoretical":[13,57],"analysis":[14,58,169,191],"of":[15,32,45,52,80,115,118,150,170,180,183,192,214,219,226],"support":[16,172],"recovery":[17],"for":[18,127],"the":[19,38,50,63,71,77,81,84,103,106,116,119,123,154,171,178,194,202,206,217,224],"so-called":[20],"beurling":[21],"least":[22,39,124],"angle":[23,40],"regression":[24],"(BLASSO)":[25],"method,":[26],"which":[27],"is":[28,44,59,68,99,166],"an":[29,147],"off-the-grid":[30],"generalization":[31],"$\\ell^1$":[33],"regularization":[34],"(also":[35],"known":[36],"as":[37],"regression).":[41],"While":[42],"paramount":[46],"importance":[47],"overcoming":[49],"limitations":[51],"many":[53],"imaging":[54],"devices,":[55],"its":[56],"still":[60],"lacking":[61],"beyond":[62],"one-dimensional":[64],"case.":[65],"The":[66],"reason":[67],"that":[69],"two-dimensional":[72],"(2-D)":[73],"case":[74,179],"and":[75,86,122,144,174,222],"beyond,":[76],"relative":[78],"position":[79],"spikes":[82,107],"enters":[83],"picture,":[85],"different":[87,92,212],"geometrical":[88],"configurations":[89],"lead":[90,145],"to":[91,146,153,201],"stability":[93,173],"properties.":[94],"Our":[95],"first":[96],"main":[97,164],"contribution":[98,165],"connection,":[101],"limit":[104],"where":[105],"cluster":[108],"at":[109,160],"given":[111],"point,":[112],"between":[113,205],"solutions":[114,152],"dual":[117,155],"BLASSO":[120],"problem":[121],"interpolant":[125],"space":[126],"Hermite":[128],"polynomial":[129],"interpolation.":[130],"interpolation":[132],"space,":[133],"introduced":[134],"by":[135,141],"De":[136],"Boor,":[137],"can":[138],"be":[139],"computed":[140],"Gaussian":[142],"elimination":[143],"algorithmic":[148],"description":[149],"limiting":[151],"problem.":[156],"With":[157],"this":[158,220],"construction":[159],"hand,":[161],"our":[162],"second":[163],"detailed":[168],"effect":[176],"pair":[182],"spikes.":[184,207],"includes":[186],"particular":[188],"sharp":[190],"how":[193],"signal-to-noise":[195],"ratio":[196],"should":[197],"scale":[198],"with":[199],"respect":[200],"separation":[203],"distance":[204],"Lastly,":[208],"numerical":[209],"simulations":[210],"on":[211],"classes":[213],"kernels":[215],"show":[216],"applicability":[218],"theory":[221],"highlight":[223],"richness":[225],"2-D.":[229]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}