{"id":"https://openalex.org/W4388705259","doi":"https://doi.org/10.1137/23m1551730","title":"An Operator Theory for Analyzing the Resolution of Multi-illumination Imaging Modalities","display_name":"An Operator Theory for Analyzing the Resolution of Multi-illumination Imaging Modalities","publication_year":2023,"publication_date":"2023-11-15","ids":{"openalex":"https://openalex.org/W4388705259","doi":"https://doi.org/10.1137/23m1551730"},"language":"en","primary_location":{"id":"doi:10.1137/23m1551730","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1137/23m1551730","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/A5022091224","display_name":"Ping Liu","orcid":"https://orcid.org/0000-0002-7857-7040"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Ping Liu","raw_affiliation_strings":["Department of Mathematics, ETH Z\u00fcrich, CH-8092 Z\u00fcrich, Switzerland"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, ETH Z\u00fcrich, CH-8092 Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041497235","display_name":"Habib Ammari","orcid":"https://orcid.org/0000-0001-7278-4877"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Habib Ammari","raw_affiliation_strings":["Department of Mathematics, ETH Z\u00fcrich, CH-8092 Z\u00fcrich, Switzerland"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, ETH Z\u00fcrich, CH-8092 Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5022091224"],"corresponding_institution_ids":["https://openalex.org/I35440088"],"apc_list":null,"apc_paid":null,"fwci":0.7322,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.82242332,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"16","issue":"4","first_page":"2105","last_page":"2143"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10540","display_name":"Advanced Fluorescence Microscopy Techniques","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1304","display_name":"Biophysics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10540","display_name":"Advanced Fluorescence Microscopy Techniques","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1304","display_name":"Biophysics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T12015","display_name":"Photoacoustic and Ultrasonic Imaging","score":0.9986000061035156,"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/T10638","display_name":"Optical measurement and interference techniques","score":0.9944000244140625,"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/superresolution","display_name":"Superresolution","score":0.617755651473999},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.6165832877159119},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5946558713912964},{"id":"https://openalex.org/keywords/point-spread-function","display_name":"Point spread function","score":0.579910933971405},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5147952437400818},{"id":"https://openalex.org/keywords/resolution","display_name":"Resolution (logic)","score":0.504318118095398},{"id":"https://openalex.org/keywords/image-resolution","display_name":"Image resolution","score":0.4933728277683258},{"id":"https://openalex.org/keywords/snapshot","display_name":"Snapshot (computer storage)","score":0.44402745366096497},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4261774718761444},{"id":"https://openalex.org/keywords/imaging-science","display_name":"Imaging science","score":0.4169788658618927},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4082452058792114},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3798156976699829},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.37792444229125977},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3492240309715271},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.3411213159561157},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.28039950132369995},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23210355639457703},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07700526714324951}],"concepts":[{"id":"https://openalex.org/C141239990","wikidata":"https://www.wikidata.org/wiki/Q957423","display_name":"Superresolution","level":3,"score":0.617755651473999},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6165832877159119},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5946558713912964},{"id":"https://openalex.org/C69179731","wikidata":"https://www.wikidata.org/wiki/Q510427","display_name":"Point spread function","level":2,"score":0.579910933971405},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5147952437400818},{"id":"https://openalex.org/C138268822","wikidata":"https://www.wikidata.org/wiki/Q1051925","display_name":"Resolution (logic)","level":2,"score":0.504318118095398},{"id":"https://openalex.org/C205372480","wikidata":"https://www.wikidata.org/wiki/Q210521","display_name":"Image resolution","level":2,"score":0.4933728277683258},{"id":"https://openalex.org/C55282118","wikidata":"https://www.wikidata.org/wiki/Q252683","display_name":"Snapshot (computer storage)","level":2,"score":0.44402745366096497},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4261774718761444},{"id":"https://openalex.org/C57177791","wikidata":"https://www.wikidata.org/wiki/Q1038886","display_name":"Imaging science","level":2,"score":0.4169788658618927},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4082452058792114},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3798156976699829},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.37792444229125977},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3492240309715271},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.3411213159561157},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.28039950132369995},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23210355639457703},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07700526714324951},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/23m1551730","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1137/23m1551730","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/G2475573017","display_name":null,"funder_award_id":"200021-200307","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1969266036","https://openalex.org/W1980212654","https://openalex.org/W1992858116","https://openalex.org/W2013669507","https://openalex.org/W2054455698","https://openalex.org/W2061729391","https://openalex.org/W2064173118","https://openalex.org/W2090763677","https://openalex.org/W2095434499","https://openalex.org/W2101336703","https://openalex.org/W2106316394","https://openalex.org/W2109042903","https://openalex.org/W2109781296","https://openalex.org/W2113146347","https://openalex.org/W2119499160","https://openalex.org/W2138004508","https://openalex.org/W2144955418","https://openalex.org/W2149241780","https://openalex.org/W2963709974","https://openalex.org/W2964325628","https://openalex.org/W3003920102","https://openalex.org/W3021322543","https://openalex.org/W3025444082","https://openalex.org/W3036489009","https://openalex.org/W3093566224","https://openalex.org/W3158144721","https://openalex.org/W3167557279","https://openalex.org/W3196903455","https://openalex.org/W3203155614","https://openalex.org/W3211495999","https://openalex.org/W4200060815","https://openalex.org/W4249166508"],"related_works":["https://openalex.org/W2542847180","https://openalex.org/W4242963054","https://openalex.org/W1681535064","https://openalex.org/W2075729794","https://openalex.org/W3004000015","https://openalex.org/W2027012404","https://openalex.org/W2559771220","https://openalex.org/W3206868371","https://openalex.org/W4387300017","https://openalex.org/W2167191464"],"abstract_inverted_index":{".By":[0],"introducing":[1],"a":[2,8,33,103],"new":[3,34,72,166],"operator":[4,171],"theory,":[5],"we":[6,137],"provide":[7],"unified":[9,104],"mathematical":[10],"theory":[11,101,172],"for":[12,143,186],"general":[13],"source":[14],"resolution":[15,58,109,141,157,175],"in":[16,96,117,124,182,196],"the":[17,41,45,50,57,66,71,80,83,87,92,97,108,118,130,133,140,156,165],"multi-illumination":[18,27,60,134,159],"imaging":[19,28,31,35,51,61,73,135,160,167],"problem.":[20],"Our":[21,100],"main":[22],"idea":[23],"is":[24,62,76,161],"to":[25,106],"transform":[26],"into":[29],"single-snapshot":[30],"with":[32],"kernel":[36,168],"that":[37,56,155],"depends":[38],"on":[39,129],"both":[40,145],"illumination":[42,98],"patterns":[43],"and":[44,91,115,147,173],"point":[46,88],"spread":[47,89],"function":[48,90],"of":[49,59,70,82,86,110,132,158],"system.":[52],"We":[53,153],"therefore":[54],"prove":[55],"approximately":[63,162],"determined":[64,163],"by":[65,79,150,164,179],"essential":[67,94],"cutoff":[68,84],"frequency":[69,85,95],"kernel,":[74],"which":[75],"roughly":[77],"limited":[78],"sum":[81],"maximum":[93],"patterns.":[99],"provides":[102],"way":[105],"estimate":[107,139],"various":[111],"existing":[112],"super-resolution":[113,199],"modalities":[114],"results":[116],"same":[119],"estimates":[120],"as":[121],"those":[122],"obtained":[123],"experiments.":[125],"In":[126],"addition,":[127],"based":[128],"reformulation":[131],"problem,":[136],"also":[138],"limits":[142],"resolving":[144,187],"complex":[146],"positive":[148],"sources":[149],"sparsity-based":[151,198],"approaches.":[152],"show":[154],"from":[169],"our":[170],"better":[174],"can":[176],"be":[177],"realized":[178],"sparsity-promoting":[180],"techniques":[181],"practice":[183],"but":[184],"only":[185],"very":[188],"sparse":[189],"sources.":[190],"This":[191],"explains":[192],"experimentally":[193],"observed":[194],"phenomena":[195],"some":[197],"modalities.Keywordssuper-resolutionresolution":[200],"enhancementmulti-illumination":[201],"imagingoperator":[202],"theorylocation":[203],"recoverysource":[204],"number":[205],"recoveryMSC":[206],"codes65R3242A1015A0994A0894A12":[207]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2025-12-25T23:11:45.687758","created_date":"2025-10-10T00:00:00"}
