{"id":"https://openalex.org/W3022626249","doi":"https://doi.org/10.1137/21m1407902","title":"On the Convergence Rate of Projected Gradient Descent for a Back-Projection Based Objective","display_name":"On the Convergence Rate of Projected Gradient Descent for a Back-Projection Based Objective","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3022626249","doi":"https://doi.org/10.1137/21m1407902","mag":"3022626249"},"language":"en","primary_location":{"id":"doi:10.1137/21m1407902","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1407902","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2005.00959","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059245152","display_name":"Tom Tirer","orcid":"https://orcid.org/0000-0003-3249-2460"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Tom Tirer","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5072571599","display_name":"Raja Giryes","orcid":"https://orcid.org/0000-0002-2830-0297"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Raja Giryes","raw_affiliation_strings":["Tel Aviv University *"],"affiliations":[{"raw_affiliation_string":"Tel Aviv University *","institution_ids":["https://openalex.org/I16391192"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5059245152"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3544,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.51206113,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"14","issue":"4","first_page":"1504","last_page":"1531"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998000264167786,"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":0.9998000264167786,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T12015","display_name":"Photoacoustic and Ultrasonic Imaging","score":0.9976000189781189,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/proximal-gradient-methods","display_name":"Proximal Gradient Methods","score":0.6466985940933228},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6308215260505676},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.628393828868866},{"id":"https://openalex.org/keywords/fidelity","display_name":"Fidelity","score":0.5902956128120422},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.5798365473747253},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.5762285590171814},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5455798506736755},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5412696003913879},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5108861327171326},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4909830391407013},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.477358341217041},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4755518138408661},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4512757360935211},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.4490339756011963},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4456428587436676},{"id":"https://openalex.org/keywords/descent-direction","display_name":"Descent direction","score":0.42228105664253235},{"id":"https://openalex.org/keywords/trust-region","display_name":"Trust region","score":0.4220235049724579},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16774699091911316},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.130264550447464},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.09657466411590576},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06617709994316101}],"concepts":[{"id":"https://openalex.org/C10494615","wikidata":"https://www.wikidata.org/wiki/Q17086765","display_name":"Proximal Gradient Methods","level":4,"score":0.6466985940933228},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6308215260505676},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.628393828868866},{"id":"https://openalex.org/C2776459999","wikidata":"https://www.wikidata.org/wiki/Q2119376","display_name":"Fidelity","level":2,"score":0.5902956128120422},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.5798365473747253},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.5762285590171814},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5455798506736755},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5412696003913879},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5108861327171326},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4909830391407013},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.477358341217041},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4755518138408661},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4512757360935211},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4490339756011963},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4456428587436676},{"id":"https://openalex.org/C116149140","wikidata":"https://www.wikidata.org/wiki/Q2070951","display_name":"Descent direction","level":4,"score":0.42228105664253235},{"id":"https://openalex.org/C89109886","wikidata":"https://www.wikidata.org/wiki/Q1535924","display_name":"Trust region","level":3,"score":0.4220235049724579},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16774699091911316},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.130264550447464},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.09657466411590576},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06617709994316101},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/21m1407902","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1407902","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"},{"id":"pmh:oai:arXiv.org:2005.00959","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2005.00959","pdf_url":"https://arxiv.org/pdf/2005.00959","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:3022626249","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/2005.00959","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":"doi:10.48550/arxiv.2005.00959","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2005.00959","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":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2005.00959","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2005.00959","pdf_url":"https://arxiv.org/pdf/2005.00959","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"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320309480","display_name":"Nvidia","ror":"https://ror.org/03jdj4y14"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3022626249.pdf","grobid_xml":"https://content.openalex.org/works/W3022626249.grobid-xml"},"referenced_works_count":53,"referenced_works":["https://openalex.org/W74946117","https://openalex.org/W1506342804","https://openalex.org/W1522301498","https://openalex.org/W1953936588","https://openalex.org/W1978259121","https://openalex.org/W2025223969","https://openalex.org/W2044810215","https://openalex.org/W2048364349","https://openalex.org/W2054640142","https://openalex.org/W2056370875","https://openalex.org/W2099471712","https://openalex.org/W2100556411","https://openalex.org/W2103559027","https://openalex.org/W2113920645","https://openalex.org/W2115706991","https://openalex.org/W2118103795","https://openalex.org/W2119667497","https://openalex.org/W2121058967","https://openalex.org/W2123031198","https://openalex.org/W2146842127","https://openalex.org/W2149479098","https://openalex.org/W2163935418","https://openalex.org/W2167077875","https://openalex.org/W2173520492","https://openalex.org/W2296616510","https://openalex.org/W2508457857","https://openalex.org/W2595294663","https://openalex.org/W2607011356","https://openalex.org/W2763081248","https://openalex.org/W2765989888","https://openalex.org/W2787898208","https://openalex.org/W2889923760","https://openalex.org/W2890629002","https://openalex.org/W2938629629","https://openalex.org/W2951004968","https://openalex.org/W2963299521","https://openalex.org/W2964309963","https://openalex.org/W2964322027","https://openalex.org/W2994867875","https://openalex.org/W2995268367","https://openalex.org/W2998280611","https://openalex.org/W3016108778","https://openalex.org/W3018878055","https://openalex.org/W3090291564","https://openalex.org/W3105299938","https://openalex.org/W3106359998","https://openalex.org/W3114480714","https://openalex.org/W3118793468","https://openalex.org/W3122742231","https://openalex.org/W3123837026","https://openalex.org/W3124617746","https://openalex.org/W3128448487","https://openalex.org/W4250955649"],"related_works":["https://openalex.org/W3098600672","https://openalex.org/W2891337355","https://openalex.org/W2768927505","https://openalex.org/W2789587413","https://openalex.org/W3115825947","https://openalex.org/W2965853004","https://openalex.org/W3123272904","https://openalex.org/W3181406714","https://openalex.org/W2162287622","https://openalex.org/W2774134159","https://openalex.org/W2555340375","https://openalex.org/W2159915812","https://openalex.org/W2935973677","https://openalex.org/W2883309838","https://openalex.org/W3092826017","https://openalex.org/W2963363119","https://openalex.org/W1946919140","https://openalex.org/W1629222029","https://openalex.org/W3092802849","https://openalex.org/W2164535072"],"abstract_inverted_index":{"Ill-posed":[0],"linear":[1,149],"inverse":[2,52],"problems":[3],"appear":[4],"in":[5],"many":[6],"scientific":[7],"setups,":[8],"and":[9,23,46,160],"are":[10,18],"typically":[11],"addressed":[12],"by":[13],"solving":[14],"optimization":[15,74],"problems,":[16],"which":[17],"composed":[19],"of":[20,73,84,136,145],"data":[21],"fidelity":[22,35],"prior":[24],"terms.":[25],"Recently,":[26],"several":[27],"works":[28,55],"have":[29,56],"considered":[30],"a":[31,128],"back-projection":[32],"(BP)":[33],"based":[34],"term":[36],"as":[37],"an":[38,100],"alternative":[39],"to":[40,98,108],"the":[41,62,67,81,85,92,110,121,133,137,143,148],"common":[42],"least":[43],"squares":[44],"(LS),":[45],"demonstrated":[47],"excellent":[48],"results":[49],"for":[50,91,103],"popular":[51],"problems.":[53],"These":[54],"also":[57,119],"empirically":[58],"shown":[59],"that":[60],"using":[61,109],"BP":[63,93,146],"term,":[64,69],"rather":[65],"than":[66],"LS":[68,111],"requires":[70],"fewer":[71],"iterations":[72],"algorithms.":[75],"In":[76],"this":[77],"paper,":[78],"we":[79],"examine":[80],"convergence":[82,106],"rate":[83],"projected":[86],"gradient":[87,125],"descent":[88],"(PGD)":[89],"algorithm":[90],"objective.":[94],"Our":[95],"analysis":[96,140],"allows":[97],"identify":[99],"inherent":[101],"source":[102],"its":[104],"faster":[105],"compared":[107],"objective,":[112],"while":[113],"making":[114],"only":[115],"mild":[116],"assumptions.":[117],"We":[118],"analyze":[120],"more":[122],"general":[123],"proximal":[124,134],"method":[126],"under":[127],"relaxed":[129],"contraction":[130],"condition":[131],"on":[132],"mapping":[135],"prior.":[138],"This":[139],"further":[141],"highlights":[142],"advantage":[144],"when":[147],"measurement":[150],"operator":[151],"is":[152],"badly":[153],"conditioned.":[154],"Numerical":[155],"experiments":[156],"with":[157],"both":[158],"$\\ell_1$-norm":[159],"GAN-based":[161],"priors":[162],"corroborate":[163],"our":[164],"theoretical":[165],"results.":[166]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}