{"id":"https://openalex.org/W2620883262","doi":"https://doi.org/10.1109/tit.2018.2841379","title":"Inexact Gradient Projection and Fast Data Driven Compressed Sensing","display_name":"Inexact Gradient Projection and Fast Data Driven Compressed Sensing","publication_year":2018,"publication_date":"2018-05-28","ids":{"openalex":"https://openalex.org/W2620883262","doi":"https://doi.org/10.1109/tit.2018.2841379","mag":"2620883262"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2018.2841379","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2841379","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.research.ed.ac.uk/files/57210728/inexactIPG_single.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056404513","display_name":"Mohammad Golbabaee","orcid":"https://orcid.org/0000-0001-5822-2990"},"institutions":[{"id":"https://openalex.org/I20039902","display_name":"Digital Curation Centre","ror":"https://ror.org/01k9d6864","country_code":"GB","type":"other","lineage":["https://openalex.org/I20039902"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Mohammad Golbabaee","raw_affiliation_strings":["School of Engineering, Institute for Digital Communications, Edinburgh, U.K"],"raw_orcid":"https://orcid.org/0000-0001-5822-2990","affiliations":[{"raw_affiliation_string":"School of Engineering, Institute for Digital Communications, Edinburgh, U.K","institution_ids":["https://openalex.org/I20039902"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057962470","display_name":"Mike E. Davies","orcid":"https://orcid.org/0000-0003-2327-236X"},"institutions":[{"id":"https://openalex.org/I20039902","display_name":"Digital Curation Centre","ror":"https://ror.org/01k9d6864","country_code":"GB","type":"other","lineage":["https://openalex.org/I20039902"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Mike E. Davies","raw_affiliation_strings":["School of Engineering, Institute for Digital Communications, Edinburgh, U.K"],"raw_orcid":"https://orcid.org/0000-0003-2327-236X","affiliations":[{"raw_affiliation_string":"School of Engineering, Institute for Digital Communications, Edinburgh, U.K","institution_ids":["https://openalex.org/I20039902"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I20039902"],"apc_list":null,"apc_paid":null,"fwci":2.6656,"has_fulltext":true,"cited_by_count":24,"citation_normalized_percentile":{"value":0.89001836,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"64","issue":"10","first_page":"6707","last_page":"6721"},"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9909999966621399,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9846000075340271,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/algorithm","display_name":"Algorithm","score":0.6249403953552246},{"id":"https://openalex.org/keywords/cover-tree","display_name":"Cover tree","score":0.5457897782325745},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.5205360651016235},{"id":"https://openalex.org/keywords/oracle","display_name":"Oracle","score":0.5097624659538269},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5089333057403564},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5034608244895935},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.47463592886924744},{"id":"https://openalex.org/keywords/compressed-sensing","display_name":"Compressed sensing","score":0.4509371221065521},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.44448330998420715},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.430019736289978},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.41377878189086914},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.373159259557724},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.36658886075019836}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6249403953552246},{"id":"https://openalex.org/C53661774","wikidata":"https://www.wikidata.org/wiki/Q13108095","display_name":"Cover tree","level":5,"score":0.5457897782325745},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5205360651016235},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.5097624659538269},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5089333057403564},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5034608244895935},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.47463592886924744},{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.4509371221065521},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.44448330998420715},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.430019736289978},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.41377878189086914},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.373159259557724},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36658886075019836},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C115903868","wikidata":"https://www.wikidata.org/wiki/Q80993","display_name":"Software engineering","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.0},{"id":"https://openalex.org/C94641424","wikidata":"https://www.wikidata.org/wiki/Q5172845","display_name":"Correlation clustering","level":3,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C104047586","wikidata":"https://www.wikidata.org/wiki/Q5033439","display_name":"Canopy clustering algorithm","level":4,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tit.2018.2841379","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2841379","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:pure.ed.ac.uk:publications/49caf720-d277-4248-8646-b24b536decb0","is_oa":true,"landing_page_url":"https://www.research.ed.ac.uk/en/publications/49caf720-d277-4248-8646-b24b536decb0","pdf_url":"https://www.research.ed.ac.uk/files/57210728/inexactIPG_single.pdf","source":{"id":"https://openalex.org/S4306400321","display_name":"Edinburgh Research Explorer (University of Edinburgh)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I98677209","host_organization_name":"University of Edinburgh","host_organization_lineage":["https://openalex.org/I98677209"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Golbabaee, M & Davies, M 2018, 'Inexact Gradient Projection and Fast Data Driven Compressed Sensing', IEEE Transactions on Information Theory, vol. 64, no. 10, pp. 6707 - 6721. https://doi.org/10.1109/TIT.2018.2841379","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pure.ed.ac.uk:publications/93efdc75-0e1e-4c8c-8d2b-e17aa919d5f2","is_oa":false,"landing_page_url":"http://adsabs.harvard.edu/abs/2017arXiv170600092G","pdf_url":null,"source":{"id":"https://openalex.org/S4406922455","display_name":"Edinburgh Research Explorer","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"pmh:oai:pure.ed.ac.uk:publications/49caf720-d277-4248-8646-b24b536decb0","is_oa":false,"landing_page_url":"https://hdl.handle.net/20.500.11820/49caf720-d277-4248-8646-b24b536decb0","pdf_url":null,"source":{"id":"https://openalex.org/S4406922455","display_name":"Edinburgh Research Explorer","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"pmh:oai:pure.ed.ac.uk:publications/49caf720-d277-4248-8646-b24b536decb0","is_oa":true,"landing_page_url":"https://www.research.ed.ac.uk/en/publications/49caf720-d277-4248-8646-b24b536decb0","pdf_url":"https://www.research.ed.ac.uk/files/57210728/inexactIPG_single.pdf","source":{"id":"https://openalex.org/S4306400321","display_name":"Edinburgh Research Explorer (University of Edinburgh)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I98677209","host_organization_name":"University of Edinburgh","host_organization_lineage":["https://openalex.org/I98677209"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Golbabaee, M & Davies, M 2018, 'Inexact Gradient Projection and Fast Data Driven Compressed Sensing', IEEE Transactions on Information Theory, vol. 64, no. 10, pp. 6707 - 6721. https://doi.org/10.1109/TIT.2018.2841379","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4192948056","display_name":"Compressed Quantitative MRI","funder_award_id":"EP/M019802/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4753587921","display_name":null,"funder_award_id":"ERC-ADG-2015-694888","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"},{"id":"https://openalex.org/G7049000420","display_name":null,"funder_award_id":"EP/M019802/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320320006","display_name":"Royal Society","ror":"https://ror.org/03wnrjx87"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2620883262.pdf","grobid_xml":"https://content.openalex.org/works/W2620883262.grobid-xml"},"referenced_works_count":73,"referenced_works":["https://openalex.org/W14625021","https://openalex.org/W114517082","https://openalex.org/W1500801837","https://openalex.org/W1523004878","https://openalex.org/W1536329667","https://openalex.org/W1874232560","https://openalex.org/W1967138577","https://openalex.org/W1974774078","https://openalex.org/W1974973278","https://openalex.org/W1986736933","https://openalex.org/W2000062601","https://openalex.org/W2001380973","https://openalex.org/W2009234246","https://openalex.org/W2011359124","https://openalex.org/W2015839735","https://openalex.org/W2018429487","https://openalex.org/W2019786292","https://openalex.org/W2020629258","https://openalex.org/W2023101933","https://openalex.org/W2024930473","https://openalex.org/W2025079166","https://openalex.org/W2030161963","https://openalex.org/W2034188144","https://openalex.org/W2035808554","https://openalex.org/W2038082462","https://openalex.org/W2044610104","https://openalex.org/W2045110278","https://openalex.org/W2050958540","https://openalex.org/W2056804312","https://openalex.org/W2061375390","https://openalex.org/W2066629794","https://openalex.org/W2077520262","https://openalex.org/W2092663520","https://openalex.org/W2097717989","https://openalex.org/W2100875869","https://openalex.org/W2106221905","https://openalex.org/W2117756735","https://openalex.org/W2118123209","https://openalex.org/W2119449648","https://openalex.org/W2121210949","https://openalex.org/W2124608575","https://openalex.org/W2124768887","https://openalex.org/W2125680629","https://openalex.org/W2130357047","https://openalex.org/W2132001804","https://openalex.org/W2133296809","https://openalex.org/W2141426461","https://openalex.org/W2144288697","https://openalex.org/W2145096794","https://openalex.org/W2147825506","https://openalex.org/W2152402969","https://openalex.org/W2164431108","https://openalex.org/W2167077875","https://openalex.org/W2168914046","https://openalex.org/W2171463570","https://openalex.org/W2176777789","https://openalex.org/W2323307905","https://openalex.org/W2524385150","https://openalex.org/W2615253071","https://openalex.org/W2962817023","https://openalex.org/W2963002486","https://openalex.org/W2963116674","https://openalex.org/W2963322354","https://openalex.org/W2964012263","https://openalex.org/W2979473749","https://openalex.org/W3101339175","https://openalex.org/W3123607434","https://openalex.org/W4250955649","https://openalex.org/W6639227602","https://openalex.org/W6659084945","https://openalex.org/W6682597329","https://openalex.org/W6685044387","https://openalex.org/W6727533652"],"related_works":["https://openalex.org/W2158224665","https://openalex.org/W2073713056","https://openalex.org/W2379589510","https://openalex.org/W3110702597","https://openalex.org/W2351377961","https://openalex.org/W1942228078","https://openalex.org/W2086942802","https://openalex.org/W2046073294","https://openalex.org/W2170408898","https://openalex.org/W4389741222"],"abstract_inverted_index":{"We":[0,26,57,102],"study":[1],"the":[2,5,18,37,42,48,53,60,68,74,78,84,100,136,158,165],"convergence":[3,72],"of":[4,30,32,71,73,111,157,168],"iterative":[6,120],"projected":[7],"gradient":[8,19],"(IPG)":[9],"algorithm":[10,76,150],"for":[11,52],"arbitrary":[12],"(possibly":[13],"non-convex)":[14],"sets":[15,126,143],"when":[16],"both":[17],"and":[20,41,95],"projection":[21],"oracles":[22,45],"are":[23],"computed":[24],"approximately.":[25],"consider":[27],"different":[28],"notions":[29],"approximation":[31],"which":[33],"we":[34,118,178],"show":[35,58],"that":[36,59],"progressive":[38],"fixed":[39],"precision":[40],"(1+":[43],"\u03b5)-optimal":[44],"can":[46],"achieve":[47],"same":[49,79],"accuracy":[50],"as":[51,162,182],"exact":[54,75],"IPG":[55],"algorithm.":[56],"former":[61],"scheme":[62],"is":[63],"also":[64],"able":[65],"to":[66,106,164],"maintain":[67],"(linear)":[69],"rate":[70],"under":[77],"embedding":[80,90],"assumption.":[81],"In":[82],"contrast,":[83],"(1+\u03b5)-approximate":[85],"oracle":[86],"requires":[87],"a":[88,109,152,169],"stronger":[89],"condition,":[91],"moderate":[92],"compression":[93],"ratios":[94],"it":[96],"typically":[97],"slows":[98],"down":[99],"convergence.":[101],"apply":[103],"our":[104,148,185],"results":[105],"accelerate":[107],"solving":[108],"class":[110],"data":[112,125,139,142,159],"driven":[113],"compressed":[114],"sensing":[115],"problems,":[116],"where":[117],"replace":[119],"exhaustive":[121],"searches":[122],"over":[123],"large":[124],"by":[127,184],"fast":[128],"approximate":[129],"nearest":[130],"neighbor":[131],"search":[132],"strategies":[133],"based":[134],"on":[135],"cover":[137],"tree":[138],"structure.":[140],"For":[141],"with":[144],"low":[145],"intrinsic":[146],"dimensions,":[147],"proposed":[149],"achieves":[151],"complexity":[153,167],"logarithmic":[154],"in":[155],"terms":[156],"set":[160],"population":[161],"opposed":[163],"linear":[166],"brute":[170],"force":[171],"search.":[172],"By":[173],"running":[174],"several":[175],"numerical":[176],"experiments,":[177],"conclude":[179],"similar":[180],"observations":[181],"predicted":[183],"theoretical":[186],"analysis.":[187]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2026-07-18T07:39:51.176621","created_date":"2025-10-10T00:00:00"}