{"id":"https://openalex.org/W3011139149","doi":"https://doi.org/10.1109/tsp.2020.3032231","title":"Convergence Guarantees for Non-Convex Optimisation With Cauchy-Based Penalties","display_name":"Convergence Guarantees for Non-Convex Optimisation With Cauchy-Based Penalties","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3011139149","doi":"https://doi.org/10.1109/tsp.2020.3032231","mag":"3011139149"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2020.3032231","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2020.3032231","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2003.04798","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053586101","display_name":"Oktay Karaku\u015f","orcid":"https://orcid.org/0000-0001-8009-9319"},"institutions":[{"id":"https://openalex.org/I36234482","display_name":"University of Bristol","ror":"https://ror.org/0524sp257","country_code":"GB","type":"education","lineage":["https://openalex.org/I36234482"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Oktay Karakus","raw_affiliation_strings":["Visual Information Laboratory, University of Bristol, Bristol, U.K"],"affiliations":[{"raw_affiliation_string":"Visual Information Laboratory, University of Bristol, Bristol, U.K","institution_ids":["https://openalex.org/I36234482"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037114688","display_name":"Perla Mayo","orcid":"https://orcid.org/0000-0002-5224-9014"},"institutions":[{"id":"https://openalex.org/I36234482","display_name":"University of Bristol","ror":"https://ror.org/0524sp257","country_code":"GB","type":"education","lineage":["https://openalex.org/I36234482"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Perla Mayo","raw_affiliation_strings":["Visual Information Laboratory, University of Bristol, Bristol, U.K"],"affiliations":[{"raw_affiliation_string":"Visual Information Laboratory, University of Bristol, Bristol, U.K","institution_ids":["https://openalex.org/I36234482"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001624119","display_name":"Alin Achim","orcid":"https://orcid.org/0000-0002-0982-7798"},"institutions":[{"id":"https://openalex.org/I36234482","display_name":"University of Bristol","ror":"https://ror.org/0524sp257","country_code":"GB","type":"education","lineage":["https://openalex.org/I36234482"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Alin Achim","raw_affiliation_strings":["Visual Information Laboratory, University of Bristol, Bristol, U.K"],"affiliations":[{"raw_affiliation_string":"Visual Information Laboratory, University of Bristol, Bristol, U.K","institution_ids":["https://openalex.org/I36234482"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5053586101"],"corresponding_institution_ids":["https://openalex.org/I36234482"],"apc_list":null,"apc_paid":null,"fwci":5.0231,"has_fulltext":false,"cited_by_count":45,"citation_normalized_percentile":{"value":0.96684518,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"68","issue":null,"first_page":"6159","last_page":"6170"},"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/T10727","display_name":"Ultrasound Imaging and Elastography","score":0.9995999932289124,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9988999962806702,"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/cauchy-distribution","display_name":"Cauchy distribution","score":0.7167454957962036},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.6226329803466797},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5878823399543762},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5437752604484558},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5319530963897705},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5000543594360352},{"id":"https://openalex.org/keywords/penalty-method","display_name":"Penalty method","score":0.49385935068130493},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.47242867946624756},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4568614959716797},{"id":"https://openalex.org/keywords/deblurring","display_name":"Deblurring","score":0.44929611682891846},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.41637110710144043},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4132139980792999},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3274036645889282},{"id":"https://openalex.org/keywords/image-restoration","display_name":"Image restoration","score":0.31016117334365845},{"id":"https://openalex.org/keywords/image-processing","display_name":"Image processing","score":0.19862204790115356},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17880770564079285},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10757690668106079},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.0985153317451477}],"concepts":[{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.7167454957962036},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.6226329803466797},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5878823399543762},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5437752604484558},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5319530963897705},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5000543594360352},{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.49385935068130493},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47242867946624756},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4568614959716797},{"id":"https://openalex.org/C2777693668","wikidata":"https://www.wikidata.org/wiki/Q25053743","display_name":"Deblurring","level":5,"score":0.44929611682891846},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41637110710144043},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4132139980792999},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3274036645889282},{"id":"https://openalex.org/C106430172","wikidata":"https://www.wikidata.org/wiki/Q6002272","display_name":"Image restoration","level":4,"score":0.31016117334365845},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.19862204790115356},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17880770564079285},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10757690668106079},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0985153317451477},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/tsp.2020.3032231","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2020.3032231","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2003.04798","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2003.04798","pdf_url":"https://arxiv.org/pdf/2003.04798","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":"pmh:oai:https://orca.cardiff.ac.uk:145180","is_oa":false,"landing_page_url":"https://orca.cardiff.ac.uk/id/eprint/145180/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401195","display_name":"ORCA Online Research @Cardiff (Cardiff University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79510175","host_organization_name":"Cardiff University","host_organization_lineage":["https://openalex.org/I79510175"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:research-information.bris.ac.uk:publications/8a0e6982-a9c3-432e-b079-f567e21fd34c","is_oa":false,"landing_page_url":"https://hdl.handle.net/1983/8a0e6982-a9c3-432e-b079-f567e21fd34c","pdf_url":null,"source":{"id":"https://openalex.org/S7407055359","display_name":"Explore Bristol Research","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":"Karakus, O, Mayo Diaz De Leon, P J & Achim, A M 2020, 'Convergence Guarantees for Non-Convex Optimisation with Cauchy-Based Penalties', IEEE Transactions on Signal Processing, vol. 68, no. 1. https://doi.org/10.1109/TSP.2020.3032231","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:research-information.bris.ac.uk:publications/8a0e6982-a9c3-432e-b079-f567e21fd34c","is_oa":false,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/8a0e6982-a9c3-432e-b079-f567e21fd34c","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"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:arXiv.org:2003.04798","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2003.04798","pdf_url":"https://arxiv.org/pdf/2003.04798","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":[{"score":0.7799999713897705,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G461037485","display_name":"Assessment of Sea Surface Signatures for Naval Platforms Using SAR Imagery (AssenSAR)","funder_award_id":"EP/R009260/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6214462845","display_name":null,"funder_award_id":"EP/R009260/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W1457323852","https://openalex.org/W1686180572","https://openalex.org/W1915743070","https://openalex.org/W1916935112","https://openalex.org/W1946620893","https://openalex.org/W1963824880","https://openalex.org/W1977169914","https://openalex.org/W2005089986","https://openalex.org/W2021834312","https://openalex.org/W2033726108","https://openalex.org/W2044810215","https://openalex.org/W2063870433","https://openalex.org/W2074577749","https://openalex.org/W2078414346","https://openalex.org/W2081930078","https://openalex.org/W2106219791","https://openalex.org/W2111854674","https://openalex.org/W2122072454","https://openalex.org/W2149632685","https://openalex.org/W2152498207","https://openalex.org/W2157011125","https://openalex.org/W2161882007","https://openalex.org/W2344441077","https://openalex.org/W2344964557","https://openalex.org/W2566924527","https://openalex.org/W2570790349","https://openalex.org/W2584677438","https://openalex.org/W2588776893","https://openalex.org/W2613864614","https://openalex.org/W2620850570","https://openalex.org/W2727207057","https://openalex.org/W2768751982","https://openalex.org/W2909370557","https://openalex.org/W2913192828","https://openalex.org/W2913535645","https://openalex.org/W2945776902","https://openalex.org/W2987692455","https://openalex.org/W2998830245","https://openalex.org/W3023956684","https://openalex.org/W3035711000","https://openalex.org/W3098466966","https://openalex.org/W3099748020","https://openalex.org/W3104630443","https://openalex.org/W3123837026","https://openalex.org/W4244393449","https://openalex.org/W4244769743","https://openalex.org/W6681940934","https://openalex.org/W6733216812"],"related_works":["https://openalex.org/W2066613488","https://openalex.org/W2031788393","https://openalex.org/W791927757","https://openalex.org/W2182590612","https://openalex.org/W3153582293","https://openalex.org/W2905397092","https://openalex.org/W2269775642","https://openalex.org/W3080537281","https://openalex.org/W2289746762","https://openalex.org/W2139384960"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"propose":[4],"a":[5,10,23,91,130],"proximal":[6,29,42,92],"splitting":[7,43,93],"methodology":[8],"with":[9],"non-convex":[11,153],"penalty":[12,65,154,158],"function":[13,83,155],"based":[14,64,98,152],"on":[15,99],"the":[16,28,32,48,55,62,68,73,80,115,137,146,149],"heavy-tailed":[17],"Cauchy":[18,33,63,100,151],"distribution.":[19],"We":[20,45,134],"first":[21],"suggest":[22],"closed-form":[24],"expression":[25],"for":[26,51,141],"calculating":[27],"operator":[30],"of":[31,148],"prior,":[34],"which":[35],"then":[36],"makes":[37],"it":[38],"applicable":[39],"in":[40,58,114,129],"generic":[41,106],"algorithms.":[44],"further":[46],"derive":[47],"condition":[49,75],"required":[50],"guaranteed":[52],"convergence":[53,77,139],"to":[54],"global":[56],"minimum":[57],"optimisation":[59],"problems":[60],"involving":[61],"function.":[66],"Setting":[67],"system":[69],"parameters":[70],"by":[71,104],"satisfying":[72],"proposed":[74,96,138,150],"ensures":[76],"even":[78],"though":[79],"overall":[81],"cost":[82],"is":[84,88,102],"non-convex,":[85],"when":[86],"minimisation":[87],"performed":[89],"via":[90],"algorithm.":[94],"The":[95],"method":[97],"regularisation":[101],"evaluated":[103],"solving":[105],"signal":[107,112],"processing":[108],"examples,":[109],"i.e.":[110],"1D":[111],"denoising":[113],"frequency":[116],"domain,":[117],"two":[118],"image":[119],"reconstruction":[120],"tasks":[121],"including":[122],"deblurring":[123],"and":[124,126,144,166],"denoising,":[125],"error":[127],"recovery":[128],"multiple-antenna":[131],"communication":[132],"system.":[133],"experimentally":[135],"verify":[136],"conditions":[140],"various":[142],"cases,":[143],"show":[145],"effectiveness":[147],"over":[156],"state-of-the-art":[157],"functions":[159],"such":[160],"as":[161],"L":[162],"<sub":[163],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[164],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sub>":[165],"total":[167],"variation":[168],"(TV":[169],")":[170],"norms.":[171]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":6}],"updated_date":"2026-03-21T08:13:44.787528","created_date":"2020-03-23T00:00:00"}
