{"id":"https://openalex.org/W1971641950","doi":"https://doi.org/10.1109/tip.2015.2401430","title":"On the Convergence of Nonconvex Minimization Methods for Image Recovery","display_name":"On the Convergence of Nonconvex Minimization Methods for Image Recovery","publication_year":2015,"publication_date":"2015-02-06","ids":{"openalex":"https://openalex.org/W1971641950","doi":"https://doi.org/10.1109/tip.2015.2401430","mag":"1971641950","pmid":"https://pubmed.ncbi.nlm.nih.gov/25675457"},"language":"en","primary_location":{"id":"doi:10.1109/tip.2015.2401430","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2015.2401430","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"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 Image Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5029920041","display_name":"Jin Xiao","orcid":"https://orcid.org/0000-0001-5011-7870"},"institutions":[{"id":"https://openalex.org/I154833797","display_name":"Lingnan Normal University","ror":"https://ror.org/01h6ecw13","country_code":"CN","type":"education","lineage":["https://openalex.org/I154833797"]},{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jin Xiao","raw_affiliation_strings":["College of Mathematics and Econometrics, Hunan University, Changsha, China","School of Mathematics and Computation Science, Lingnan Normal University, Zhanjiang, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Econometrics, Hunan University, Changsha, China","institution_ids":["https://openalex.org/I16609230"]},{"raw_affiliation_string":"School of Mathematics and Computation Science, Lingnan Normal University, Zhanjiang, China","institution_ids":["https://openalex.org/I154833797"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010561682","display_name":"Michael K. Ng","orcid":"https://orcid.org/0000-0001-6833-5227"},"institutions":[{"id":"https://openalex.org/I141568987","display_name":"Hong Kong Baptist University","ror":"https://ror.org/0145fw131","country_code":"HK","type":"education","lineage":["https://openalex.org/I141568987"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Michael Kwok-Po Ng","raw_affiliation_strings":["Department of Mathematics, Hong Kong Baptist University, Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hong Kong Baptist University, Hong Kong","institution_ids":["https://openalex.org/I141568987"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028464253","display_name":"Yufei Yang","orcid":"https://orcid.org/0000-0002-1335-038X"},"institutions":[{"id":"https://openalex.org/I198357462","display_name":"Changsha University","ror":"https://ror.org/011d8sm39","country_code":"CN","type":"education","lineage":["https://openalex.org/I198357462"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yu-Fei Yang","raw_affiliation_strings":["Department of Information and Computing Science, Changsha University, Changsha, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Information and Computing Science, Changsha University, Changsha, China","institution_ids":["https://openalex.org/I198357462"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.909,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.89510019,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"24","issue":"5","first_page":"1587","last_page":"1598"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9990000128746033,"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/T10052","display_name":"Medical Image Segmentation Techniques","score":0.994700014591217,"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/minification","display_name":"Minification","score":0.8222032189369202},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.6916041374206543},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.6654496192932129},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6201254725456238},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5403665900230408},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.48449966311454773},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40594011545181274},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39807507395744324},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35973772406578064},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09626397490501404},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06510022282600403}],"concepts":[{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.8222032189369202},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.6916041374206543},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.6654496192932129},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6201254725456238},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5403665900230408},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.48449966311454773},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40594011545181274},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39807507395744324},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35973772406578064},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09626397490501404},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06510022282600403},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tip.2015.2401430","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2015.2401430","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"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 Image Processing","raw_type":"journal-article"},{"id":"pmid:25675457","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/25675457","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on image processing : a publication of the IEEE Signal Processing Society","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2321416715","display_name":null,"funder_award_id":"60872129","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4405897671","display_name":null,"funder_award_id":"2014SK3235","funder_id":"https://openalex.org/F4320330206","funder_display_name":"Science and Technology Program of Hunan Province"},{"id":"https://openalex.org/G5274903103","display_name":null,"funder_award_id":"71431008","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G745338437","display_name":"\u9ad8\u901f\u7cbe\u5bc6\u5236\u9020\u751f\u4ea7\u7ebf\u7684\u89c6\u89c9\u68c0\u6d4b\u4e0e\u667a\u80fd\u4f18\u5316\u63a7\u5236\u6280\u672f\u7814\u7a76","funder_award_id":"60835004","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320330206","display_name":"Science and Technology Program of Hunan Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W26023427","https://openalex.org/W40037269","https://openalex.org/W1964152012","https://openalex.org/W1967138577","https://openalex.org/W1978333359","https://openalex.org/W2000462146","https://openalex.org/W2008473145","https://openalex.org/W2020999234","https://openalex.org/W2021361347","https://openalex.org/W2022164193","https://openalex.org/W2022541060","https://openalex.org/W2026289804","https://openalex.org/W2027026120","https://openalex.org/W2027982384","https://openalex.org/W2028912194","https://openalex.org/W2033330000","https://openalex.org/W2033603511","https://openalex.org/W2046367659","https://openalex.org/W2048304654","https://openalex.org/W2068357778","https://openalex.org/W2078853581","https://openalex.org/W2100115174","https://openalex.org/W2103559027","https://openalex.org/W2111841405","https://openalex.org/W2123224804","https://openalex.org/W2129732816","https://openalex.org/W2142224912","https://openalex.org/W2149846618","https://openalex.org/W2151514667","https://openalex.org/W2156523995","https://openalex.org/W2157011125","https://openalex.org/W2162052349","https://openalex.org/W2162988958","https://openalex.org/W2166388529","https://openalex.org/W2171413647","https://openalex.org/W2320459610","https://openalex.org/W2951084471","https://openalex.org/W2952855561","https://openalex.org/W4206519171","https://openalex.org/W4249513058","https://openalex.org/W4253250161","https://openalex.org/W6637235014"],"related_works":["https://openalex.org/W3103325625","https://openalex.org/W1486898455","https://openalex.org/W3090727460","https://openalex.org/W2041905724","https://openalex.org/W2047986527","https://openalex.org/W4306313719","https://openalex.org/W2991463004","https://openalex.org/W4311726894","https://openalex.org/W4387701909","https://openalex.org/W2782547861"],"abstract_inverted_index":{"Nonconvex":[0],"nonsmooth":[1,30,75,85],"regularization":[2,86],"method":[3],"has":[4],"been":[5,22],"shown":[6],"to":[7,26,40,68,83,105],"be":[8],"effective":[9],"for":[10],"restoring":[11],"images":[12],"with":[13,88],"neat":[14],"edges.":[15],"Fast":[16],"alternating":[17,46,64],"minimization":[18,31,47,65,99],"schemes":[19],"have":[20],"also":[21,79],"proposed":[23],"and":[24,91],"developed":[25],"solve":[27],"the":[28,42,51,59,63,81,97],"nonconvex":[29,74,84],"problem.":[32],"The":[33],"main":[34],"contribution":[35],"of":[36,44,72,96],"this":[37,73],"paper":[38],"is":[39],"show":[41,57],"convergence":[43,94,108],"these":[45],"schemes,":[48],"based":[49],"on":[50],"Kurdyka-\u0141ojasiewicz":[52],"property.":[53],"In":[54],"particular,":[55],"we":[56],"that":[58],"iterates":[60],"generated":[61],"by":[62],"scheme,":[66],"converges":[67],"a":[69],"critical":[70],"point":[71],"objective":[76],"function.":[77],"We":[78],"extend":[80],"analysis":[82],"model":[87],"box":[89],"constraints,":[90],"obtain":[92],"similar":[93],"results":[95],"related":[98],"algorithm.":[100],"Numerical":[101],"examples":[102],"are":[103],"given":[104],"illustrate":[106],"our":[107],"analysis.":[109]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}