{"id":"https://openalex.org/W4292171919","doi":"https://doi.org/10.3390/a15080288","title":"A Coupled Variational System for Image Decomposition along with Edges Detection","display_name":"A Coupled Variational System for Image Decomposition along with Edges Detection","publication_year":2022,"publication_date":"2022-08-16","ids":{"openalex":"https://openalex.org/W4292171919","doi":"https://doi.org/10.3390/a15080288"},"language":"en","primary_location":{"id":"doi:10.3390/a15080288","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a15080288","pdf_url":"https://www.mdpi.com/1999-4893/15/8/288/pdf?version=1660649048","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/15/8/288/pdf?version=1660649048","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076093418","display_name":"Jianlou Xu","orcid":"https://orcid.org/0000-0002-8550-6283"},"institutions":[{"id":"https://openalex.org/I167383011","display_name":"Henan University of Science and Technology","ror":"https://ror.org/05d80kz58","country_code":"CN","type":"education","lineage":["https://openalex.org/I167383011"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jianlou Xu","raw_affiliation_strings":["School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China","institution_ids":["https://openalex.org/I167383011"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060554339","display_name":"Yuying Guo","orcid":"https://orcid.org/0000-0002-6179-9982"},"institutions":[{"id":"https://openalex.org/I167383011","display_name":"Henan University of Science and Technology","ror":"https://ror.org/05d80kz58","country_code":"CN","type":"education","lineage":["https://openalex.org/I167383011"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuying Guo","raw_affiliation_strings":["School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China","institution_ids":["https://openalex.org/I167383011"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100708038","display_name":"Yan Hao","orcid":"https://orcid.org/0000-0003-2118-2299"},"institutions":[{"id":"https://openalex.org/I167383011","display_name":"Henan University of Science and Technology","ror":"https://ror.org/05d80kz58","country_code":"CN","type":"education","lineage":["https://openalex.org/I167383011"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yan Hao","raw_affiliation_strings":["School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China","institution_ids":["https://openalex.org/I167383011"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071380059","display_name":"Leigang Huo","orcid":"https://orcid.org/0000-0002-3124-3860"},"institutions":[{"id":"https://openalex.org/I4210151929","display_name":"Nanning Normal University","ror":"https://ror.org/04dx82x73","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210151929"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Leigang Huo","raw_affiliation_strings":["School of Computer and Information Engineering, Nanning Normal University, Nanning 530001, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer and Information Engineering, Nanning Normal University, Nanning 530001, China","institution_ids":["https://openalex.org/I4210151929"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5076093418"],"corresponding_institution_ids":["https://openalex.org/I167383011"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.07151137,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":"8","first_page":"288","last_page":"288"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9995999932289124,"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"}},{"id":"https://openalex.org/T11105","display_name":"Advanced Image Processing Techniques","score":0.9991000294685364,"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"}},{"id":"https://openalex.org/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9984999895095825,"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/tikhonov-regularization","display_name":"Tikhonov regularization","score":0.9136759638786316},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.6704074740409851},{"id":"https://openalex.org/keywords/variational-method","display_name":"Variational method","score":0.5885111093521118},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5770035982131958},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5044595003128052},{"id":"https://openalex.org/keywords/edge-detection","display_name":"Edge detection","score":0.4617479145526886},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.44982805848121643},{"id":"https://openalex.org/keywords/gauss","display_name":"Gauss","score":0.4462006092071533},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42957448959350586},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.40658584237098694},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3601292371749878},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35868537425994873},{"id":"https://openalex.org/keywords/image-processing","display_name":"Image processing","score":0.30317628383636475},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.286899209022522},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2499162256717682},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.14795362949371338},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09144869446754456}],"concepts":[{"id":"https://openalex.org/C152442038","wikidata":"https://www.wikidata.org/wiki/Q2778212","display_name":"Tikhonov regularization","level":3,"score":0.9136759638786316},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.6704074740409851},{"id":"https://openalex.org/C64618476","wikidata":"https://www.wikidata.org/wiki/Q164296","display_name":"Variational method","level":2,"score":0.5885111093521118},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5770035982131958},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5044595003128052},{"id":"https://openalex.org/C193536780","wikidata":"https://www.wikidata.org/wiki/Q1513153","display_name":"Edge detection","level":4,"score":0.4617479145526886},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.44982805848121643},{"id":"https://openalex.org/C161794534","wikidata":"https://www.wikidata.org/wiki/Q177493","display_name":"Gauss","level":2,"score":0.4462006092071533},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42957448959350586},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.40658584237098694},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3601292371749878},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35868537425994873},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.30317628383636475},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.286899209022522},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2499162256717682},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.14795362949371338},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09144869446754456},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/a15080288","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a15080288","pdf_url":"https://www.mdpi.com/1999-4893/15/8/288/pdf?version=1660649048","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:186031e56b044e0ca7748d0df0410e7a","is_oa":true,"landing_page_url":"https://doaj.org/article/186031e56b044e0ca7748d0df0410e7a","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 15, Iss 8, p 288 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1999-4893/15/8/288/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/a15080288","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms; Volume 15; Issue 8; Pages: 288","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/a15080288","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a15080288","pdf_url":"https://www.mdpi.com/1999-4893/15/8/288/pdf?version=1660649048","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1216688737","display_name":null,"funder_award_id":"22A120006","funder_id":"https://openalex.org/F4320335955","funder_display_name":"Key Scientific Research Project of Colleges and Universities in Henan Province"},{"id":"https://openalex.org/G2539266330","display_name":null,"funder_award_id":"No. 22A120006","funder_id":"https://openalex.org/F4320335955","funder_display_name":"Key Scientific Research Project of Colleges and Universities in Henan Province"},{"id":"https://openalex.org/G5976392586","display_name":null,"funder_award_id":"2018GXNSFBA281086","funder_id":"https://openalex.org/F4320322768","funder_display_name":"Natural Science Foundation of Guangxi Province"},{"id":"https://openalex.org/G8589142596","display_name":null,"funder_award_id":"U1504603","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/F4320322768","display_name":"Natural Science Foundation of Guangxi Province","ror":null},{"id":"https://openalex.org/F4320335955","display_name":"Key Scientific Research Project of Colleges and Universities in Henan Province","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4292171919.pdf","grobid_xml":"https://content.openalex.org/works/W4292171919.grobid-xml"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W207373900","https://openalex.org/W418408683","https://openalex.org/W1488881187","https://openalex.org/W1614049993","https://openalex.org/W1966329403","https://openalex.org/W1972568768","https://openalex.org/W1973700755","https://openalex.org/W2004346156","https://openalex.org/W2008076677","https://openalex.org/W2024774629","https://openalex.org/W2026260232","https://openalex.org/W2039878129","https://openalex.org/W2043469084","https://openalex.org/W2045559171","https://openalex.org/W2063237083","https://openalex.org/W2066630786","https://openalex.org/W2071142766","https://openalex.org/W2078718577","https://openalex.org/W2092231222","https://openalex.org/W2093109539","https://openalex.org/W2099139574","https://openalex.org/W2103559027","https://openalex.org/W2119658486","https://openalex.org/W2123597619","https://openalex.org/W2123606372","https://openalex.org/W2135411024","https://openalex.org/W2150134853","https://openalex.org/W2154996879","https://openalex.org/W2662110177","https://openalex.org/W2811153570","https://openalex.org/W2906425348","https://openalex.org/W2907879453","https://openalex.org/W2914597164","https://openalex.org/W2967259503","https://openalex.org/W2997920897","https://openalex.org/W3010224595","https://openalex.org/W3011612142","https://openalex.org/W3113304539","https://openalex.org/W3160361014","https://openalex.org/W4205293221","https://openalex.org/W4312908055"],"related_works":["https://openalex.org/W2337734184","https://openalex.org/W2388364587","https://openalex.org/W2322955667","https://openalex.org/W2373176546","https://openalex.org/W2127000180","https://openalex.org/W2050033254","https://openalex.org/W2561531189","https://openalex.org/W2152224705","https://openalex.org/W2385735574","https://openalex.org/W2057439054"],"abstract_inverted_index":{"In":[0],"order":[1],"to":[2,34,76,130],"better":[3],"decompose":[4],"the":[5,36,41,46,57,61,83,91,96,106,115,123,132,135],"images":[6],"and":[7,38,102,117],"protect":[8],"their":[9],"edges,":[10],"in":[11,45],"this":[12],"paper,":[13],"we":[14,94,109],"proposed":[15,136],"a":[16,49,79],"coupled":[17,92,107],"variational":[18,30,68,141],"system":[19],"consisting":[20],"of":[21,60,134],"two":[22],"steps.":[23],"The":[24],"first":[25],"step,":[26,48],"an":[27],"improved":[28],"weighted":[29],"model":[31,73],"is":[32,53,74,87],"introduced":[33],"obtain":[35],"cartoon":[37,43,116],"texture.":[39],"Using":[40,105],"obtained":[42,54,84],"image,":[44],"second":[47],"new":[50],"vector":[51,85],"function":[52,86],"for":[55],"describing":[56],"pseudo":[58],"edge":[59],"considered":[62],"image":[63],"by":[64],"one":[65],"Tikhonov":[66,71],"regularization":[67,72],"model.":[69],"Because":[70],"equivalent":[75],"carrying":[77],"out":[78,114],"Gaussian":[80],"linear":[81],"filtering,":[82],"smoother.":[88],"To":[89],"solve":[90],"system,":[93,108],"give":[95],"alternating":[97],"direction":[98],"method,":[99],"primal-dual":[100],"method":[101,137],"Gauss-Seidel":[103],"iteration.":[104],"can":[110],"not":[111],"only":[112],"separate":[113],"texture":[118],"parts,":[119],"but":[120],"also":[121],"extract":[122],"edge.":[124],"Extensive":[125],"numerical":[126],"experiments":[127],"are":[128],"given":[129],"show":[131],"effectiveness":[133],"compared":[138],"with":[139],"other":[140],"methods.":[142]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2022-08-18T00:00:00"}
