{"id":"https://openalex.org/W2920893547","doi":"https://doi.org/10.1155/2019/3650128","title":"Image Restoration by Second\u2010Order Total Generalized Variation and Wavelet Frame Regularization","display_name":"Image Restoration by Second\u2010Order Total Generalized Variation and Wavelet Frame Regularization","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2920893547","doi":"https://doi.org/10.1155/2019/3650128","mag":"2920893547"},"language":"en","primary_location":{"id":"doi:10.1155/2019/3650128","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/3650128","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/3650128.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/complexity/2019/3650128.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040074946","display_name":"Jianguang Zhu","orcid":"https://orcid.org/0000-0002-4610-330X"},"institutions":[{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianguang Zhu","raw_affiliation_strings":["College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590","institution_ids":["https://openalex.org/I80143920"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076586054","display_name":"Kai Li","orcid":"https://orcid.org/0000-0001-6429-8465"},"institutions":[{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kai Li","raw_affiliation_strings":["College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590","institution_ids":["https://openalex.org/I80143920"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101665990","display_name":"Binbin Hao","orcid":"https://orcid.org/0000-0002-9612-9663"},"institutions":[{"id":"https://openalex.org/I4210162190","display_name":"China University of Petroleum, East China","ror":"https://ror.org/05gbn2817","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210162190"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Binbin Hao","raw_affiliation_strings":["College of Science, China University of Petroleum, Qingdao 266580"],"raw_orcid":"https://orcid.org/0000-0002-9612-9663","affiliations":[{"raw_affiliation_string":"College of Science, China University of Petroleum, Qingdao 266580","institution_ids":["https://openalex.org/I4210162190"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101665990"],"corresponding_institution_ids":["https://openalex.org/I4210162190"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":0.5084,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.68185899,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"2019","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9994000196456909,"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/T12015","display_name":"Photoacoustic and Ultrasonic Imaging","score":0.9977999925613403,"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/regularization","display_name":"Regularization (linguistics)","score":0.8184337019920349},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.7358930110931396},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.672802746295929},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5322705507278442},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.507651686668396},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4960654675960541},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4725741446018219},{"id":"https://openalex.org/keywords/total-variation-denoising","display_name":"Total variation denoising","score":0.4695226550102234},{"id":"https://openalex.org/keywords/multiplier","display_name":"Multiplier (economics)","score":0.4120739996433258},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33645308017730713},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2629797160625458},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.26221463084220886},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09262722730636597}],"concepts":[{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.8184337019920349},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.7358930110931396},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.672802746295929},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5322705507278442},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.507651686668396},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4960654675960541},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4725741446018219},{"id":"https://openalex.org/C207282899","wikidata":"https://www.wikidata.org/wiki/Q7828156","display_name":"Total variation denoising","level":3,"score":0.4695226550102234},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.4120739996433258},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33645308017730713},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2629797160625458},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.26221463084220886},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09262722730636597},{"id":"https://openalex.org/C139719470","wikidata":"https://www.wikidata.org/wiki/Q39680","display_name":"Macroeconomics","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2019/3650128","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/3650128","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/3650128.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:complx:3650128","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/8503/2019/3650128.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:7114fdd6ac0c4a5dace9682b86e126f1","is_oa":false,"landing_page_url":"https://doaj.org/article/7114fdd6ac0c4a5dace9682b86e126f1","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complexity, Vol 2019 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2019/3650128","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/3650128","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/3650128.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.8100000023841858,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[{"id":"https://openalex.org/G3812856094","display_name":"\u56fe\u50cf\u8d85\u5206\u8fa8\u91cd\u5efa\u7684\u7a00\u758f\u8868\u793a\u5efa\u6a21\u53ca\u7b97\u6cd5\u7814\u7a76","funder_award_id":"61101208","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4285538544","display_name":null,"funder_award_id":"J17KA166","funder_id":"https://openalex.org/F4320329039","funder_display_name":"Project of Shandong Province Higher Educational Science and Technology Program"},{"id":"https://openalex.org/G5375495044","display_name":null,"funder_award_id":"J17KA166","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5480818412","display_name":null,"funder_award_id":"11326186","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6152252219","display_name":null,"funder_award_id":"91746104","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6882222862","display_name":null,"funder_award_id":"2016114","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7108638857","display_name":null,"funder_award_id":"2014TDJH102","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7476390494","display_name":null,"funder_award_id":"2017YFC1405600","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7862965136","display_name":null,"funder_award_id":"2017YFC1405600","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G879360056","display_name":null,"funder_award_id":"2014TDJH102","funder_id":"https://openalex.org/F4320322522","funder_display_name":"Shandong University of Science and Technology"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322522","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98"},{"id":"https://openalex.org/F4320329039","display_name":"Project of Shandong Province Higher Educational Science and Technology Program","ror":null},{"id":"https://openalex.org/F4320335577","display_name":"Major Research Plan","ror":null},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2920893547.pdf","grobid_xml":"https://content.openalex.org/works/W2920893547.grobid-xml"},"referenced_works_count":59,"referenced_works":["https://openalex.org/W818014837","https://openalex.org/W1071054716","https://openalex.org/W1567727005","https://openalex.org/W1971917627","https://openalex.org/W1978125723","https://openalex.org/W1978333359","https://openalex.org/W1983772857","https://openalex.org/W1985453570","https://openalex.org/W1992609597","https://openalex.org/W2000594266","https://openalex.org/W2007939544","https://openalex.org/W2010276227","https://openalex.org/W2021504613","https://openalex.org/W2021535288","https://openalex.org/W2025263014","https://openalex.org/W2027988702","https://openalex.org/W2032240925","https://openalex.org/W2037366656","https://openalex.org/W2039939700","https://openalex.org/W2057227141","https://openalex.org/W2061645416","https://openalex.org/W2069250767","https://openalex.org/W2077051484","https://openalex.org/W2085289788","https://openalex.org/W2086670019","https://openalex.org/W2094634730","https://openalex.org/W2098713549","https://openalex.org/W2103559027","https://openalex.org/W2105119246","https://openalex.org/W2110505738","https://openalex.org/W2112985045","https://openalex.org/W2113030459","https://openalex.org/W2121058967","https://openalex.org/W2127436071","https://openalex.org/W2133447259","https://openalex.org/W2133665775","https://openalex.org/W2145003640","https://openalex.org/W2154996879","https://openalex.org/W2167979976","https://openalex.org/W2318896103","https://openalex.org/W2343878357","https://openalex.org/W2569089001","https://openalex.org/W2582639297","https://openalex.org/W2614611154","https://openalex.org/W2724686744","https://openalex.org/W2743521362","https://openalex.org/W2750681454","https://openalex.org/W2762516999","https://openalex.org/W2790741054","https://openalex.org/W2890431627","https://openalex.org/W2891390596","https://openalex.org/W2899484521","https://openalex.org/W2900723220","https://openalex.org/W2904647744","https://openalex.org/W2906684616","https://openalex.org/W2909094219","https://openalex.org/W2920911036","https://openalex.org/W2947879544","https://openalex.org/W4235713725"],"related_works":["https://openalex.org/W2588406281","https://openalex.org/W4296900887","https://openalex.org/W1605636162","https://openalex.org/W2344001031","https://openalex.org/W2756378021","https://openalex.org/W4292601995","https://openalex.org/W2527117583","https://openalex.org/W2890366747","https://openalex.org/W2037789795","https://openalex.org/W2613828789"],"abstract_inverted_index":{"It":[0],"has":[1,58],"been":[2],"proved":[3],"that":[4,85],"total":[5],"generalized":[6],"variation":[7],"(TGV)":[8],"can":[9,47,89],"better":[10],"preserve":[11,90],"edges":[12],"while":[13,51],"suppressing":[14],"staircase":[15,49],"effect.":[16],"In":[17],"this":[18],"paper,":[19],"we":[20],"propose":[21],"an":[22],"effective":[23],"hybrid":[24],"regularization":[25,42],"model":[26,36,88],"based":[27],"on":[28],"second\u2010order":[29],"TGV":[30,41],"and":[31,43,56,93],"wavelet":[32,44],"frame.":[33],"The":[34,68],"proposed":[35,87],"inherits":[37],"the":[38,53,64,79],"advantages":[39],"of":[40,61,72],"frame":[45],"regularization,":[46],"eliminate":[48],"effect":[50],"protecting":[52],"sharp":[54],"edge,":[55],"simultaneously":[57],"good":[59],"capability":[60],"sparsely":[62],"estimating":[63],"piecewise":[65],"smooth":[66],"functions.":[67],"alternative":[69],"direction":[70],"method":[71],"multiplier":[73],"(ADMM)":[74],"is":[75],"employed":[76],"to":[77],"solve":[78],"new":[80],"model.":[81],"Numerical":[82],"results":[83],"show":[84],"our":[86],"more":[91],"details":[92],"get":[94],"higher":[95],"image":[96],"visual":[97],"quality":[98],"than":[99],"some":[100],"current":[101],"state\u2010of\u2010the\u2010art":[102],"methods.":[103]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3}],"updated_date":"2026-06-06T09:05:17.133730","created_date":"2025-10-10T00:00:00"}
