{"id":"https://openalex.org/W2132294977","doi":"https://doi.org/10.1109/fskd.2012.6233794","title":"A robust fourth order partial differential equation for image restoration","display_name":"A robust fourth order partial differential equation for image restoration","publication_year":2012,"publication_date":"2012-05-01","ids":{"openalex":"https://openalex.org/W2132294977","doi":"https://doi.org/10.1109/fskd.2012.6233794","mag":"2132294977"},"language":"en","primary_location":{"id":"doi:10.1109/fskd.2012.6233794","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fskd.2012.6233794","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 9th International Conference on Fuzzy Systems and Knowledge Discovery","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"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/A5100932721","display_name":"Xinyong Zhao","orcid":null},"institutions":[{"id":"https://openalex.org/I4210161462","display_name":"Heilongjiang Institute of Technology","ror":"https://ror.org/05x0m9n95","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210161462"]},{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xinyong Zhao","raw_affiliation_strings":["School of Transportation Science and Engineering, Harbin Institute of Technology, Harbin, Heilongjiang, China","School of Transportation Science and Engineering, Harbin Institute of Technology, Heilongjiang 150001, China"],"affiliations":[{"raw_affiliation_string":"School of Transportation Science and Engineering, Harbin Institute of Technology, Harbin, Heilongjiang, China","institution_ids":["https://openalex.org/I4210161462","https://openalex.org/I204983213"]},{"raw_affiliation_string":"School of Transportation Science and Engineering, Harbin Institute of Technology, Heilongjiang 150001, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025947091","display_name":"Weili Zeng","orcid":"https://orcid.org/0000-0002-5266-2423"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weili Zeng","raw_affiliation_strings":["School of Transportation, South East University, Nanjing, Jiangsu, China","School of Transportation,Southeast University,Nanjing Jiangsu 210096, China)"],"affiliations":[{"raw_affiliation_string":"School of Transportation, South East University, Nanjing, Jiangsu, China","institution_ids":["https://openalex.org/I76569877"]},{"raw_affiliation_string":"School of Transportation,Southeast University,Nanjing Jiangsu 210096, China)","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066658319","display_name":"Xiaobo Lu","orcid":"https://orcid.org/0009-0003-3378-7911"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaobo Lu","raw_affiliation_strings":["School of Transportation, South East University, Nanjing, Jiangsu, China","School of Automation, Southeast University, Nanjing, Jiangsu 210096, China)"],"affiliations":[{"raw_affiliation_string":"School of Transportation, South East University, Nanjing, Jiangsu, China","institution_ids":["https://openalex.org/I76569877"]},{"raw_affiliation_string":"School of Automation, Southeast University, Nanjing, Jiangsu 210096, China)","institution_ids":["https://openalex.org/I76569877"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100932721"],"corresponding_institution_ids":["https://openalex.org/I204983213","https://openalex.org/I4210161462"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.17217617,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"1682","last_page":"1685"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11105","display_name":"Advanced Image Processing Techniques","score":0.9987999796867371,"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/T11105","display_name":"Advanced Image Processing Techniques","score":0.9987999796867371,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9980999827384949,"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/T10531","display_name":"Advanced Vision and Imaging","score":0.995199978351593,"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/partial-differential-equation","display_name":"Partial differential equation","score":0.7589473724365234},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.641005277633667},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.5745866298675537},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5417414903640747},{"id":"https://openalex.org/keywords/image-restoration","display_name":"Image restoration","score":0.523763120174408},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.5039834380149841},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.4342970550060272},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42998677492141724},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.4169802665710449},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.414439857006073},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.41254910826683044},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3867478668689728},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3717736601829529},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3464992046356201},{"id":"https://openalex.org/keywords/image-processing","display_name":"Image processing","score":0.2786591649055481},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.23435375094413757},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1872369945049286}],"concepts":[{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.7589473724365234},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.641005277633667},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.5745866298675537},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5417414903640747},{"id":"https://openalex.org/C106430172","wikidata":"https://www.wikidata.org/wiki/Q6002272","display_name":"Image restoration","level":4,"score":0.523763120174408},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.5039834380149841},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.4342970550060272},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42998677492141724},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4169802665710449},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.414439857006073},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.41254910826683044},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3867478668689728},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3717736601829529},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3464992046356201},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.2786591649055481},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.23435375094413757},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1872369945049286},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/fskd.2012.6233794","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fskd.2012.6233794","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 9th International Conference on Fuzzy Systems and Knowledge Discovery","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.6600000262260437}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W19793066","https://openalex.org/W1989893875","https://openalex.org/W2014866211","https://openalex.org/W2018837545","https://openalex.org/W2021504613","https://openalex.org/W2028955956","https://openalex.org/W2029356963","https://openalex.org/W2066898188","https://openalex.org/W2093834886","https://openalex.org/W2122287830","https://openalex.org/W2130604180","https://openalex.org/W2143049902","https://openalex.org/W2150134853","https://openalex.org/W2161214672","https://openalex.org/W2169288322","https://openalex.org/W3023411394","https://openalex.org/W4285719527","https://openalex.org/W6600792419"],"related_works":["https://openalex.org/W2357322570","https://openalex.org/W2997591215","https://openalex.org/W2227541280","https://openalex.org/W2029783634","https://openalex.org/W2979181971","https://openalex.org/W2888591766","https://openalex.org/W90581812","https://openalex.org/W2356724950","https://openalex.org/W3045416146","https://openalex.org/W2029287765"],"abstract_inverted_index":{"A":[0],"hybrid":[1],"fourth":[2,28],"order":[3,29],"partial":[4],"differential":[5],"equation":[6],"(PDE)":[7],"of":[8,58],"nonlinear":[9,26],"diffusion":[10,27],"and":[11,34,43,62],"bilateral":[12,32],"filtering":[13,33],"based":[14],"image":[15],"restoration":[16],"is":[17],"presented":[18],"in":[19],"this":[20],"paper.":[21],"The":[22],"proposed":[23,60],"model":[24,61],"combines":[25],"PDEs":[30],"with":[31],"inherits":[35],"their":[36],"advantages,":[37],"which":[38],"not":[39],"only":[40],"preserves":[41],"edge":[42],"robust":[44],"to":[45,66],"noise":[46],"but":[47],"also":[48],"avoids":[49],"the":[50,56,59,67],"staircase":[51],"effects.":[52],"Experiment":[53],"results":[54],"show":[55],"effectiveness":[57],"demonstrate":[63],"its":[64],"superiority":[65],"existing":[68],"models.":[69]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
