{"id":"https://openalex.org/W3136625658","doi":"https://doi.org/10.1109/access.2021.3066127","title":"A Novel Fractional-Order Variational Approach for Image Restoration Based on Fuzzy Membership Degrees","display_name":"A Novel Fractional-Order Variational Approach for Image Restoration Based on Fuzzy Membership Degrees","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3136625658","doi":"https://doi.org/10.1109/access.2021.3066127","mag":"3136625658"},"language":"en","primary_location":{"id":"doi:10.1109/access.2021.3066127","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2021.3066127","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1109/access.2021.3066127","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100769932","display_name":"Mushtaq Ahmad Khan","orcid":"https://orcid.org/0000-0003-3518-1748"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Mushtaq Ahmad Khan","raw_affiliation_strings":["Department of Electrical Engineering, University of Engineering and Technology Mardan, Khyber Pakhtunkhwa, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Engineering and Technology Mardan, Khyber Pakhtunkhwa, Pakistan","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045849340","display_name":"Asmat Ullah","orcid":"https://orcid.org/0000-0003-1693-0862"},"institutions":[{"id":"https://openalex.org/I90610274","display_name":"University of Engineering and Technology Peshawar","ror":"https://ror.org/00p034093","country_code":"PK","type":"education","lineage":["https://openalex.org/I90610274"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Asmat Ullah","raw_affiliation_strings":["Department of Education, University of Engineering and Technology Peshawar, Peshawar, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Education, University of Engineering and Technology Peshawar, Peshawar, Pakistan","institution_ids":["https://openalex.org/I90610274"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044352783","display_name":"Sahib Khan","orcid":"https://orcid.org/0000-0001-9385-7596"},"institutions":[{"id":"https://openalex.org/I177477856","display_name":"Polytechnic University of Turin","ror":"https://ror.org/00bgk9508","country_code":"IT","type":"education","lineage":["https://openalex.org/I177477856"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Sahib Khan","raw_affiliation_strings":["Department of Electrical Electronics and Communications Engineering, Politecnico di Torino, Italy","Department of Electrical Engineering, University of Engineering and Technology Mardan, Khyber Pakhtunkhwa, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Electronics and Communications Engineering, Politecnico di Torino, Italy","institution_ids":["https://openalex.org/I177477856"]},{"raw_affiliation_string":"Department of Electrical Engineering, University of Engineering and Technology Mardan, Khyber Pakhtunkhwa, Pakistan","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009172348","display_name":"Murtaza Ali","orcid":"https://orcid.org/0000-0003-0446-0496"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Murtaza Ali","raw_affiliation_strings":["Department of Electrical Engineering, University of Engineering and Technology Mardan, Khyber Pakhtunkhwa, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Engineering and Technology Mardan, Khyber Pakhtunkhwa, Pakistan","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031616180","display_name":"Sheraz Khan","orcid":"https://orcid.org/0000-0002-8640-5900"},"institutions":[{"id":"https://openalex.org/I177477856","display_name":"Polytechnic University of Turin","ror":"https://ror.org/00bgk9508","country_code":"IT","type":"education","lineage":["https://openalex.org/I177477856"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Sheraz Khan","raw_affiliation_strings":["Department of Electrical Electronics and Communications Engineering, Politecnico di Torino, Italy","Department of Electrical Engineering, University of Engineering and Technology Mardan, Khyber Pakhtunkhwa, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Electronics and Communications Engineering, Politecnico di Torino, Italy","institution_ids":["https://openalex.org/I177477856"]},{"raw_affiliation_string":"Department of Electrical Engineering, University of Engineering and Technology Mardan, Khyber Pakhtunkhwa, Pakistan","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023881021","display_name":"Khalil Khan","orcid":"https://orcid.org/0000-0002-0864-5255"},"institutions":[{"id":"https://openalex.org/I134276161","display_name":"Pakistan Institute of Engineering and Applied Sciences","ror":"https://ror.org/04d4mbk19","country_code":"PK","type":"education","lineage":["https://openalex.org/I134276161"]},{"id":"https://openalex.org/I4391767994","display_name":"Pak-Austria Fachhochschule: Institute of Applied Sciences and Technology","ror":"https://ror.org/05pgqgb54","country_code":null,"type":"education","lineage":["https://openalex.org/I4391767994"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Khalil Khan","raw_affiliation_strings":["Department of Information Technology and Computer Science, Pak-Austria Fachhochschule: Institute of Applied Sciences and Technology, Haripur, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Information Technology and Computer Science, Pak-Austria Fachhochschule: Institute of Applied Sciences and Technology, Haripur, Pakistan","institution_ids":["https://openalex.org/I134276161","https://openalex.org/I4391767994"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045359397","display_name":"Mehedi Masud","orcid":"https://orcid.org/0000-0001-6019-7245"},"institutions":[{"id":"https://openalex.org/I179331831","display_name":"Taif University","ror":"https://ror.org/014g1a453","country_code":"SA","type":"education","lineage":["https://openalex.org/I179331831"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Mehedi Masud","raw_affiliation_strings":["Department of Computer Science, College of Computers and Information Technology, Taif University, Taif, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, College of Computers and Information Technology, Taif University, Taif, Saudi Arabia","institution_ids":["https://openalex.org/I179331831"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056586306","display_name":"Jehad Ali","orcid":"https://orcid.org/0000-0002-0589-7924"},"institutions":[{"id":"https://openalex.org/I57664883","display_name":"Ajou University","ror":"https://ror.org/03tzb2h73","country_code":"KR","type":"education","lineage":["https://openalex.org/I57664883"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Jehad Ali","raw_affiliation_strings":["Department of AI Convergence Network, Ajou University, Suwon, South Korea","Department of Computer Engineering, Ajou University, Suwon, South Korea"],"affiliations":[{"raw_affiliation_string":"Department of AI Convergence Network, Ajou University, Suwon, South Korea","institution_ids":["https://openalex.org/I57664883"]},{"raw_affiliation_string":"Department of Computer Engineering, Ajou University, Suwon, South Korea","institution_ids":["https://openalex.org/I57664883"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":8,"corresponding_author_ids":["https://openalex.org/A5100769932"],"corresponding_institution_ids":[],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":0.4803,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.63310458,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"9","issue":null,"first_page":"43574","last_page":"43600"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":1.0,"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":1.0,"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":0.9997000098228455,"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/T11659","display_name":"Advanced Image Fusion Techniques","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/2214","display_name":"Media Technology"},"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/uniqueness","display_name":"Uniqueness","score":0.5961996912956238},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5447429418563843},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5193951725959778},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5026111602783203},{"id":"https://openalex.org/keywords/image-restoration","display_name":"Image restoration","score":0.49932265281677246},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49796628952026367},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.49554741382598877},{"id":"https://openalex.org/keywords/noise-reduction","display_name":"Noise reduction","score":0.4872223436832428},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4802192151546478},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4508780837059021},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.39003491401672363},{"id":"https://openalex.org/keywords/image-processing","display_name":"Image processing","score":0.3516440987586975},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.22553086280822754},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1947535276412964}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5961996912956238},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5447429418563843},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5193951725959778},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5026111602783203},{"id":"https://openalex.org/C106430172","wikidata":"https://www.wikidata.org/wiki/Q6002272","display_name":"Image restoration","level":4,"score":0.49932265281677246},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49796628952026367},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.49554741382598877},{"id":"https://openalex.org/C163294075","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Noise reduction","level":2,"score":0.4872223436832428},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4802192151546478},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4508780837059021},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.39003491401672363},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.3516440987586975},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.22553086280822754},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1947535276412964}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/access.2021.3066127","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2021.3066127","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:7a738a82e78046a39c6f160aec4cb037","is_oa":true,"landing_page_url":"https://doaj.org/article/7a738a82e78046a39c6f160aec4cb037","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 9, Pp 43574-43600 (2021)","raw_type":"article"},{"id":"pmh:oai:zenodo.org:141787","is_oa":true,"landing_page_url":"https://www.openaccessrepository.it/record/141787","pdf_url":null,"source":{"id":"https://openalex.org/S4306402478","display_name":"INFM-OAR (INFN Catania)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210116497","host_organization_name":"Istituto Nazionale di Fisica Nucleare, Sezione di Catania","host_organization_lineage":["https://openalex.org/I4210116497"],"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":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1109/access.2021.3066127","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2021.3066127","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.6899999976158142}],"awards":[{"id":"https://openalex.org/G8669394481","display_name":null,"funder_award_id":"TURSP-2020/10","funder_id":"https://openalex.org/F4320323722","funder_display_name":"Taif University"}],"funders":[{"id":"https://openalex.org/F4320323722","display_name":"Taif University","ror":"https://ror.org/014g1a453"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W1541112376","https://openalex.org/W1915743070","https://openalex.org/W1965357430","https://openalex.org/W1968112329","https://openalex.org/W1970484278","https://openalex.org/W1976445349","https://openalex.org/W1998339281","https://openalex.org/W2000334767","https://openalex.org/W2004928853","https://openalex.org/W2010825468","https://openalex.org/W2011516671","https://openalex.org/W2013388817","https://openalex.org/W2018021323","https://openalex.org/W2021504613","https://openalex.org/W2027279136","https://openalex.org/W2030122346","https://openalex.org/W2056611489","https://openalex.org/W2069766163","https://openalex.org/W2074319623","https://openalex.org/W2078108630","https://openalex.org/W2089481079","https://openalex.org/W2094634730","https://openalex.org/W2103559027","https://openalex.org/W2107815783","https://openalex.org/W2110264793","https://openalex.org/W2122287830","https://openalex.org/W2127594500","https://openalex.org/W2127668421","https://openalex.org/W2139301071","https://openalex.org/W2142344058","https://openalex.org/W2160924560","https://openalex.org/W2237930028","https://openalex.org/W2342849074","https://openalex.org/W2506752412","https://openalex.org/W2737965552","https://openalex.org/W2801192398","https://openalex.org/W2889921656","https://openalex.org/W2963101071","https://openalex.org/W2997600526","https://openalex.org/W2999221865","https://openalex.org/W3009016150","https://openalex.org/W3047529442","https://openalex.org/W3114935388","https://openalex.org/W3148872539","https://openalex.org/W6788005086"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W4301247218","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W2129818458","https://openalex.org/W4289551052","https://openalex.org/W2340777379","https://openalex.org/W4390756076","https://openalex.org/W4243074410"],"abstract_inverted_index":{"We":[0,20,65],"propose":[1],"a":[2,33,104],"new":[3],"fractional-order":[4,96],"(space":[5],"and":[6,40,55,101,127,147],"time)":[7],"total":[8],"variation":[9],"regularized":[10],"model":[11,45,110,121],"for":[12,67],"multiplicative":[13],"noise":[14,134],"removal":[15],"in":[16,122,140],"this":[17],"research":[18],"article.":[19],"use":[21],"the":[22,30,62,68,78,81,85,94,107,116,119,129,141],"regularly":[23],"varying":[24],"fuzzy":[25],"membership":[26],"degrees":[27],"to":[28,36,43,75,106,152],"characterize":[29],"likelihood":[31],"of":[32,51,70,80,103,118],"pixel":[34],"related":[35],"edges,":[37,53],"texture":[38],"regions,":[39],"flat":[41],"regions":[42],"improve":[44],"efficiency.":[46],"This":[47],"approach":[48,89],"is":[49,90],"capable":[50],"maintaining":[52],"textures,":[54],"other":[56,153],"image":[57],"information":[58],"while":[59,132],"significantly":[60],"reducing":[61,128],"blocky":[63,130],"effect.":[64],"opt":[66],"option":[69],"local":[71],"actions.":[72],"In":[73],"order":[74],"efficiently":[76],"find":[77],"minimizer":[79],"prescribed":[82],"energy":[83],"function,":[84],"semi-implicit":[86],"gradient":[87],"descent":[88],"used":[91],"(which":[92],"derives":[93],"corresponding":[95],"Euler-Lagrange":[97],"equations).":[98],"The":[99],"existence":[100],"uniqueness":[102],"solution":[105],"suggested":[108,120],"variational":[109],"are":[111],"proved.":[112],"Experimental":[113],"results":[114],"show":[115],"efficiency":[117],"visual":[123],"enhancement,":[124],"preserving":[125],"details":[126],"effect":[131],"extracting":[133],"as":[135,137],"well":[136],"an":[138],"increase":[139],"PSNR":[142],"(dB),":[143],"SSIM,":[144],"relative":[145],"error,":[146],"less":[148],"CPU":[149],"time(s)":[150],"comparing":[151],"schemes.":[154]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2021-03-29T00:00:00"}
