{"id":"https://openalex.org/W1997003380","doi":"https://doi.org/10.1137/110854539","title":"Piecewise Linear Approximation of the Continuous Rudin--Osher--Fatemi Model for Image Denoising","display_name":"Piecewise Linear Approximation of the Continuous Rudin--Osher--Fatemi Model for Image Denoising","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W1997003380","doi":"https://doi.org/10.1137/110854539","mag":"1997003380"},"language":"en","primary_location":{"id":"doi:10.1137/110854539","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110854539","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-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/A5057710396","display_name":"Ming\u2010Jun Lai","orcid":"https://orcid.org/0000-0003-0274-2545"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ming-Jun Lai","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5069101502","display_name":"Leopold Matamba Messi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Leopold Matamba Messi","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5057710396"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5491,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.66584244,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"50","issue":"5","first_page":"2446","last_page":"2466"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9987999796867371,"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/T10688","display_name":"Image and Signal Denoising Methods","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/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9972000122070312,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9968000054359436,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8609347343444824},{"id":"https://openalex.org/keywords/bounded-variation","display_name":"Bounded variation","score":0.7193955183029175},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6300998330116272},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.6105251312255859},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.5760902166366577},{"id":"https://openalex.org/keywords/noise-reduction","display_name":"Noise reduction","score":0.5757051706314087},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5449837446212769},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.5348094701766968},{"id":"https://openalex.org/keywords/total-variation-denoising","display_name":"Total variation denoising","score":0.5281797647476196},{"id":"https://openalex.org/keywords/image-denoising","display_name":"Image denoising","score":0.5194708704948425},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5121612548828125},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.43009546399116516},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38063865900039673},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38057637214660645},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3431095480918884},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1389922797679901},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08800002932548523}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8609347343444824},{"id":"https://openalex.org/C27851653","wikidata":"https://www.wikidata.org/wiki/Q829653","display_name":"Bounded variation","level":2,"score":0.7193955183029175},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6300998330116272},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.6105251312255859},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.5760902166366577},{"id":"https://openalex.org/C163294075","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Noise reduction","level":2,"score":0.5757051706314087},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5449837446212769},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.5348094701766968},{"id":"https://openalex.org/C207282899","wikidata":"https://www.wikidata.org/wiki/Q7828156","display_name":"Total variation denoising","level":3,"score":0.5281797647476196},{"id":"https://openalex.org/C2983327147","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Image denoising","level":3,"score":0.5194708704948425},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5121612548828125},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43009546399116516},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38063865900039673},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38057637214660645},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3431095480918884},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1389922797679901},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08800002932548523},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/110854539","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110854539","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4000000059604645,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W629836974","https://openalex.org/W1480714962","https://openalex.org/W1481112305","https://openalex.org/W1489458628","https://openalex.org/W1492326914","https://openalex.org/W1533665822","https://openalex.org/W1976688370","https://openalex.org/W1985099467","https://openalex.org/W2005089986","https://openalex.org/W2006262045","https://openalex.org/W2017848200","https://openalex.org/W2039939700","https://openalex.org/W2082608952","https://openalex.org/W2103559027","https://openalex.org/W2122890444","https://openalex.org/W2142058898","https://openalex.org/W2142308565","https://openalex.org/W2171315019","https://openalex.org/W2523352299","https://openalex.org/W2595348797","https://openalex.org/W3157033134"],"related_works":["https://openalex.org/W4296900887","https://openalex.org/W2889253769","https://openalex.org/W1596838019","https://openalex.org/W3182827720","https://openalex.org/W2133947431","https://openalex.org/W2490196280","https://openalex.org/W3208509670","https://openalex.org/W2944624955","https://openalex.org/W2100864966","https://openalex.org/W2109304297"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,25,35,62],"concerned":[3],"with":[4],"the":[5,9,12,28,45,48,52,59,68],"numerical":[6],"approximation":[7],"of":[8,11,47,55,70],"minimizer":[10,46],"continuous":[13,39],"Rudin--Osher--Fatemi":[14],"(ROF)":[15],"model":[16,34,50],"for":[17],"image":[18],"denoising.":[19],"A":[20],"new":[21],"discrete":[22],"total":[23,31],"variation":[24,32],"proposed":[26],"and":[27,64],"associated":[29],"Hilbertian":[30],"denoising":[33],"used":[36],"to":[37],"construct":[38],"piecewise":[40],"linear":[41],"functions":[42],"that":[43,58],"approximate":[44],"ROF":[49],"in":[51,67],"strong":[53],"topology":[54],"$L^2(\\Omega)$,":[56],"provided":[57],"data":[60],"function":[61],"bounded":[63],"weakly":[65],"regular":[66],"sense":[69],"$\\text{Lip}(\\alpha,\\text{L}^2(\\Omega))$.":[71]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}