{"id":"https://openalex.org/W2075960401","doi":"https://doi.org/10.1137/100795504","title":"Integro-Differential Equations Based on $(BV, L^1)$ Image Decomposition","display_name":"Integro-Differential Equations Based on $(BV, L^1)$ Image Decomposition","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2075960401","doi":"https://doi.org/10.1137/100795504","mag":"2075960401"},"language":"en","primary_location":{"id":"doi:10.1137/100795504","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100795504","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"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 Imaging Sciences","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/A5027135804","display_name":"Prashant Athavale","orcid":"https://orcid.org/0000-0003-4563-9556"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Prashant Athavale","raw_affiliation_strings":["prashant@math.ucla.edu#TAB#"],"affiliations":[{"raw_affiliation_string":"prashant@math.ucla.edu#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072355478","display_name":"Eitan Tadmor","orcid":"https://orcid.org/0000-0001-7424-6327"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Eitan Tadmor","raw_affiliation_strings":["tadmor@cscamm.umd.edu#TAB#"],"affiliations":[{"raw_affiliation_string":"tadmor@cscamm.umd.edu#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5027135804"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9575,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.74370606,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"4","issue":"1","first_page":"300","last_page":"312"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9860000014305115,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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":0.984499990940094,"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/inverse","display_name":"Inverse","score":0.6685647964477539},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.6292332410812378},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.6247532963752747},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6202465295791626},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.6044602394104004},{"id":"https://openalex.org/keywords/scale-space","display_name":"Scale space","score":0.5795117020606995},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.5501497387886047},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.5212167501449585},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.4860125482082367},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.46489232778549194},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4516052007675171},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4495493471622467},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.399091899394989},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3809460401535034},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37168702483177185},{"id":"https://openalex.org/keywords/image-processing","display_name":"Image processing","score":0.36803653836250305},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2953351140022278},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2073020040988922},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2031499147415161},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09549951553344727}],"concepts":[{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.6685647964477539},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.6292332410812378},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.6247532963752747},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6202465295791626},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.6044602394104004},{"id":"https://openalex.org/C99102927","wikidata":"https://www.wikidata.org/wiki/Q3058184","display_name":"Scale space","level":4,"score":0.5795117020606995},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.5501497387886047},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.5212167501449585},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.4860125482082367},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.46489232778549194},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4516052007675171},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4495493471622467},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.399091899394989},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3809460401535034},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37168702483177185},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.36803653836250305},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2953351140022278},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2073020040988922},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2031499147415161},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09549951553344727},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/100795504","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100795504","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"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 Imaging Sciences","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.170.2119","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.170.2119","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cscamm.umd.edu/people/faculty/tadmor/pub/image_processing/Athavale_Tadmor_IDE_BVL1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.204.7518","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.204.7518","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cscamm.umd.edu/people/faculty/tadmor/pub/image_processing/Athavale_Tadmor_IDE_BVL1_SIIMS2011.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1966329403","https://openalex.org/W1993054536","https://openalex.org/W1998999283","https://openalex.org/W2012118748","https://openalex.org/W2020999234","https://openalex.org/W2038495454","https://openalex.org/W2078020354","https://openalex.org/W2084115655","https://openalex.org/W2093840813","https://openalex.org/W2103559027","https://openalex.org/W2105880637","https://openalex.org/W2111841405","https://openalex.org/W2114487471","https://openalex.org/W2118427319","https://openalex.org/W2123597619","https://openalex.org/W2123606372","https://openalex.org/W2146052399","https://openalex.org/W2150134853","https://openalex.org/W2163345036","https://openalex.org/W2172035098","https://openalex.org/W3011612142","https://openalex.org/W4246759095"],"related_works":["https://openalex.org/W55883722","https://openalex.org/W2394379345","https://openalex.org/W3215763795","https://openalex.org/W2331917905","https://openalex.org/W2350699021","https://openalex.org/W3155039083","https://openalex.org/W2374392618","https://openalex.org/W1970914699","https://openalex.org/W2168716251","https://openalex.org/W2033156724"],"abstract_inverted_index":{"A":[0],"novel":[1],"approach":[2],"for":[3,70],"multiscale":[4,33,85],"image":[5],"processing":[6],"based":[7],"on":[8,99],"integro-differential":[9],"equations":[10],"(IDEs)":[11],"was":[12],"proposed":[13],"in":[14,43],"[E.":[15],"Tadmor":[16],"and":[17],"P.":[18],"Athavale,":[19],"Inverse":[20],"Probl.":[21],"Imaging,":[22],"3":[23],"(2009),":[24],"pp.":[25],"693\u2013710].":[26],"These":[27],"IDEs,":[28],"which":[29,82],"stem":[30],"naturally":[31],"from":[32,84],"$(BV,L^2)$":[34],"hierarchical":[35,87],"decompositions,":[36],"yield":[37],"inverse":[38],"scale":[39],"representations":[40],"of":[41,50,93],"images":[42],"the":[44,47,57,62,80,102],"sense":[45],"that":[46,64],"$BV$-dual":[48],"norms":[49],"their":[51],"residuals":[52],"are":[53],"inversely":[54],"proportional":[55],"to":[56,101],"scaling":[58],"parameters.":[59],"Motivated":[60],"by":[61],"fact":[63],"$(BV,L^1)$":[65,86],"decomposition":[66],"is":[67],"more":[68],"suitable":[69],"extracting":[71],"local":[72],"scale-space":[73],"features":[74],"than":[75],"$(BV,L^2)$,":[76],"we":[77],"introduce":[78],"here":[79],"IDEs":[81],"arise":[83],"decompositions.":[88],"We":[89],"study":[90],"several":[91],"variants":[92],"this":[94],"$(BV,L^1)$-based":[95],"IDE":[96],"model,":[97],"depending":[98],"modifications":[100],"curvature":[103],"term.":[104]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}