{"id":"https://openalex.org/W1556704555","doi":"https://doi.org/10.5075/epfl-thesis-4968","title":"Optimally Localized Wavelets and Smoothing Kernels","display_name":"Optimally Localized Wavelets and Smoothing Kernels","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W1556704555","doi":"https://doi.org/10.5075/epfl-thesis-4968","mag":"1556704555"},"language":"en","primary_location":{"id":"pmh:oai:infoscience.tind.io:162113","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/62721","pdf_url":"http://infoscience.epfl.ch/record/162113","source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"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":"","raw_type":"doctoral thesis"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://infoscience.epfl.ch/record/162113","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045035201","display_name":"Kunal N. Chaudhury","orcid":"https://orcid.org/0000-0002-8136-605X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Chaudhury, Kunal Narayan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5045035201"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":0.9991999864578247,"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":0.9991999864578247,"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":0.9291999936103821,"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"}},{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.9279999732971191,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/gabor-wavelet","display_name":"Gabor wavelet","score":0.9134750366210938},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.804886519908905},{"id":"https://openalex.org/keywords/legendre-wavelet","display_name":"Legendre wavelet","score":0.7033712267875671},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6686685681343079},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.47914570569992065},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.4619375467300415},{"id":"https://openalex.org/keywords/spline","display_name":"Spline (mechanical)","score":0.4505487084388733},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.4484538733959198},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4337961673736572},{"id":"https://openalex.org/keywords/multiresolution-analysis","display_name":"Multiresolution analysis","score":0.43135982751846313},{"id":"https://openalex.org/keywords/discrete-wavelet-transform","display_name":"Discrete wavelet transform","score":0.32552075386047363},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2609524130821228},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22071951627731323}],"concepts":[{"id":"https://openalex.org/C136902061","wikidata":"https://www.wikidata.org/wiki/Q16981559","display_name":"Gabor wavelet","level":5,"score":0.9134750366210938},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.804886519908905},{"id":"https://openalex.org/C123769847","wikidata":"https://www.wikidata.org/wiki/Q6517888","display_name":"Legendre wavelet","level":5,"score":0.7033712267875671},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6686685681343079},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.47914570569992065},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.4619375467300415},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.4505487084388733},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.4484538733959198},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4337961673736572},{"id":"https://openalex.org/C121927907","wikidata":"https://www.wikidata.org/wiki/Q1952516","display_name":"Multiresolution analysis","level":5,"score":0.43135982751846313},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.32552075386047363},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2609524130821228},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22071951627731323},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:infoscience.tind.io:162113","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/62721","pdf_url":"http://infoscience.epfl.ch/record/162113","source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"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":"","raw_type":"doctoral thesis"},{"id":"pmh:oai:infoscience.epfl.ch:162113","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/162113","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"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":"","raw_type":"Text"},{"id":"doi:10.5075/epfl-thesis-4968","is_oa":true,"landing_page_url":"https://doi.org/10.5075/epfl-thesis-4968","pdf_url":null,"source":{"id":"https://openalex.org/S4306400488","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Dissertation"},{"id":"mag:1556704555","is_oa":false,"landing_page_url":"https://infoscience.epfl.ch/record/162113","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:infoscience.tind.io:162113","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/62721","pdf_url":"http://infoscience.epfl.ch/record/162113","source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"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":"","raw_type":"doctoral thesis"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W1556704555.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2089059039","https://openalex.org/W2051036272","https://openalex.org/W2056912916","https://openalex.org/W1964322372","https://openalex.org/W2117368578","https://openalex.org/W2351794214","https://openalex.org/W2800919141","https://openalex.org/W2066890549","https://openalex.org/W2183584629","https://openalex.org/W2118192096","https://openalex.org/W31312143","https://openalex.org/W2766706740","https://openalex.org/W2073331535","https://openalex.org/W2091090560","https://openalex.org/W2140051102","https://openalex.org/W2472019172","https://openalex.org/W2162965487","https://openalex.org/W2106829325","https://openalex.org/W1987339221","https://openalex.org/W2129276048"],"abstract_inverted_index":{"It":[0],"is":[1,127,146,187,213,219,463,512,626,638,666,695,730,741,765,795],"well-known":[2],"that":[3,128,181,208,223,262,281,290,332,427,450,504,551,664,796],"the":[4,16,28,39,46,54,60,64,94,98,112,140,149,172,183,188,199,209,232,241,285,291,311,317,335,347,359,366,370,392,397,406,409,416,432,439,456,468,473,478,492,509,517,523,527,537,545,569,572,594,597,604,621,634,652,657,660,710,715,745,751,758,772,786,789,807,812,823,860,870,881],"Gaussian":[5,65,556,611,624,637,734,773,791],"functions":[6],"and,":[7],"more":[8],"generally,":[9],"their":[10,836],"modulations-translations":[11],"(the":[12],"Gabor":[13,47,67,95,301,337],"functions)":[14],"have":[15],"unique":[17],"property":[18,191],"of":[19,30,41,63,82,93,105,121,151,159,170,185,192,198,215,228,244,259,278,329,362,369,377,391,408,438,446,458,482,491,495,508,526,544,571,596,607,619,636,642,651,659,676,686,709,728,744,750,771,785,788,831,845,883],"being":[20],"optimally":[21],"localized":[22,217],"in":[23,27,326,514,738,742,779,783,850,888],"space":[24],"and":[25,49,66,69,116,125,135,194,321,379,411,680,699,703,714,748,820,866,886],"frequency":[26],"sense":[29],"Heisenberg's":[31],"uncertainty":[32],"principle.":[33],"In":[34,76,522,584],"this":[35,186,269,296,375,739,780,863],"thesis,":[36,528],"we":[37,78,101,129,165,250,271,383,421,485,502,529,549,566,586,719,797,854,874],"address":[38],"construction":[40,312],"complex":[42,292,330,349],"wavelets":[43,124,193,280,331],"modeled":[44],"on":[45,53,352,374,431,477,767],"function,":[48,68],"smoothing":[50,840],"kernels":[51,126],"based":[52,766],"Gaussian.":[55,583],"We":[56,179,288,308,339,356,601,662,834],"proceed":[57],"by":[58,70,154,247,732,810,821,838,867],"relaxing":[59],"exact":[61],"form":[62,263,481,770],"approximating":[71,811,822],"them":[72],"using":[73,316,613,682,757,816,828],"spline":[74,83,123,535,574,857],"functions.":[75,338],"particular,":[77,585],"construct":[79],"a":[80,103,167,216,252,257,264,276,300,327,423,488,499,505,531,555,563,580,588,648,683,768,802,829,851,876],"family":[81,104,361,376],"wavelets,":[84,87,484],"termed":[85,536],"Gabor-like":[86,144,398,434,480],"which":[88,364,754],"provide":[89,166,387],"arbitrary":[90],"close":[91],"approximations":[92],"function.":[96],"On":[97],"other":[99,763],"hand,":[100],"introduce":[102,530],"compactly":[106],"supported":[107],"box":[108,534,539,573,599,615,674,712,752,818,856],"splines":[109,675,713],"to":[110,132,206,236,274,299,313,386,404,554,578,628,668,697,800],"approximate":[111,579],"Gaussian,":[113],"both":[114],"isotropic":[115,817],"anisotropic.":[117],"The":[118,143,202,443,461,617,640,692,726,736,762,776,793],"attractive":[119],"feature":[120,445],"these":[122,248,614,729],"are":[130,272,282,384,755,798],"able":[131,273,385,799],"develop":[133,340,422,587,720,801,855,875],"fast":[134,877],"efficient":[136,342,605],"algorithms":[137,722,841],"for":[138,255,345,466,592,647,723,805,842,880],"implementing":[139,346,806],"associated":[141,348,395,414,693,716],"transforms.":[142],"wavelet":[145,218,260,293,350,399,435],"obtained":[147],"within":[148],"framework":[150,243],"multiresolution":[152,242],"analysis":[153],"combining":[155],"Hilbert":[156,173,200,210,265,286,319,371],"transform":[157,174,211,266,320],"pairs":[158],"B-spline":[160,279],"wavelets.":[161,178,245,323],"To":[162],"begin":[163],"with,":[164],"rigorous":[168],"understanding":[169],"why":[171],"goes":[175],"well":[176],"with":[177,396,415,516,656,672],"show":[180,289,503,550,567],"at":[182,455],"heart":[184],"characteristic":[189],"vanishing-moment":[190],"certain":[195],"fundamental":[196,367],"invariances":[197,368],"transform.":[201,287,372,400,417],"former":[203],"allows":[204,234,402],"us":[205,235,403],"ensure":[207],"(which":[212],"non-local)":[214],"again":[220],"well-localized":[221],"provided":[222,487],"it":[224,239,451,552,665],"has":[225],"sufficient":[226],"number":[227,641,685],"vanishing":[229],"moments,":[230],"while":[231],"latter":[233],"seamlessly":[237],"integrate":[238],"into":[240],"Guided":[246],"facts,":[249],"formulate":[251],"general":[253],"recipe":[254],"constructing":[256],"pair":[258,277,297],"bases":[261],"pair.":[267,475],"Using":[268,862],"recipe,":[270],"identify":[275,358],"related":[283],"through":[284],"derived":[294],"from":[295],"converges":[298,553],"function":[302],"as":[303,557],"its":[304,380,558],"order":[305,559],"gets":[306,560],"large.":[307,561,639],"next":[309,357,602],"extend":[310],"higher":[314],"dimensions":[315],"directional":[318,336],"tensor-products":[322],"This":[324,401],"results":[325],"system":[328],"closely":[333],"resemble":[334],"an":[341,388,419,542,670,707,848],"numerical":[343],"algorithm":[344,426,591,694,804,879],"transforms":[351,363,378],"finite":[353],"periodic":[354],"data.":[355],"complete":[360],"share":[365],"Based":[373,476],"particular":[381,479,532,864],"properties,":[382],"amplitude-phase":[389],"interpretation":[390],"signal":[393],"representation":[394],"understand":[405],"significance":[407],"amplitude":[410],"phase":[412],"information":[413],"As":[418,541,706,847],"application,":[420],"coarse-to-fine":[424],"stereo-matching":[425],"does":[428],"dynamic":[429,519],"programming":[430,520],"sub-sampled":[433],"pyramid":[436,448],"instead":[437],"raw":[440],"pixel":[441,646,689],"intensities.":[442],"crucial":[444],"our":[447,483,496],"was":[449,782],"provides":[452],"near":[453,493],"translation-invariance":[454,462,494],"cost":[457],"moderate":[459],"redundancy.":[460],"absolutely":[464],"essential":[465],"encoding":[467],"local":[469,704,759],"spatial":[470,777,790,814],"translations":[471],"between":[472],"stereo":[474],"also":[486],"mathematical":[489],"explanation":[490],"pyramid.":[497],"From":[498],"computational":[500],"standpoint,":[501],"significant":[506],"reduction":[507],"run":[510],"time":[511],"achieved":[513],"comparison":[515],"standard":[518],"algorithm.":[521],"second":[524],"half":[525],"bivariate":[533],"radially-uniform":[538],"spline.":[540],"application":[543,708,849],"Central":[546],"Limit":[547],"Theorem,":[548],"For":[562],"fixed":[564,581,684,824],"order,":[565],"how":[568],"parameters":[570],"can":[575],"be":[576,629],"tuned":[577],"anisotropic":[582,733],"simple":[589,622,701],"root-finding":[590],"controlling":[593],"anisotropy":[595],"elliptical":[598],"splines.":[600,616],"investigate":[603],"realization":[606,618],"space-variant":[608,724,769],"(or":[609],"non-convolution)":[610],"filters":[612,858],"even":[620],"convolution":[623],"filter":[625,653,669,809,815,826],"known":[627],"computationally":[630],"challenging,":[631],"particularly":[632],"when":[633],"size":[635,658,787],"computations":[643,687],"required":[644],"per":[645,688],"direct":[649],"implementation":[650],"scales":[654],"linearly":[655],"filter.":[661,775,792],"demonstrated":[663],"possible":[667],"image":[671,760],"Gaussian-like":[673,711],"varying":[677],"size,":[678,746],"elongation":[679],"orientation":[681,749],"(constant-time":[690],"implementation).":[691],"easy":[696],"implement":[698],"uses":[700],"pre-integrations":[702],"finite-differences.":[705],"filtering":[717,872],"algorithm,":[718,873],"two":[721],"filtering.":[725],"first":[727],"inspired":[731],"diffusion.":[735],"space-variance":[737],"case":[740,781],"terms":[743,784],"elongation,":[747],"splines,":[753,819],"controlled":[756],"features.":[761],"scheme":[764],"bilateral":[774,808],"adaptability":[778],"highlight":[794],"constant-time":[803],"variable":[813],"range":[825],"(locally)":[827],"class":[830],"shiftable":[832],"kernels.":[833],"demonstrate":[835],"usage":[837],"developing":[839],"signal-adaptive":[843],"denoising":[844],"images.":[846,890],"different":[852],"direction,":[853],"resembling":[859],"Laplacian-of-Gaussian.":[861],"detector,":[865],"appropriately":[868],"modifying":[869],"basic":[871],"template-matching":[878],"detection":[882],"bright":[884],"cells":[885],"nuclei":[887],"fluorescence":[889]},"counts_by_year":[],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}
