{"id":"https://openalex.org/W1501620083","doi":"https://doi.org/10.5075/epfl-thesis-4257","title":"Operator-like wavelets with application to functional magnetic resonance imaging","display_name":"Operator-like wavelets with application to functional magnetic resonance imaging","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W1501620083","doi":"https://doi.org/10.5075/epfl-thesis-4257","mag":"1501620083"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.611.3581","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.611.3581","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://bigwww.epfl.ch/publications/khalidov0901.pdf","raw_type":"text"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://infoscience.epfl.ch/record/128799","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034540773","display_name":"Ildar Khalidov","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Khalidov, Ildar","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5034540773"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0578862,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9990000128746033,"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"}},{"id":"https://openalex.org/T12015","display_name":"Photoacoustic and Ultrasonic Imaging","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/wavelet","display_name":"Wavelet","score":0.8678967952728271},{"id":"https://openalex.org/keywords/legendre-wavelet","display_name":"Legendre wavelet","score":0.7822073698043823},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5339867472648621},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5169267058372498},{"id":"https://openalex.org/keywords/differential-operator","display_name":"Differential operator","score":0.507004976272583},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.44377297163009644},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.43329286575317383},{"id":"https://openalex.org/keywords/spline","display_name":"Spline (mechanical)","score":0.421150267124176},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.41058364510536194},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3715119957923889},{"id":"https://openalex.org/keywords/discrete-wavelet-transform","display_name":"Discrete wavelet transform","score":0.34174835681915283},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.33083003759384155},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32801592350006104},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12766581773757935}],"concepts":[{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.8678967952728271},{"id":"https://openalex.org/C123769847","wikidata":"https://www.wikidata.org/wiki/Q6517888","display_name":"Legendre wavelet","level":5,"score":0.7822073698043823},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5339867472648621},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5169267058372498},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.507004976272583},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44377297163009644},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.43329286575317383},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.421150267124176},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.41058364510536194},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3715119957923889},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.34174835681915283},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.33083003759384155},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32801592350006104},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12766581773757935},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.611.3581","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.611.3581","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://bigwww.epfl.ch/publications/khalidov0901.pdf","raw_type":"text"},{"id":"pmh:oai:infoscience.epfl.ch:128799","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/128799","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":"pmh:oai:infoscience.tind.io:128799","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/30559","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":null,"raw_type":"doctoral thesis"},{"id":"doi:10.5075/epfl-thesis-4257","is_oa":true,"landing_page_url":"https://doi.org/10.5075/epfl-thesis-4257","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Dissertation"},{"id":"mag:1501620083","is_oa":false,"landing_page_url":"http://bigwww.epfl.ch/publications/khalidov0901.pdf","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.epfl.ch:128799","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/128799","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"},"sustainable_development_goals":[{"score":0.5899999737739563,"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":83,"referenced_works":["https://openalex.org/W16960563","https://openalex.org/W35117296","https://openalex.org/W1481646516","https://openalex.org/W1595114968","https://openalex.org/W1632601927","https://openalex.org/W1658679052","https://openalex.org/W1967226382","https://openalex.org/W1968632888","https://openalex.org/W1968694834","https://openalex.org/W1975474302","https://openalex.org/W1976751422","https://openalex.org/W1977813492","https://openalex.org/W1978641348","https://openalex.org/W1983924090","https://openalex.org/W1986931325","https://openalex.org/W1988782428","https://openalex.org/W1991118037","https://openalex.org/W2006231299","https://openalex.org/W2006262045","https://openalex.org/W2008844048","https://openalex.org/W2016444985","https://openalex.org/W2019089428","https://openalex.org/W2024240534","https://openalex.org/W2025458350","https://openalex.org/W2032871739","https://openalex.org/W2035136970","https://openalex.org/W2037489965","https://openalex.org/W2041045861","https://openalex.org/W2048050362","https://openalex.org/W2050996151","https://openalex.org/W2060899536","https://openalex.org/W2062102668","https://openalex.org/W2063978378","https://openalex.org/W2064563223","https://openalex.org/W2067701673","https://openalex.org/W2072116332","https://openalex.org/W2073178967","https://openalex.org/W2078203941","https://openalex.org/W2082191514","https://openalex.org/W2082442136","https://openalex.org/W2083136232","https://openalex.org/W2090344516","https://openalex.org/W2097323375","https://openalex.org/W2098012923","https://openalex.org/W2098914003","https://openalex.org/W2100970997","https://openalex.org/W2101789093","https://openalex.org/W2102634042","https://openalex.org/W2107187638","https://openalex.org/W2107949125","https://openalex.org/W2108454251","https://openalex.org/W2108862142","https://openalex.org/W2110157363","https://openalex.org/W2112250360","https://openalex.org/W2115706991","https://openalex.org/W2115755118","https://openalex.org/W2119330876","https://openalex.org/W2122768752","https://openalex.org/W2123586737","https://openalex.org/W2130561641","https://openalex.org/W2130575020","https://openalex.org/W2131938193","https://openalex.org/W2140598595","https://openalex.org/W2140832824","https://openalex.org/W2141695111","https://openalex.org/W2141964005","https://openalex.org/W2149153247","https://openalex.org/W2151951544","https://openalex.org/W2153058280","https://openalex.org/W2153319807","https://openalex.org/W2154332973","https://openalex.org/W2158252006","https://openalex.org/W2158940042","https://openalex.org/W2159548955","https://openalex.org/W2160557924","https://openalex.org/W2162471611","https://openalex.org/W2163889321","https://openalex.org/W2170797424","https://openalex.org/W2280882684","https://openalex.org/W2322026200","https://openalex.org/W2899801603","https://openalex.org/W2954811775","https://openalex.org/W3021168970"],"related_works":["https://openalex.org/W2246111347","https://openalex.org/W2588254089","https://openalex.org/W1969859985","https://openalex.org/W2149134525","https://openalex.org/W2096413202","https://openalex.org/W3030944633","https://openalex.org/W2094621673","https://openalex.org/W2371361504","https://openalex.org/W1570384079","https://openalex.org/W1991795934","https://openalex.org/W2090955007","https://openalex.org/W2904828658","https://openalex.org/W2087646733","https://openalex.org/W114250020","https://openalex.org/W1521660348","https://openalex.org/W2031462013","https://openalex.org/W1536902747","https://openalex.org/W2018042728","https://openalex.org/W1486128415","https://openalex.org/W2158133196"],"abstract_inverted_index":{"We":[0,82,143,226,249,257,294,307],"introduce":[1],"a":[2,10,33,40,46,89,145,172,200,242,245,262,284,303],"new":[3,165],"class":[4,286],"of":[5,23,32,39,43,76,100,148,181,203,287,317],"wavelets":[6,95,134,213,313],"that":[7,96,124,132,191,228,297,309],"behave":[8],"like":[9],"given":[11],"differential":[12,91,189,288],"operator":[13,52,109],"L.":[14,101],"Our":[15],"construction":[16,123,282],"is":[17,110,127],"inspired":[18],"by":[19,50,88,240],"the":[20,29,37,57,63,69,77,84,98,105,108,119,130,133,136,141,159,164,179,188,193,196,204,208,229,237,251,279],"derivative-like":[21],"behavior":[22,99],"classical":[24],"wavelets.":[25,81,275],"Within":[26],"our":[27,318],"framework,":[28],"wavelet":[30,59,106,166,281],"coefficients":[31],"signal":[34,71,224,239],"y":[35,66],"are":[36,218,231,314],"samples":[38],"smoothed":[41],"version":[42,147],"L{y}.":[44],"For":[45,187],"linear":[47,90,201],"system":[48,64,85,190],"characterized":[49],"an":[51,111],"equation":[53,92],"L{y}":[54],"=":[55],"x,":[56],"operator-like":[58,280],"transform":[60],"essentially":[61],"deconvolves":[62],"output":[65],"and":[67,93,107,135,161,195,235,311],"extracts":[68],"\"innovation\"":[70],"x.":[72],"The":[73,102,122,211],"main":[74],"contributions":[75],"thesis":[78],"include:":[79],"Exponential-spline":[80],"consider":[83],"L":[86,290,298],"described":[87],"build":[94],"mimic":[97],"link":[103],"between":[104],"exponential":[112],"B-spline":[113],"function;":[114],"its":[115,269],"integer":[116],"shifts":[117],"span":[118],"multiresolution":[120,305],"space.":[121],"we":[125,177,198,277],"obtain":[126],"non-stationary":[128],"in":[129,163,169,184,233,291],"sense":[131],"scaling":[137],"functions":[138],"depend":[139],"on":[140],"scale.":[142],"propose":[144],"generalized":[146],"Mallat's":[149],"fast":[150],"filterbank":[151],"algorithm":[152],"with":[153,244,253],"scale-dependent":[154],"filters":[155],"to":[156,261,267,271,301],"efficiently":[157],"perform":[158],"decomposition":[160],"reconstruction":[162],"basis.":[167],"Activelets":[168],"fMRI.":[170,186],"As":[171],"practical":[173],"biomedical":[174],"imaging":[175],"application,":[176],"study":[178],"problem":[180],"activity":[182],"detection":[183],"event-related":[185],"links":[192],"measurements":[194],"stimuli,":[197],"use":[199],"approximation":[202],"balloon/windkessel":[205],"model":[206],"for":[207,221,283],"hemodynamic":[209],"response.":[210],"corresponding":[212],"(we":[214],"call":[215],"them":[216],"activelets)":[217],"specially":[219],"tuned":[220],"temporal":[222],"fMRI":[223,255,264],"analysis.":[225,306],"assume":[227],"stimuli":[230],"sparse":[232],"time":[234],"extract":[236],"activity-related":[238],"optimizing":[241],"criterion":[243],"sparsity":[246],"regularization":[247],"term.":[248],"test":[250],"method":[252],"synthetic":[254],"data.":[256,273],"then":[258],"apply":[259],"it":[260],"high-resolution":[263],"retinotopy":[265],"dataset":[266],"demonstrate":[268],"applicability":[270],"real":[272],"Operator-like":[274],"Finally,":[276],"generalize":[278],"wide":[285],"operators":[289],"multiple":[292],"dimensions.":[293],"give":[295],"conditions":[296],"must":[299],"satisfy":[300],"generate":[302],"valid":[304],"show":[308],"Mat\u00e9rn":[310],"polyharmonic":[312],"particular":[315],"cases":[316],"construction.":[319]},"counts_by_year":[],"updated_date":"2026-07-23T05:56:39.545243","created_date":"2025-10-10T00:00:00"}