{"id":"https://openalex.org/W4409356009","doi":"https://doi.org/10.1109/lsp.2025.3560170","title":"Hilbert Transform on Graphs: Let There Be Phase","display_name":"Hilbert Transform on Graphs: Let There Be Phase","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4409356009","doi":"https://doi.org/10.1109/lsp.2025.3560170"},"language":"en","primary_location":{"id":"doi:10.1109/lsp.2025.3560170","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2025.3560170","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"is_oa":false,"is_in_doaj":false,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Signal Processing Letters","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/A5007694333","display_name":"Chun Hei Michael Chan","orcid":null},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Chun Hei Michael Chan","raw_affiliation_strings":["Neuro-X Institute, Ecole polytechnique fédérale de Lausanne, Lausanne, Switzerland","Neuro-X Institute, Ecole polytechnique fédérale de Lausanne, Switzerland"],"raw_orcid":"https://orcid.org/0009-0007-7189-7475","affiliations":[{"raw_affiliation_string":"Neuro-X Institute, Ecole polytechnique fédérale de Lausanne, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]},{"raw_affiliation_string":"Neuro-X Institute, Ecole polytechnique fédérale de Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002183850","display_name":"Alexandre Cionca","orcid":"https://orcid.org/0000-0002-1910-9650"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Alexandre Cionca","raw_affiliation_strings":["Neuro-X Institute, Ecole polytechnique fédérale de Lausanne, Lausanne, Switzerland","Neuro-X Institute, Ecole polytechnique fédérale de Lausanne, Switzerland"],"raw_orcid":"https://orcid.org/0000-0002-1910-9650","affiliations":[{"raw_affiliation_string":"Neuro-X Institute, Ecole polytechnique fédérale de Lausanne, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]},{"raw_affiliation_string":"Neuro-X Institute, Ecole polytechnique fédérale de Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003693672","display_name":"Dimitri Van De Ville","orcid":"https://orcid.org/0000-0002-2879-3861"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Dimitri Van De Ville","raw_affiliation_strings":["Neuro-X Institute, Ecole polytechnique fédérale de Lausanne, Lausanne, Switzerland","Neuro-X Institute, Ecole polytechnique fédérale de Lausanne, Switzerland"],"raw_orcid":"https://orcid.org/0000-0002-2879-3861","affiliations":[{"raw_affiliation_string":"Neuro-X Institute, Ecole polytechnique fédérale de Lausanne, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]},{"raw_affiliation_string":"Neuro-X Institute, Ecole polytechnique fédérale de Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5007694333"],"corresponding_institution_ids":["https://openalex.org/I5124864"],"apc_list":null,"apc_paid":null,"fwci":1.3257,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.80782664,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"32","issue":null,"first_page":"1725","last_page":"1729"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9314000010490417,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9314000010490417,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4637288451194763},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3734615743160248},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35399678349494934},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3269144892692566}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4637288451194763},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3734615743160248},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35399678349494934},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3269144892692566}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/lsp.2025.3560170","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2025.3560170","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"is_oa":false,"is_in_doaj":false,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Signal Processing Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W391578156","https://openalex.org/W1693636274","https://openalex.org/W1698699930","https://openalex.org/W1969662777","https://openalex.org/W1990488619","https://openalex.org/W1991252559","https://openalex.org/W2003411364","https://openalex.org/W2004891702","https://openalex.org/W2016926874","https://openalex.org/W2018095698","https://openalex.org/W2090090048","https://openalex.org/W2091764829","https://openalex.org/W2101491865","https://openalex.org/W2135269154","https://openalex.org/W2171923309","https://openalex.org/W2688953010","https://openalex.org/W2795527331","https://openalex.org/W2796431263","https://openalex.org/W2898149957","https://openalex.org/W2963482031","https://openalex.org/W3000307447","https://openalex.org/W3012995967","https://openalex.org/W3021345226","https://openalex.org/W3026118515","https://openalex.org/W3095449605","https://openalex.org/W4379780949","https://openalex.org/W4387382674","https://openalex.org/W4392903050","https://openalex.org/W6679390398"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027"],"abstract_inverted_index":{"In":[0],"the":[1,13,24,34,50,54,65,93,122,129,137,142,155,177,185,192],"past":[2],"years,":[3],"many":[4],"signal":[5,127],"processing":[6],"operations":[7],"have":[8],"been":[9],"successfully":[10],"adapted":[11],"to":[12,22,39,59,89,154,166,174],"graph":[14,28,42,47,100,181,186],"setting.":[15],"One":[16],"elegant":[17,172],"and":[18,95,116,171],"effective":[19],"approach":[20,193],"is":[21,62,68,119,194],"exploit":[23,176],"eigendecomposition":[25],"of":[26,56,87,92,110,125,136,169,180,191],"a":[27,41,79,84,98,113,126,134,160,167],"shift":[29],"operator":[30],"(GSO),":[31],"such":[32,107],"as":[33],"adjacency":[35],"or":[36],"Laplacian":[37],"operator,":[38],"define":[40],"Fourier":[43,101,187],"transform":[44,139,158],"for":[45,121],"projecting":[46],"signals":[48,182],"on":[49,159,196],"corresponding":[51],"basis.":[52],"However,":[53],"extension":[55],"this":[57],"scheme":[58],"directed":[60],"graphs":[61],"challenging":[63],"since":[64],"associated":[66],"GSO":[67,94],"non-symmetric":[69],"and,":[70],"in":[71],"general,":[72],"not":[73],"diagonalizable.":[74],"Here,":[75],"we":[76,104,132],"build":[77],"upon":[78],"recent":[80],"framework":[81],"that":[82,106,117],"adds":[83],"minimal":[85,108],"number":[86,168],"edges":[88,111],"allow":[90],"diagonalization":[91],"thus":[96],"provide":[97],"proper":[99],"transform.":[102,188],"Furthermore,":[103],"show":[105],"addition":[109],"creates":[112],"cycle":[114,144],"cover":[115],"it":[118],"essential":[120],"phase":[123,178],"analysis":[124],"throughout":[128],"graph.":[130],"Concurrently,":[131],"propose":[133],"generalization":[135,164],"Hilbert":[138,151,157],"interpreted":[140],"over":[141],"newfound":[143],"cover,":[145],"which":[146],"re-establishes":[147],"intuitions":[148],"from":[149],"traditional":[150],"transform,":[152],"equivalent":[153],"generalized":[156],"single":[161],"cycle.":[162],"This":[163],"leads":[165],"simple":[170],"recipes":[173],"effectively":[175],"information":[179],"provided":[183],"by":[184],"The":[189],"feasibility":[190],"demonstrated":[195],"several":[197],"examples.":[198]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}