{"id":"https://openalex.org/W3015826334","doi":"https://doi.org/10.1109/icassp40776.2020.9052996","title":"Riemannian Geometry and Cram\u00e9r-rao Bound for Blind Separation of Gaussian Sources","display_name":"Riemannian Geometry and Cram\u00e9r-rao Bound for Blind Separation of Gaussian Sources","publication_year":2020,"publication_date":"2020-04-09","ids":{"openalex":"https://openalex.org/W3015826334","doi":"https://doi.org/10.1109/icassp40776.2020.9052996","mag":"3015826334"},"language":"en","primary_location":{"id":"doi:10.1109/icassp40776.2020.9052996","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icassp40776.2020.9052996","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.univ-grenoble-alpes.fr/hal-02571093","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079968302","display_name":"Florent Bouchard","orcid":"https://orcid.org/0000-0003-3003-7317"},"institutions":[{"id":"https://openalex.org/I70900168","display_name":"Universit\u00e9 Savoie Mont Blanc","ror":"https://ror.org/04gqg1a07","country_code":"FR","type":"education","lineage":["https://openalex.org/I70900168"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Florent Bouchard","raw_affiliation_strings":["Univ. Savoie Mont Blanc,LISTIC,Annecy,France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Univ. Savoie Mont Blanc,LISTIC,Annecy,France","institution_ids":["https://openalex.org/I70900168"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059566872","display_name":"Arnaud Breloy","orcid":"https://orcid.org/0000-0002-3802-9015"},"institutions":[{"id":"https://openalex.org/I40434647","display_name":"Universit\u00e9 Paris Nanterre","ror":"https://ror.org/013bkhk48","country_code":"FR","type":"education","lineage":["https://openalex.org/I40434647"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Arnaud Breloy","raw_affiliation_strings":["Univ. Paris Nanterre,LEME,France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Univ. Paris Nanterre,LEME,France","institution_ids":["https://openalex.org/I40434647"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044736586","display_name":"Alexandre Renaux","orcid":"https://orcid.org/0000-0003-3413-1765"},"institutions":[{"id":"https://openalex.org/I40434647","display_name":"Universit\u00e9 Paris Nanterre","ror":"https://ror.org/013bkhk48","country_code":"FR","type":"education","lineage":["https://openalex.org/I40434647"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Alexandre Renaux","raw_affiliation_strings":["Univ. Paris Nanterre,LEME,France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Univ. Paris Nanterre,LEME,France","institution_ids":["https://openalex.org/I40434647"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057632387","display_name":"Guillaume Ginolhac","orcid":"https://orcid.org/0000-0001-9318-028X"},"institutions":[{"id":"https://openalex.org/I70900168","display_name":"Universit\u00e9 Savoie Mont Blanc","ror":"https://ror.org/04gqg1a07","country_code":"FR","type":"education","lineage":["https://openalex.org/I70900168"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Guillaume Ginolhac","raw_affiliation_strings":["Univ. Savoie Mont Blanc,LISTIC,Annecy,France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Univ. Savoie Mont Blanc,LISTIC,Annecy,France","institution_ids":["https://openalex.org/I70900168"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"4717","last_page":"4721"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11447","display_name":"Blind Source Separation Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10640","display_name":"Spectroscopy and Chemometric Analyses","score":0.9925000071525574,"subfield":{"id":"https://openalex.org/subfields/1602","display_name":"Analytical Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10860","display_name":"Speech and Audio Processing","score":0.9528999924659729,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/information-geometry","display_name":"Information geometry","score":0.7279629707336426},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6817251443862915},{"id":"https://openalex.org/keywords/orthonormal-basis","display_name":"Orthonormal basis","score":0.6386616230010986},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5854250192642212},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5680786371231079},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.5468052625656128},{"id":"https://openalex.org/keywords/cram\u00e9r\u2013rao-bound","display_name":"Cram\u00e9r\u2013Rao bound","score":0.5410858392715454},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5398728847503662},{"id":"https://openalex.org/keywords/tangent-space","display_name":"Tangent space","score":0.5382229089736938},{"id":"https://openalex.org/keywords/statistical-manifold","display_name":"Statistical manifold","score":0.533632218837738},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.5122960805892944},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5077584981918335},{"id":"https://openalex.org/keywords/riemannian-geometry","display_name":"Riemannian geometry","score":0.5073263049125671},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.47504734992980957},{"id":"https://openalex.org/keywords/fisher-information","display_name":"Fisher information","score":0.47281327843666077},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.47024598717689514},{"id":"https://openalex.org/keywords/riemannian-manifold","display_name":"Riemannian manifold","score":0.4355050325393677},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43371888995170593},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4282380938529968},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3836843967437744},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.21987375617027283},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1968049705028534},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15235206484794617}],"concepts":[{"id":"https://openalex.org/C109546454","wikidata":"https://www.wikidata.org/wiki/Q3798604","display_name":"Information geometry","level":4,"score":0.7279629707336426},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6817251443862915},{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.6386616230010986},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5854250192642212},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5680786371231079},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.5468052625656128},{"id":"https://openalex.org/C4978587","wikidata":"https://www.wikidata.org/wiki/Q1138810","display_name":"Cram\u00e9r\u2013Rao bound","level":3,"score":0.5410858392715454},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5398728847503662},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.5382229089736938},{"id":"https://openalex.org/C169391604","wikidata":"https://www.wikidata.org/wiki/Q7604402","display_name":"Statistical manifold","level":5,"score":0.533632218837738},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.5122960805892944},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5077584981918335},{"id":"https://openalex.org/C181104567","wikidata":"https://www.wikidata.org/wiki/Q761383","display_name":"Riemannian geometry","level":2,"score":0.5073263049125671},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.47504734992980957},{"id":"https://openalex.org/C29406490","wikidata":"https://www.wikidata.org/wiki/Q1420659","display_name":"Fisher information","level":2,"score":0.47281327843666077},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.47024598717689514},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.4355050325393677},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43371888995170593},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4282380938529968},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3836843967437744},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.21987375617027283},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1968049705028534},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15235206484794617},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.0},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/icassp40776.2020.9052996","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icassp40776.2020.9052996","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)","raw_type":"proceedings-article"},{"id":"pmh:oai:HAL:hal-02571093v1","is_oa":true,"landing_page_url":"https://hal.univ-grenoble-alpes.fr/hal-02571093","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), May 2020, Barcelona, Spain. &#x27E8;10.1109/icassp40776.2020.9052996&#x27E9;","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-02571093v1","is_oa":true,"landing_page_url":"https://hal.univ-grenoble-alpes.fr/hal-02571093","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), May 2020, Barcelona, Spain. &#x27E8;10.1109/icassp40776.2020.9052996&#x27E9;","raw_type":"info:eu-repo/semantics/conferenceObject"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5027824404","display_name":"Modern Adaptive Radar: Great Advances in Robust and Inference Techniques and Application","funder_award_id":"ANR-17-ASTR-0015","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W88077589","https://openalex.org/W1588644029","https://openalex.org/W1755563775","https://openalex.org/W1983104971","https://openalex.org/W2001169189","https://openalex.org/W2017587562","https://openalex.org/W2019543362","https://openalex.org/W2079329591","https://openalex.org/W2107110735","https://openalex.org/W2110476671","https://openalex.org/W2112220340","https://openalex.org/W2124195644","https://openalex.org/W2124757684","https://openalex.org/W2142638745","https://openalex.org/W2142975003","https://openalex.org/W2155779374","https://openalex.org/W2792697231","https://openalex.org/W2903931732","https://openalex.org/W2963305046","https://openalex.org/W2963684104","https://openalex.org/W3000334627","https://openalex.org/W6603558344","https://openalex.org/W6681158929","https://openalex.org/W6725705423"],"related_works":["https://openalex.org/W4297911919","https://openalex.org/W3143767508","https://openalex.org/W1742234374","https://openalex.org/W334503494","https://openalex.org/W1964020044","https://openalex.org/W3164174180","https://openalex.org/W2125882322","https://openalex.org/W176248852","https://openalex.org/W2030711521","https://openalex.org/W1609560631"],"abstract_inverted_index":{"We":[0],"consider":[1,70],"the":[2,30,42,48,59,71,78,81,84,117,129,145,153,157],"optimal":[3,60],"performance":[4,50,62],"of":[5,8,23,26,37,51,63,80,83,119,131,156],"blind":[6],"separation":[7],"Gaussian":[9],"sources.":[10],"In":[11],"practice,":[12],"this":[13,38,94],"estimation":[14,22,123],"problem":[15],"is":[16,126,141],"solved":[17],"by":[18],"a":[19,24,52,90,112],"two-step":[20],"procedure:":[21],"set":[25,39],"covariance":[27],"matrices":[28],"from":[29,144],"observed":[31],"data":[32],"and":[33,110,149],"approximate":[34],"joint":[35],"diagonalization":[36],"to":[40],"find":[41],"unmixing":[43],"matrix.":[44],"Rather":[45],"than":[46],"studying":[47],"theoretical":[49,161],"specific":[53],"method,":[54],"we":[55,69,108],"are":[56,163],"interested":[57],"in":[58,93],"attainable":[61],"any":[64,101],"estimator.":[65],"To":[66,104],"do":[67],"so,":[68],"so-called":[72],"intrinsic":[73],"Cram\u00e9r-Rao":[74,91],"bound,":[75,107],"which":[76],"exploits":[77],"geometry":[79],"parameters":[82,118],"model.":[85],"Unlike":[86],"previous":[87],"works":[88],"developing":[89],"bound":[92],"context,":[95],"our":[96,106,132,160],"solution":[97],"does":[98],"not":[99],"require":[100],"additional":[102],"hypotheses.":[103],"obtain":[105],"define":[109],"study":[111],"new":[113],"Riemannian":[114,133],"manifold":[115],"holding":[116],"interest.":[120],"An":[121],"original":[122],"error":[124],"measure":[125],"defined":[127],"with":[128],"help":[130],"distance":[134],"function.":[135],"The":[136],"corresponding":[137],"Fisher":[138,146],"information":[139,147],"matrix":[140],"then":[142],"obtained":[143],"metric":[148],"orthonormal":[150],"bases":[151],"on":[152,165],"tangent":[154],"spaces":[155],"manifold.":[158],"Finally,":[159],"results":[162],"validated":[164],"simulated":[166],"data.":[167]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
