{"id":"https://openalex.org/W3021895078","doi":"https://doi.org/10.1137/20m1335315","title":"M$^2$ Spectral Estimation: A Flexible Approach Ensuring Rational Solutions","display_name":"M$^2$ Spectral Estimation: A Flexible Approach Ensuring Rational Solutions","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3021895078","doi":"https://doi.org/10.1137/20m1335315","mag":"3021895078"},"language":"en","primary_location":{"id":"doi:10.1137/20m1335315","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1335315","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2004.14778","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035375604","display_name":"Bin Zhu","orcid":"https://orcid.org/0000-0003-2297-0828"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bin Zhu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005905901","display_name":"Augusto Ferrante","orcid":"https://orcid.org/0000-0002-9001-8962"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Augusto Ferrante","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065730184","display_name":"Johan Karlsson","orcid":"https://orcid.org/0000-0001-5158-9255"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Johan Karlsson","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5088792059","display_name":"Mattia Zorzi","orcid":"https://orcid.org/0000-0002-5581-5210"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mattia Zorzi","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-5581-5210","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00386184,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"59","issue":"4","first_page":"2977","last_page":"2996"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9983999729156494,"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"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/divergence","display_name":"Divergence (linguistics)","score":0.6629543900489807},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5889454483985901},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.5687674283981323},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.551977276802063},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.502638578414917},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.483549565076828},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.45896056294441223},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.45371636748313904},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.44352322816848755},{"id":"https://openalex.org/keywords/spectral-density-estimation","display_name":"Spectral density estimation","score":0.43716636300086975},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.43234097957611084},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4274665117263794},{"id":"https://openalex.org/keywords/trigonometric-functions","display_name":"Trigonometric functions","score":0.41647815704345703},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.41303592920303345},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.32226496934890747},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2140330970287323},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.16417330503463745}],"concepts":[{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.6629543900489807},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5889454483985901},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.5687674283981323},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.551977276802063},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.502638578414917},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.483549565076828},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.45896056294441223},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.45371636748313904},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.44352322816848755},{"id":"https://openalex.org/C30049272","wikidata":"https://www.wikidata.org/wiki/Q6555326","display_name":"Spectral density estimation","level":3,"score":0.43716636300086975},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.43234097957611084},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4274665117263794},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.41647815704345703},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.41303592920303345},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.32226496934890747},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2140330970287323},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.16417330503463745},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/20m1335315","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1335315","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2004.14778","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2004.14778","pdf_url":"https://arxiv.org/pdf/2004.14778","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"mag:3021895078","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2004.14778v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2004.14778","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2004.14778","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2004.14778","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2004.14778","pdf_url":"https://arxiv.org/pdf/2004.14778","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4474495461","display_name":null,"funder_award_id":"ZORZ SID19 01","funder_id":"https://openalex.org/F4320321966","funder_display_name":"Universit\u00e0 degli Studi di Padova"}],"funders":[{"id":"https://openalex.org/F4320321160","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71"},{"id":"https://openalex.org/F4320321966","display_name":"Universit\u00e0 degli Studi di Padova","ror":"https://ror.org/00240q980"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W622930292","https://openalex.org/W1456532987","https://openalex.org/W1511099976","https://openalex.org/W1594563152","https://openalex.org/W1622369672","https://openalex.org/W1685862830","https://openalex.org/W1867429253","https://openalex.org/W1927802821","https://openalex.org/W1968741713","https://openalex.org/W1976033737","https://openalex.org/W1991286145","https://openalex.org/W1993964048","https://openalex.org/W1995213069","https://openalex.org/W1998895316","https://openalex.org/W2004987046","https://openalex.org/W2006115473","https://openalex.org/W2017754977","https://openalex.org/W2031149397","https://openalex.org/W2102762459","https://openalex.org/W2103637013","https://openalex.org/W2105139914","https://openalex.org/W2125327144","https://openalex.org/W2133186968","https://openalex.org/W2143689730","https://openalex.org/W2151042543","https://openalex.org/W2159520972","https://openalex.org/W2168088676","https://openalex.org/W2170060163","https://openalex.org/W2290929774","https://openalex.org/W2330766129","https://openalex.org/W2611901612","https://openalex.org/W2759246745","https://openalex.org/W2767923613","https://openalex.org/W2946806501","https://openalex.org/W3011908428","https://openalex.org/W3037028994","https://openalex.org/W3100152849","https://openalex.org/W3102134837","https://openalex.org/W3106352524","https://openalex.org/W3116511422","https://openalex.org/W3120465847"],"related_works":["https://openalex.org/W3106352524","https://openalex.org/W2519414928","https://openalex.org/W2909756873","https://openalex.org/W2102719812","https://openalex.org/W1867429253","https://openalex.org/W2754707236","https://openalex.org/W2766340440","https://openalex.org/W3081343354","https://openalex.org/W2570255130","https://openalex.org/W2956759947","https://openalex.org/W2411869579","https://openalex.org/W2079546778","https://openalex.org/W3106354228","https://openalex.org/W2769660485","https://openalex.org/W2952727528","https://openalex.org/W2078857903","https://openalex.org/W3120198147","https://openalex.org/W2511693576","https://openalex.org/W194251728","https://openalex.org/W2765240685"],"abstract_inverted_index":{"This":[0,54],"paper":[1],"concerns":[2],"a":[3,14,26,34,107,118,140,148,156],"spectral":[4,149],"estimation":[5],"problem":[6,21,46,56],"for":[7,33],"multivariate":[8],"(i.e.,":[9],"vector-valued)":[10],"signals":[11],"defined":[12],"on":[13,106],"multidimensional":[15],"domain,":[16],"abbreviated":[17],"as":[18,24,42,78,159],"M$^2$.":[19],"The":[20],"is":[22,39,139,147],"posed":[23],"solving":[25],"finite":[27],"number":[28],"of":[29,50,101,121,132],"trigonometric":[30],"moment":[31],"equations":[32],"nonnegative":[35],"matricial":[36],"measure,":[37],"which":[38,151],"well":[40],"known":[41],"the":[43,48,66,97,102,114,130,133,136,145],"covariance":[44],"extension":[45],"in":[47,65,74,161],"literature":[49],"systems":[51],"and":[52,57,70,80,84,104],"control.":[53],"inverse":[55],"its":[58],"various":[59],"generalizations":[60],"have":[61],"been":[62],"extensively":[63],"studied":[64],"past":[67],"three":[68],"decades,":[69],"they":[71],"find":[72],"applications":[73],"diverse":[75],"fields":[76],"such":[77],"modeling":[79],"system":[81],"identification,":[82],"signal":[83],"image":[85],"processing,":[86],"robust":[87],"control,":[88],"circuit":[89],"theory,":[90],"etc.":[91],"In":[92],"this":[93,122],"paper,":[94],"we":[95,124],"address":[96],"challenging":[98],"M$^2$":[99],"version":[100],"problem,":[103],"elaborate":[105],"solution":[108,146],"technique":[109],"via":[110],"convex":[111],"optimization":[112],"with":[113],"$\\tau$-divergence":[115],"family.":[116],"As":[117],"major":[119],"contribution":[120],"work,":[123],"show":[125],"that":[126,143],"by":[127,155],"properly":[128],"choosing":[129],"parameter":[131],"divergence":[134],"index,":[135],"optimal":[137],"spectrum":[138],"rational":[141],"function,":[142],"is,":[144],"density":[150],"can":[152],"be":[153],"represented":[154],"finite-dimensional":[157],"system,":[158],"desired":[160],"many":[162],"practical":[163],"applications.":[164]},"counts_by_year":[],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
