{"id":"https://openalex.org/W4214704409","doi":"https://doi.org/10.1109/tit.2022.3152734","title":"Statistically Optimal Estimation of Signals in Modulation Spaces Using Gabor Frames","display_name":"Statistically Optimal Estimation of Signals in Modulation Spaces Using Gabor Frames","publication_year":2022,"publication_date":"2022-02-25","ids":{"openalex":"https://openalex.org/W4214704409","doi":"https://doi.org/10.1109/tit.2022.3152734"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2022.3152734","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3152734","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Transactions on Information Theory","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/A5047150999","display_name":"Stephan Dahlke","orcid":"https://orcid.org/0000-0003-0168-7257"},"institutions":[{"id":"https://openalex.org/I161103922","display_name":"Philipps University of Marburg","ror":"https://ror.org/01rdrb571","country_code":"DE","type":"education","lineage":["https://openalex.org/I161103922"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Stephan Dahlke","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, Philipps-Universit&#x00E4;t Marburg, Marburg, Germany"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Philipps-Universit&#x00E4;t Marburg, Marburg, Germany","institution_ids":["https://openalex.org/I161103922"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064993952","display_name":"Sven Heuer","orcid":null},"institutions":[{"id":"https://openalex.org/I161103922","display_name":"Philipps University of Marburg","ror":"https://ror.org/01rdrb571","country_code":"DE","type":"education","lineage":["https://openalex.org/I161103922"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Sven Heuer","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, Philipps-Universit&#x00E4;t Marburg, Marburg, Germany"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Philipps-Universit&#x00E4;t Marburg, Marburg, Germany","institution_ids":["https://openalex.org/I161103922"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024834862","display_name":"Hajo Holzmann","orcid":"https://orcid.org/0000-0003-4931-0061"},"institutions":[{"id":"https://openalex.org/I161103922","display_name":"Philipps University of Marburg","ror":"https://ror.org/01rdrb571","country_code":"DE","type":"education","lineage":["https://openalex.org/I161103922"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Hajo Holzmann","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, Philipps-Universit&#x00E4;t Marburg, Marburg, Germany"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Philipps-Universit&#x00E4;t Marburg, Marburg, Germany","institution_ids":["https://openalex.org/I161103922"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012377775","display_name":"Pavel Tafo","orcid":null},"institutions":[{"id":"https://openalex.org/I161103922","display_name":"Philipps University of Marburg","ror":"https://ror.org/01rdrb571","country_code":"DE","type":"education","lineage":["https://openalex.org/I161103922"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Pavel Tafo","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, Philipps-Universit&#x00E4;t Marburg, Marburg, Germany"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Philipps-Universit&#x00E4;t Marburg, Marburg, Germany","institution_ids":["https://openalex.org/I161103922"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5047150999"],"corresponding_institution_ids":["https://openalex.org/I161103922"],"apc_list":null,"apc_paid":null,"fwci":0.2042,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.45103183,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"68","issue":"6","first_page":"4182","last_page":"4200"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9993000030517578,"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":0.9993000030517578,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9955999851226807,"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/T11698","display_name":"Underwater Acoustics Research","score":0.9898999929428101,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/thresholding","display_name":"Thresholding","score":0.6907962560653687},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6858344078063965},{"id":"https://openalex.org/keywords/gabor-transform","display_name":"Gabor transform","score":0.6834890246391296},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6472955942153931},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.6470251679420471},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.5407888889312744},{"id":"https://openalex.org/keywords/time\u2013frequency-analysis","display_name":"Time\u2013frequency analysis","score":0.5351262092590332},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5272613763809204},{"id":"https://openalex.org/keywords/fourier-series","display_name":"Fourier series","score":0.4602230191230774},{"id":"https://openalex.org/keywords/modulation","display_name":"Modulation (music)","score":0.4478411078453064},{"id":"https://openalex.org/keywords/frequency-modulation","display_name":"Frequency modulation","score":0.43215256929397583},{"id":"https://openalex.org/keywords/frame","display_name":"Frame (networking)","score":0.41121572256088257},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28507429361343384},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2727000415325165},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24681887030601501},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.17774298787117004},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.17224255204200745},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.16564199328422546},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.09359461069107056}],"concepts":[{"id":"https://openalex.org/C191178318","wikidata":"https://www.wikidata.org/wiki/Q2256906","display_name":"Thresholding","level":3,"score":0.6907962560653687},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6858344078063965},{"id":"https://openalex.org/C173149727","wikidata":"https://www.wikidata.org/wiki/Q996397","display_name":"Gabor transform","level":4,"score":0.6834890246391296},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6472955942153931},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.6470251679420471},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.5407888889312744},{"id":"https://openalex.org/C142433447","wikidata":"https://www.wikidata.org/wiki/Q7806653","display_name":"Time\u2013frequency analysis","level":3,"score":0.5351262092590332},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5272613763809204},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.4602230191230774},{"id":"https://openalex.org/C123079801","wikidata":"https://www.wikidata.org/wiki/Q750240","display_name":"Modulation (music)","level":2,"score":0.4478411078453064},{"id":"https://openalex.org/C11930861","wikidata":"https://www.wikidata.org/wiki/Q181417","display_name":"Frequency modulation","level":3,"score":0.43215256929397583},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.41121572256088257},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28507429361343384},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2727000415325165},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24681887030601501},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.17774298787117004},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.17224255204200745},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.16564199328422546},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.09359461069107056},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"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/C107038049","wikidata":"https://www.wikidata.org/wiki/Q35986","display_name":"Aesthetics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2022.3152734","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3152734","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Transactions on Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1481424961","https://openalex.org/W1502503665","https://openalex.org/W1511694993","https://openalex.org/W1570089119","https://openalex.org/W1605417594","https://openalex.org/W1723773034","https://openalex.org/W1964809923","https://openalex.org/W1970684339","https://openalex.org/W1998630480","https://openalex.org/W2018289562","https://openalex.org/W2032013306","https://openalex.org/W2042619744","https://openalex.org/W2074148972","https://openalex.org/W2075769032","https://openalex.org/W2079724595","https://openalex.org/W2080023718","https://openalex.org/W2108472799","https://openalex.org/W2115388399","https://openalex.org/W2115706991","https://openalex.org/W2115755118","https://openalex.org/W2126057043","https://openalex.org/W2134651899","https://openalex.org/W2143600836","https://openalex.org/W2149745547","https://openalex.org/W2158252006","https://openalex.org/W2911341523","https://openalex.org/W4214806317","https://openalex.org/W4242704675","https://openalex.org/W6637576844","https://openalex.org/W6906705981"],"related_works":["https://openalex.org/W2390244057","https://openalex.org/W2606578966","https://openalex.org/W2360182727","https://openalex.org/W1905998934","https://openalex.org/W2384007269","https://openalex.org/W2025656090","https://openalex.org/W4206389873","https://openalex.org/W2374277333","https://openalex.org/W1922252152","https://openalex.org/W1590865552"],"abstract_inverted_index":{"Time-frequency":[0],"analysis":[1],"deals":[2],"with":[3],"signals":[4,47],"for":[5],"which":[6,22,51,101],"the":[7,18,24,60,79,89,92,96,117,126,137],"underlying":[8],"spectral":[9],"characteristics":[10],"change":[11],"over":[12],"time.":[13],"The":[14,64,81],"essential":[15],"tool":[16],"is":[17],"short-time":[19,61],"Fourier":[20,25,62],"transform,":[21],"localizes":[23],"transform":[26],"in":[27,48,54,105,108,142],"time":[28,106],"by":[29,71,145],"means":[30,72],"of":[31,46,56,59,73,91,98,120,139],"a":[32,36],"window":[33],"function.":[34],"In":[35],"white":[37],"noise":[38],"model,":[39],"we":[40],"derive":[41],"rate-optimal":[42],"and":[43,76,88,107,111,136],"adaptive":[44],"estimators":[45,65],"modulation":[49,143],"spaces,":[50],"measure":[52],"smoothness":[53],"terms":[55],"decay":[57],"properties":[58],"transform.":[63],"are":[66],"based":[67],"on":[68,77],"series":[69],"expansions":[70],"Gabor":[74,146],"frames":[75],"thresholding":[78],"coefficients.":[80],"minimax":[82],"rates":[83],"have":[84],"interesting":[85],"new":[86],"features,":[87],"derivation":[90],"lower":[93],"bounds":[94],"requires":[95],"use":[97],"test":[99],"functions":[100],"approximately":[102],"localize":[103],"both":[104],"frequency.":[109],"Simulations":[110],"applications":[112],"to":[113],"audio":[114],"recordings":[115],"illustrate":[116],"practical":[118],"relevance":[119],"our":[121],"methods.":[122],"We":[123],"also":[124],"discuss":[125],"best":[127],"<inline-formula":[128],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[129],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[130],"<tex-math":[131],"notation=\"LaTeX\">$N$":[132],"</tex-math></inline-formula>":[133],"-term":[134],"approximation":[135,138],"variational":[140],"problems":[141],"spaces":[144],"frame":[147],"expansions.":[148]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2026-03-05T09:29:38.588285","created_date":"2025-10-10T00:00:00"}
