{"id":"https://openalex.org/W29582437","doi":null,"title":"Micrological analysis, smooth frames and denoising in Fourier space","display_name":"Micrological analysis, smooth frames and denoising in Fourier space","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W29582437","mag":"29582437"},"language":"en","primary_location":{"id":"mag:29582437","doi":null,"is_oa":false,"landing_page_url":"http://www.osaka-kyoiku.ac.jp/~ashino/pdf/aisl.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306463674","display_name":"Nova Science Publishers eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310320144","host_organization_name":"Nova Publishers","host_organization_lineage":["https://openalex.org/P4310320144"],"host_organization_lineage_names":["Nova Publishers"],"type":"ebook platform"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"Nova Science Publishers, Inc. eBooks","raw_type":null},"volume":null,"type":"book","indexed_in":[],"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/A5085378838","display_name":"Ryuichi Ashino","orcid":"https://orcid.org/0000-0003-4807-4300","observed_orcids":["https://orcid.org/0000-0003-4807-4300"]},"institutions":[{"id":"https://openalex.org/I141479679","display_name":"Osaka Kyoiku University","ror":"https://ror.org/051j8zv27","country_code":"JP","type":"education","lineage":["https://openalex.org/I141479679"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Ryuichi Ashino","raw_affiliation_strings":["Mathematical Sciences, Osaka Kyoiku University, Kashiwara, Osaka 582-8582, Japan"],"raw_orcid":"https://orcid.org/0000-0003-4807-4300","affiliations":[{"raw_affiliation_string":"Mathematical Sciences, Osaka Kyoiku University, Kashiwara, Osaka 582-8582, Japan","institution_ids":["https://openalex.org/I141479679"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078733297","display_name":"Steven J. Desjardins","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I153718931","display_name":"University of Ottawa","ror":"https://ror.org/03c4mmv16","country_code":"CA","type":"education","lineage":["https://openalex.org/I153718931"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Steven J. Desjardins","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, Canada KIN 6N5"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, Canada KIN 6N5","institution_ids":["https://openalex.org/I153718931"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029430004","display_name":"Christopher Heil","orcid":"https://orcid.org/0000-0003-2873-3436","observed_orcids":["https://orcid.org/0000-0003-2873-3436"]},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Christopher Heil","raw_affiliation_strings":["School of Mathematics, Georgia Institute of Technology Atlanta Georgia"],"raw_orcid":"https://orcid.org/0000-0003-2873-3436","affiliations":[{"raw_affiliation_string":"School of Mathematics, Georgia Institute of Technology Atlanta Georgia","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110352129","display_name":"Michihiro Nagase","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I98285908","display_name":"The University of Osaka","ror":"https://ror.org/035t8zc32","country_code":"JP","type":"education","lineage":["https://openalex.org/I98285908"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Michihiro Nagase","raw_affiliation_strings":["Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, 560-0043, Japan#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, 560-0043, Japan#TAB#","institution_ids":["https://openalex.org/I98285908"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109371455","display_name":"R\u00e9mi Vaillancourt","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I153718931","display_name":"University of Ottawa","ror":"https://ror.org/03c4mmv16","country_code":"CA","type":"education","lineage":["https://openalex.org/I153718931"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"R\u00e9mi Vaillancourt","raw_affiliation_strings":["Department of Mathematics and Statistics University of Ottawa, Ottawa, ON, Canada K1N 6N5"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics University of Ottawa, Ottawa, ON, Canada K1N 6N5","institution_ids":["https://openalex.org/I153718931"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1315,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.73493976,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"153","last_page":"160"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9589999914169312,"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":0.9589999914169312,"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":0.0406000018119812,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.0,"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/microlocal-analysis","display_name":"microlocal analysis","score":0.9549999833106995},{"id":"https://openalex.org/keywords/multiwavelets","display_name":"multiwavelets","score":0.8220000267028809},{"id":"https://openalex.org/keywords/wavelet-coefficients","display_name":"wavelet coefficients","score":0.6830000281333923},{"id":"https://openalex.org/keywords/image-denoising","display_name":"image denoising","score":0.9039999842643738},{"id":"https://openalex.org/keywords/pseudodifferential-operators","display_name":"pseudodifferential operators","score":0.9769999980926514},{"id":"https://openalex.org/keywords/fourier-space","display_name":"Fourier space","score":0.9179999828338623}],"concepts":[{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.8002793788909912},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.6515544652938843},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6074855923652649},{"id":"https://openalex.org/C129683796","wikidata":"https://www.wikidata.org/wiki/Q430450","display_name":"Microlocal analysis","level":4,"score":0.5309820771217346},{"id":"https://openalex.org/C163294075","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Noise reduction","level":2,"score":0.5270749926567078},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5221484303474426},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4861838221549988},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.47838130593299866},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.47124582529067993},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.4347582161426544},{"id":"https://openalex.org/C2983327147","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Image denoising","level":3,"score":0.4181731343269348},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.23095008730888367},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21680444478988647},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.20663344860076904},{"id":"https://openalex.org/C191832335","wikidata":"https://www.wikidata.org/wiki/Q4262191","display_name":"Fourier integral operator","level":3,"score":0.13974499702453613},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10542482137680054},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"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/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:29582437","doi":null,"is_oa":false,"landing_page_url":"http://www.osaka-kyoiku.ac.jp/~ashino/pdf/aisl.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306463674","display_name":"Nova Science Publishers eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310320144","host_organization_name":"Nova Publishers","host_organization_lineage":["https://openalex.org/P4310320144"],"host_organization_lineage_names":["Nova Publishers"],"type":"ebook platform"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"Nova Science Publishers, Inc. eBooks","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W11563317","https://openalex.org/W58621250","https://openalex.org/W1575723423","https://openalex.org/W1966732334","https://openalex.org/W2014933473","https://openalex.org/W2057326186","https://openalex.org/W2062024414","https://openalex.org/W2087377426","https://openalex.org/W2126777570","https://openalex.org/W2146052399"],"related_works":["https://openalex.org/W7095253298","https://openalex.org/W7096378011","https://openalex.org/W11563317","https://openalex.org/W2119217393","https://openalex.org/W7099245392","https://openalex.org/W2057326186","https://openalex.org/W2128641296","https://openalex.org/W2324595411","https://openalex.org/W6925836710","https://openalex.org/W7101165171"],"abstract_inverted_index":{"Microlocal":[0],"filtering":[1],"is":[2,40,50],"performed":[3],"with":[4],"adapted":[5],"orthonormal":[6],"multiwavelets":[7,11],"and":[8],"smooth":[9],"frame":[10],"in":[12],"Rn.":[13],"The":[14],"values":[15],"of":[16,20,27,38,45,53],"the":[17,43,51],"wavelet":[18],"coefficients":[19],"a":[21,24,46],"function":[22],"give":[23],"rough":[25],"estimate":[26],"its":[28],"microlocal":[29],"content,":[30],"as":[31,42],"shown":[32],"by":[33],"an":[34],"example.":[35],"Multidirectional":[36],"denoising":[37],"images":[39],"presented":[41],"action":[44],"pseudodifferential":[47],"operator":[48],"which":[49],"product":[52],"directional":[54],"diffusion":[55],"equations.":[56]},"counts_by_year":[],"updated_date":"2026-10-31T12:09:11.096373","created_date":"2016-06-24T00:00:00"}
