{"id":"https://openalex.org/W2122270609","doi":"https://doi.org/10.1080/00207160801939144","title":"The regularity analysis of multivariate refinable functions from generalized Bernstein bases and application in remote sensing image compression","display_name":"The regularity analysis of multivariate refinable functions from generalized Bernstein bases and application in remote sensing image compression","publication_year":2008,"publication_date":"2008-08-13","ids":{"openalex":"https://openalex.org/W2122270609","doi":"https://doi.org/10.1080/00207160801939144","mag":"2122270609"},"language":"en","primary_location":{"id":"doi:10.1080/00207160801939144","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160801939144","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5101798003","display_name":"Xiaoyuan Yang","orcid":"https://orcid.org/0000-0002-7367-0115"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiaoyuan Yang","raw_affiliation_strings":["Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Department of Mathematics , School of Science, Beihang University , Beijing, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Department of Mathematics , School of Science, Beihang University , Beijing, People's Republic of China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100758169","display_name":"Bo Li","orcid":"https://orcid.org/0000-0001-5980-4861"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bo Li","raw_affiliation_strings":["Digital Media Laboratory , School of Computer Science and Engineering, Beihang University , Beijing, China","Digital Media Laboratory, School of Computer Science and Engineering, Beihang University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Digital Media Laboratory , School of Computer Science and Engineering, Beihang University , Beijing, China","institution_ids":["https://openalex.org/I82880672"]},{"raw_affiliation_string":"Digital Media Laboratory, School of Computer Science and Engineering, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100441858","display_name":"Xudong Zhang","orcid":"https://orcid.org/0000-0002-8341-0878"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xudong Zhang","raw_affiliation_strings":["Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Department of Mathematics , School of Science, Beihang University , Beijing, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Department of Mathematics , School of Science, Beihang University , Beijing, People's Republic of China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026257114","display_name":"Rui Yang","orcid":"https://orcid.org/0000-0002-1783-9051"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Rui Yang","raw_affiliation_strings":["Digital Media Laboratory , School of Computer Science and Engineering, Beihang University , Beijing, China","Digital Media Laboratory, School of Computer Science and Engineering, Beihang University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Digital Media Laboratory , School of Computer Science and Engineering, Beihang University , Beijing, China","institution_ids":["https://openalex.org/I82880672"]},{"raw_affiliation_string":"Digital Media Laboratory, School of Computer Science and Engineering, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5101798003"],"corresponding_institution_ids":["https://openalex.org/I82880672"],"apc_list":null,"apc_paid":null,"fwci":1.0535,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.80100531,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"87","issue":"1","first_page":"12","last_page":"37"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9994000196456909,"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":0.9994000196456909,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9970999956130981,"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/mathematics","display_name":"Mathematics","score":0.741620659828186},{"id":"https://openalex.org/keywords/biorthogonal-system","display_name":"Biorthogonal system","score":0.6958368420600891},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.5103568434715271},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5092505216598511},{"id":"https://openalex.org/keywords/compression","display_name":"Compression (physics)","score":0.49864721298217773},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.49473831057548523},{"id":"https://openalex.org/keywords/image-compression","display_name":"Image compression","score":0.47040778398513794},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.45294803380966187},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4528244435787201},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.4440997242927551},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.44390904903411865},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4401160478591919},{"id":"https://openalex.org/keywords/invariant-subspace","display_name":"Invariant subspace","score":0.4307985305786133},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42878854274749756},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.3837319612503052},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3210480809211731},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2773894667625427},{"id":"https://openalex.org/keywords/image-processing","display_name":"Image processing","score":0.19019174575805664},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17823132872581482},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.162156879901886},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.10277193784713745},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.10186988115310669},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10127848386764526}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.741620659828186},{"id":"https://openalex.org/C158453530","wikidata":"https://www.wikidata.org/wiki/Q864692","display_name":"Biorthogonal system","level":4,"score":0.6958368420600891},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.5103568434715271},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5092505216598511},{"id":"https://openalex.org/C180016635","wikidata":"https://www.wikidata.org/wiki/Q2712821","display_name":"Compression (physics)","level":2,"score":0.49864721298217773},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.49473831057548523},{"id":"https://openalex.org/C13481523","wikidata":"https://www.wikidata.org/wiki/Q412438","display_name":"Image compression","level":4,"score":0.47040778398513794},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.45294803380966187},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4528244435787201},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.4440997242927551},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.44390904903411865},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4401160478591919},{"id":"https://openalex.org/C2777059694","wikidata":"https://www.wikidata.org/wiki/Q2706744","display_name":"Invariant subspace","level":3,"score":0.4307985305786133},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42878854274749756},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.3837319612503052},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3210480809211731},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2773894667625427},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.19019174575805664},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17823132872581482},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.162156879901886},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.10277193784713745},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.10186988115310669},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10127848386764526},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160801939144","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160801939144","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334924","display_name":"Program for New Century Excellent Talents in University","ror":"https://ror.org/01mv9t934"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W76406933","https://openalex.org/W1492914911","https://openalex.org/W1517916370","https://openalex.org/W1592007248","https://openalex.org/W1774981766","https://openalex.org/W1984093439","https://openalex.org/W1995113957","https://openalex.org/W2048247182","https://openalex.org/W2062024414","https://openalex.org/W2066717565","https://openalex.org/W2072307436","https://openalex.org/W2076044146","https://openalex.org/W2081925616","https://openalex.org/W2087166809","https://openalex.org/W2090055402","https://openalex.org/W2097566357","https://openalex.org/W2097938951","https://openalex.org/W2146378993","https://openalex.org/W3005363104","https://openalex.org/W3029645440","https://openalex.org/W4241868268","https://openalex.org/W4244739844","https://openalex.org/W4255272544"],"related_works":["https://openalex.org/W4235906205","https://openalex.org/W1970434788","https://openalex.org/W1968891974","https://openalex.org/W4301478900","https://openalex.org/W2348707928","https://openalex.org/W102084567","https://openalex.org/W2973283381","https://openalex.org/W2333831800","https://openalex.org/W2948021207","https://openalex.org/W2118409924"],"abstract_inverted_index":{"In":[0],"this":[1,74],"paper,":[2],"we":[3],"investigate":[4],"the":[5,20,24,48,57,67,70,86,89,93],"smoothness":[6],"properties":[7],"of":[8,19,23,56,59,69,88],"multivariate":[9],"refinable":[10],"functions":[11,44],"based":[12],"on":[13],"generalized":[14],"Bernstein":[15],"bases":[16],"in":[17,73],"terms":[18],"spectral":[21],"radius":[22],"corresponding":[25],"transition":[26],"operator":[27],"restricted":[28],"to":[29,40,76],"a":[30,37,53],"suitable":[31],"finite-dimensional":[32],"invariant":[33],"subspace,":[34],"and":[35,46,85],"present":[36],"general":[38],"algorithm":[39],"construct":[41],"biorthogonal":[42],"scaling":[43],"\u03c6":[45],"with":[47,61],"largest":[49],"possible":[50],"regularity.":[51],"Moreover,":[52],"new":[54],"family":[55],"parameterization":[58],"filters":[60],"symmetry":[62],"are":[63],"constructed.":[64],"We":[65],"explore":[66],"applicability":[68],"transforms":[71],"presented":[72],"paper":[75],"remote":[77],"sensing":[78],"image":[79],"compression":[80,83],"at":[81],"high":[82],"rates,":[84],"results":[87],"experiments":[90],"show":[91],"that":[92],"performance":[94],"is":[95],"outstanding.":[96]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}