[{"_1":2,"_3":-5,"_4":-5},"loaderData",{"_5":6,"_7":8,"_9":10},"actionData","errors","root",{"_270":271},"routes/_layout",{"_11":190},"routes/entity.$type.$id",{"_11":12,"_13":14,"_15":16,"_17":18,"_19":20,"_21":22,"_23":24,"_25":26,"_27":28},"dehydratedState",{"_74":75,"_76":77},"type","paper","id","paper_W1990805796","section","technologies","entity",{"_15":16,"_29":30,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":38,"_39":-5,"_40":41,"_42":43,"_44":45,"_46":47,"_48":-5,"_49":50,"_51":30,"_52":53,"_54":55,"_56":57,"_58":59,"_60":61,"_62":-5,"_63":64,"_65":66,"_67":68,"_69":30,"_70":-5},"canonical","https://www.hugmap.com/entity/paper/paper_W1990805796/technologies","siteBaseUrl","https://www.hugmap.com","sectionCount",2,"jsonLd","{\"@context\":\"https://schema.org\",\"@graph\":[{\"name\":\"Resolution of the wavefront set using continuous shearlets\",\"url\":\"https://www.hugmap.com/entity/paper/paper_W1990805796/technologies\",\"@type\":\"ScholarlyArticle\",\"headline\":\"Resolution of the wavefront set using continuous shearlets\",\"datePublished\":\"2008-10-24\",\"isPartOf\":{\"@type\":\"Periodical\",\"name\":\"Transactions of the American Mathematical Society\"}},{\"@type\":\"CollectionPage\",\"name\":\"Resolution of the wavefront set using continuous shearlets 相关技术\",\"description\":\"Resolution of the wavefront set using continuous shearlets 在 HugMap 中的相关技术，共 2 条，含结构化关联信息与详情链接。\",\"url\":\"https://www.hugmap.com/entity/paper/paper_W1990805796/technologies\",\"inLanguage\":\"zh-CN\"},{\"@type\":\"BreadcrumbList\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"首页\",\"item\":\"https://www.hugmap.com/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"论文\",\"item\":\"https://www.hugmap.com/search?type=paper\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Resolution of the wavefront set using continuous shearlets\",\"item\":\"https://www.hugmap.com/entity/paper/paper_W1990805796\"},{\"@type\":\"ListItem\",\"position\":4,\"name\":\"相关技术\",\"item\":\"https://www.hugmap.com/entity/paper/paper_W1990805796/technologies\"}]}]}","name","Resolution of the wavefront set using continuous shearlets","nameZh","aliases","description","descriptionZh","status","active","externalIds","{\"openalex\":\"W1990805796\",\"doi\":\"10.1090/s0002-9947-08-04700-4\"}","properties","source","openalex","createdAt","2026-05-21T11:57:55.211985457","updatedAt","2026-05-21T11:57:55.237980166","doi","10.1090/s0002-9947-08-04700-4","arxivId","openalexId","W1990805796","title","abstractText","It is known that the Continuous Wavelet Transform of a distribution f f decays rapidly near the points where f f is smooth, while it decays slowly near the irregular points. This property allows the identification of the singular support of f f . However, the Continuous Wavelet Transform is unable to describe the geometry of the set of singularities of f f and, in particular, identify the wavefront set of a distribution. In this paper, we employ the same framework of affine systems which is at the core of the construction of the wavelet transform to introduce the Continuous Shearlet Transform. This is defined by S H ψ f ( a , s , t ) = ⟨ f ψ a s t ⟩ \\mathcal {SH}_\\psi f(a,s,t) = \\langle {f}{\\psi _{ast}}\\rangle , where the analyzing elements ψ a s t \\psi _{ast} are dilated and translated copies of a single generating function ψ \\psi . The dilation matrices form a two-parameter matrix group consisting of products of parabolic scaling and shear matrices. We show that the elements { ψ a s t } \\{\\psi _{ast}\\} form a system of smooth functions at continuous scales a > 0 a>0 , locations t ∈ R 2 t \\in \\mathbb {R}^2 ","publishedDate","2008-10-24","publishedYear",2008,"venue","Transactions of the American Mathematical Society","citationCount",288,"authors","keywords",[71,72,73],"pdfUrl","https://www.ams.org/tran/2009-361-05/S0002-9947-08-04700-4/S0002-9947-08-04700-4.pdf","topVenue",false,"displayName","displayDescription","Mathematical Analysis and Transform Methods","Advanced Numerical Analysis Techniques","Image and Signal Denoising Methods","mutations",[],"queries",[78],{"_79":80,"_81":82,"_83":84,"_85":86},"dehydratedAt",1781983831585,"state",{"_88":89,"_90":91,"_92":80,"_93":-5,"_94":95,"_96":95,"_97":95,"_98":-5,"_99":-5,"_100":68,"_35":101,"_102":103},"queryKey",[87,19,14,16],"queryHash","[\"portal\",\"entity\",\"paper\",\"paper_W1990805796\"]","portal","data",{"_19":20,"_104":105,"_106":107,"_108":109,"_110":111,"_18":112,"_62":113},"dataUpdateCount",1,"dataUpdatedAt","error","errorUpdateCount",0,"errorUpdatedAt","fetchFailureCount","fetchFailureReason","fetchMeta","isInvalidated","success","fetchStatus","idle","entityType","Paper","taxonomies",[157,158,159],"events",[],"articles",[],[137,138],[114,115],{"_15":131,"_29":132,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":133,"_39":-5,"_40":41,"_42":134,"_44":135,"_121":136,"_51":-5,"_123":-5,"_124":-5,"_125":-5,"_60":-5,"_126":-5,"_127":-5,"_128":-5,"_129":-5,"_130":-5,"_69":132,"_70":-5},{"_15":116,"_29":117,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":118,"_39":-5,"_40":41,"_42":119,"_44":120,"_121":122,"_51":-5,"_123":-5,"_124":-5,"_125":-5,"_60":-5,"_126":-5,"_127":-5,"_128":-5,"_129":-5,"_130":-5,"_69":117,"_70":-5},"person_A5090767423","Gitta Kutyniok","{\"openalex\":\"A5090767423\",\"orcid\":\"0000-0001-9738-2487\"}","2026-05-14T01:36:17.260428538","2026-05-22T23:06:10.177885604","orcid","0000-0001-9738-2487","affiliation","researchArea","paperCount","homepage","linkedin","twitter","github","hindex","person_A5042165292","Demetrio Labate","{\"openalex\":\"A5042165292\",\"orcid\":\"0000-0002-9718-789X\"}","2026-05-14T13:21:56.243484857","2026-05-22T23:06:10.19154523","0000-0002-9718-789X",{"_15":153,"_29":71,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":154,"_39":-5,"_40":141,"_42":155,"_44":156,"_144":145,"_146":147,"_148":-5,"_149":150,"_151":-5,"_125":-5,"_152":-5,"_69":71,"_70":-5},{"_15":139,"_29":73,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":140,"_39":-5,"_40":141,"_42":142,"_44":143,"_144":145,"_146":147,"_148":-5,"_149":150,"_151":-5,"_125":-5,"_152":-5,"_69":73,"_70":-5},"tech_oa_T10688","{\"taxonomy_id\":\"tax_rd_T10688\"}","openalex_topics","2026-05-17T09:00:14.245350499","2026-05-17T09:00:14.245353063","techType","algorithm","domain","Physical Sciences","proposedYear","maturityLevel","growing","wikipediaUrl","patentCount","tech_oa_T11210","{\"taxonomy_id\":\"tax_rd_T11210\"}","2026-05-17T09:00:15.355267528","2026-05-17T09:00:15.355270292",{"_15":184,"_29":73,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":185,"_39":-5,"_40":41,"_42":186,"_44":187,"_164":165,"_166":-5,"_167":168,"_169":188,"_171":189,"_173":95,"_174":175,"_176":95,"_177":-5,"_69":73,"_70":-5},{"_15":178,"_29":71,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":179,"_39":-5,"_40":41,"_42":180,"_44":181,"_164":165,"_166":-5,"_167":168,"_169":182,"_171":183,"_173":95,"_174":175,"_176":95,"_177":-5,"_69":71,"_70":-5},{"_15":160,"_29":72,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":161,"_39":-5,"_40":41,"_42":162,"_44":163,"_164":165,"_166":-5,"_167":168,"_169":170,"_171":172,"_173":95,"_174":175,"_176":95,"_177":-5,"_69":72,"_70":-5},"tax_rd_T11245","{\"openalex_topic\":\"T11245\"}","2026-05-14T00:50:24.390555717","2026-05-23T12:19:53.414209612","taxonomyType","RESEARCH_DOMAIN","code","level",3,"parentId","tax_rd_2206","path","Physical Sciences/Engineering/Computational Mechanics/Advanced Numerical Analysis Techniques","sortOrder","isLeaf",true,"entityCount","children","tax_rd_T11210","{\"openalex_topic\":\"T11210\"}","2026-05-14T00:30:27.268102456","2026-05-23T12:19:53.40441387","tax_rd_2604","Physical Sciences/Mathematics/Applied Mathematics/Mathematical Analysis and Transform Methods","tax_rd_T10688","{\"openalex_topic\":\"T10688\"}","2026-05-14T00:29:43.301492204","2026-05-23T12:37:45.266960685","tax_rd_1707","Physical Sciences/Computer Science/Computer Vision and Pattern Recognition/Image and Signal Denoising Methods",{"_74":191,"_76":192},[],[193],{"_79":194,"_81":195,"_83":196,"_85":197},1781983828004,{"_88":199,"_90":91,"_92":194,"_93":-5,"_94":95,"_96":95,"_97":95,"_98":-5,"_99":-5,"_100":68,"_35":101,"_102":103},[87,198],"[\"portal\",\"industries\"]","industries",[200,201,202,203,204,205,206,207,208,209,210,211],{"_15":263,"_29":264,"_31":-5,"_32":265,"_33":266,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":215,"_42":-5,"_44":-5,"_164":216,"_166":-5,"_167":91,"_169":217,"_171":267,"_173":95,"_174":68,"_176":95,"_177":-5,"_69":264,"_70":266},{"_15":259,"_29":260,"_31":-5,"_32":-5,"_33":261,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":215,"_42":-5,"_44":-5,"_164":216,"_166":-5,"_167":91,"_169":217,"_171":262,"_173":95,"_174":68,"_176":95,"_177":-5,"_69":260,"_70":261},{"_15":253,"_29":254,"_31":-5,"_32":255,"_33":256,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":215,"_42":-5,"_44":-5,"_164":216,"_166":-5,"_167":91,"_169":217,"_171":257,"_173":95,"_174":68,"_176":95,"_177":-5,"_69":254,"_70":256},{"_15":249,"_29":250,"_31":-5,"_32":-5,"_33":251,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":215,"_42":-5,"_44":-5,"_164":216,"_166":-5,"_167":91,"_169":217,"_171":252,"_173":95,"_174":68,"_176":95,"_177":-5,"_69":250,"_70":251},{"_15":245,"_29":246,"_31":-5,"_32":-5,"_33":247,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":215,"_42":-5,"_44":-5,"_164":216,"_166":-5,"_167":91,"_169":217,"_171":248,"_173":95,"_174":68,"_176":95,"_177":-5,"_69":246,"_70":247},{"_15":239,"_29":240,"_31":-5,"_32":241,"_33":242,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":215,"_42":-5,"_44":-5,"_164":216,"_166":-5,"_167":91,"_169":217,"_171":243,"_173":95,"_174":68,"_176":95,"_177":-5,"_69":240,"_70":242},{"_15":235,"_29":236,"_31":-5,"_32":-5,"_33":237,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":215,"_42":-5,"_44":-5,"_164":216,"_166":-5,"_167":91,"_169":217,"_171":238,"_173":95,"_174":175,"_176":95,"_177":-5,"_69":236,"_70":237},{"_15":231,"_29":232,"_31":-5,"_32":-5,"_33":233,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":215,"_42":-5,"_44":-5,"_164":216,"_166":-5,"_167":91,"_169":217,"_171":234,"_173":95,"_174":68,"_176":95,"_177":-5,"_69":232,"_70":233},{"_15":227,"_29":228,"_31":-5,"_32":-5,"_33":229,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":215,"_42":-5,"_44":-5,"_164":216,"_166":-5,"_167":91,"_169":217,"_171":230,"_173":95,"_174":68,"_176":95,"_177":-5,"_69":228,"_70":229},{"_15":223,"_29":224,"_31":-5,"_32":-5,"_33":225,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":215,"_42":-5,"_44":-5,"_164":216,"_166":-5,"_167":91,"_169":217,"_171":226,"_173":95,"_174":68,"_176":95,"_177":-5,"_69":224,"_70":225},{"_15":219,"_29":220,"_31":-5,"_32":-5,"_33":221,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":215,"_42":-5,"_44":-5,"_164":216,"_166":-5,"_167":91,"_169":217,"_171":222,"_173":95,"_174":68,"_176":95,"_177":-5,"_69":220,"_70":221},{"_15":212,"_29":213,"_31":-5,"_32":-5,"_33":214,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":215,"_42":-5,"_44":-5,"_164":216,"_166":-5,"_167":91,"_169":217,"_171":218,"_173":95,"_174":68,"_176":95,"_177":-5,"_69":213,"_70":214},"tax_ind_smartphone","智能手机","Smartphone","manual","INDUSTRY","tax_ind_root","科技行业/智能手机","tax_ind_robot","机器人","Robotics","科技行业/机器人","tax_ind_wearable","智能穿戴","Smart Wearables","科技行业/智能穿戴","tax_ind_energy","新能源与智能制造","New Energy & Smart Manufacturing","科技行业/新能源与智能制造","tax_ind_biotech","生物科技","Biotech","科技行业/生物科技","tax_ind_quantum","量子计算","Quantum Computing","科技行业/量子计算","tax_ind_blockchain","区块链",[244],"Blockchain","科技行业/区块链","Web3","tax_ind_enterprise","企业软件","Enterprise Software","科技行业/企业软件","tax_ind_security","网络安全","Cybersecurity","科技行业/网络安全","tax_ind_semi","半导体",[258],"Semiconductor","科技行业/半导体","芯片","tax_ind_cloud","云计算","Cloud Computing","科技行业/云计算","tax_ind_ai","人工智能",[268,269],"Artificial Intelligence","科技行业/人工智能","AI","AI 技术","env",{"_272":24},"SITE_BASE_URL"]

Resolution of the wavefront set using continuous shearlets 论文

Resolution of the wavefront set using continuous shearlets · 相关技术

相关技术