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【40周年校庆学术活动】荔园学者Colloquium第三十二期:Directional Tensor Product Complex Tight Framelets and Directional Multivariate Quasi-tight Framelets

时间:2023-06-19 10:27

主讲人 讲座时间
讲座地点 实际会议时间日
实际会议时间年月

bat365官网登录入口四十周年校庆暨数学学科四十周年庆

荔园学者Colloquium第三十二


讲座题目:Directional Tensor Product Complex Tight Framelets and Directional Multivariate Quasi-tight Framelets

主讲人:韩斌  教授 University of Alberta)

讲座时间:2023年6月191630-1730

讲座地点:bat365官网登录入口粤海校区汇星楼一楼三号教室

内容概述:

Directional representation systems are required to effectively capture edge singularities for many high-dimensional problems. In this talk, we first discuss directional tensor product complex tight framelets and their applications to image/video processing. However, constructing compactly supported multivariate tight framelets is known to be a challenging problem because it is linked to sum of squares and factorization of multivariate Laurent polynomials in algebraic geometry. To circumvent this difficulty, next we introduce the notion of quasi-tight framelets, which behaves almost identical to a tight framelet. From an arbitrary compactly supported multivariate refinable function (such as refinable box splines) with a general dilation matrix, we constructively prove that we can always derive a directional compactly supported quasi-tight framelet with vanishing moments. The key ingredient in constructing multivariate quasi-tight framelets is the generalized matrix spectral factorization of multivariate polynomials. This talk is based on several joint works with Chenzhe Diao, Ran Lu, Qun Mo, Yi Shen, Zhenpeng Zhao and Xiaosheng Zhuang.

主讲人简介:  韩斌教授,加拿大阿尔伯塔大学(University of Alberta)。1998年获加拿大阿尔伯塔大学理学博士学位,2007年晋升为加拿大阿尔伯塔大学数学系终身教授,担任加拿大阿尔伯塔大学应用数学系主任,2007年获得Alexander von Humboldt研究奖学金。其研究领域主要包括:应用与计算哈密顿分析,小波分析,小波方法在计算机图形学、信号处理、图像处理、数值计算中的应用。曾作为Ingrid Daubechies教授的博士后在普林斯顿大学访问,以Alexander von Humboldt research fellowship身份与Wolfgang Dahmen教授(Leibniz奖获得者)开展合作研究,发表了学术论文112余篇和专著1部,担任JAMS、Adv Math、SIAM等期刊的审稿人。先后主持加拿大国家自然科学基金3项,加拿大PIMS基金1项,加拿大MITACS基金1项。荣居近10年来世界上前170位数学家之列,并在小波、逼近论、应用与计算哈密顿分析方面的多个国际会议上做报告。


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                                             数学与统计学院

2023年06月19




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