报告题目：Riesz transform associated with the fractional Fourier transform and applications in image edge detection

主讲人：傅尊伟

单位：临沂大学

时间：12月3日14:00

腾讯会议：522-550-617

密码：254631

摘要：The fractional Hilbert transform was introduced by Zayed [30, Zayed, 1998] and has been widely used in signal processing.  In view of is connection with the fractional Fourier transform, Chen, the first, second and fourth authors of this paper in [6, Chen et al., 2021] studied the fractional Hilbert transform and other fractional multiplier operators on the real line. The present paper is concerned with a natural extension of the fractional Hilbert transform to higher dimensions: this extension is the fractional Riesz transform which is defined by multiplication which a suitable chirp function on the fractional Fourier transform side. In addition to a thorough study of the fractional Riesz transforms, in this work we also investigate the boundedness of singular integral operators with chirp functions on rotation invariant spaces, chirp Hardy spaces and their relation to chirp BMO spaces, as well as applications of the theory of fractional multipliers in partial differential equations. Through numerical simulation, we provide physical and geometric interpretations of high-dimensional fractional multipliers. Finally, we present an application of the fractional Riesz transforms in edge detection which verifies a hypothesis insinuated in [26, Xu et al., 2016]. In fact our numerical implementation confirms that amplitude, phase, and direction information can be simultaneously extracted by controlling the order of the fractional Riesz transform. This is joint work with Prof. Grafakos, Prof. Lin, Prof. Wu and Dr. Yang.

简介：傅尊伟，博士、教授，中韩大数据与人工智能研究中心主任；临沂大学英国威廉希尔公司经理；水原大学博士生导师；山东师范大学博士生导师。山东省特级教师工作坊主持人，山东省大数据专业建设委员会副主任委员。山东省“应用数学”重点学科首席专家。山东省“五一劳动奖章”获得者、全省教育先进工作者；香港“求是”研究生奖学金获得者；全国优秀教师。在《IEEETrans》系列、《ACHA》、《JDE》和《中国科学》等学术杂志上发表论文100余篇。获得山东省高校优秀科研成果奖一等奖1项、山东省公司产品成果奖一等奖2项。先后主持国家自然科学基金5项。国家一流专业建设点负责人、数学一级学科硕士点带头人、国家一流课程《数学分析》主讲教师。IEEE会员，美国《数学评论》评论员，中国高等教育学会教育数学专委会常务理事。曾应邀在英国剑桥大学举行的“第二届世界青年数学家大会”上做45分钟学术报告。