Generalized Convolution Theorems for Quaternion Linear Canonical Transforms and Their Applications
高洁欣
（澳门大学）
报告时间：14：00-15：00，2025-06-19（星期四）
报告地点：沙河校区E806
内容简介：The Quaternion Linear Canonical Transform (QLCT) is a powerful mathematical tool that extends the classical Linear Canonical Transform (LCT) to quaternion-valued signals, offering enhanced capabilities in analyzing non-commutative and multi-dimensional data. This paper explores key applications of the QLCT in signal processing, image analysis, and optical systems, where its ability to capture joint time-frequency and space-frequency properties is particularly advantageous. A central focus is the development of convolution theorems for the QLCT, which generalize classical results to the quaternionic domain, enabling efficient filtering and modulation techniques. Additionally, we investigate the Quaternion Analytic Signal (QAS) and its interplay with the QLCT, establishing novel convolution and correlation theorems that facilitate the analysis of instantaneous amplitude, phase, and orientation in hypercomplex signals. These theoretical advances are supported by illustrative examples, demonstrating their utility in applications such as color image processing, 3D signal analysis, and optical engineering. The results highlight the QLCT’s versatility and its potential to address challenges in multi-channel and non-stationary signal analysis.
报告人简介：高洁欣教授现任澳门大学副教授，在高维信号分析领域拥有20多年的研究经验，主要研究方向包括四元数、傅里叶变换和张量分析在高维信号处理中的应用。她主持或参与了27项科研项目，获得澳门科技发展基金、国家自然科学基金及广东省科技厅等机构的资助，并发表了130余篇学术论文。其研究成果《四元数和线性正则分析在彩色人脸识别与边缘检测中的应用》曾荣获2018年澳门科学技术奖（自然科学奖）三等奖。
高教授长期担任多个国际期刊的特邀编辑和审稿人，目前还担任英国剑桥大学Clare Hall终身会员、应用数学研究中心成员，以及澳门核医学分子影像学会外务理事等职务。（更多信息请访问：http://www.fst.umac.mo/en/staff/fstkik.html）
邀请人：崔春风、夏勇
