【数学与统计及交叉学科前沿论坛------高端学术讲座第160场】
报告题目：Quaternionic Signal Processing: Generalized Sampling, Quaternion difference equations and Image Encryption
报 告 人：高洁欣(Kit Ian KOU) 澳门大学教授
报告时间：7月10日周四10：30-11：30
报告地点: 阜成路西校区教二楼302
报告摘要: Abstract: Quaternions, a four-dimensional extension of complex numbers, offer a powerful framework for signal processing by efficiently capturing multidimensional data relationships. This presentation explores three key aspects of quaternionic signal processing: (1) generalized sampling techniques for quaternion-valued signals, enabling efficient reconstruction from non-uniform samples; (2) stability and solution methods for quaternion difference equations, which model dynamic systems in hypercomplex domains; and (3) novel image encryption algorithms leveraging quaternion transformations for enhanced security. By unifying these topics, we demonstrate how quaternions address limitations of traditional real- and complex-valued methods, particularly in preserving phase and orientation information. Theoretical analyses are supported by numerical simulations, including applications to color image encryption, where quaternion-based schemes outperform scalar approaches in robustness and key sensitivity. Our results highlight the versatility of quaternions in modern signal processing, with implications for communications, biomedical imaging, and multimedia security.
报告人简介：高洁欣(Kit Ian KOU) 现任澳门大学教授，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）
