工程科学学院名师讲坛第十一期

报告题目：统计信号处理与应用——从欧基里德到黎曼

Statistical Signal Processing – from Euclid to Riemann

时 间：2015年10月29日16:00-18:00
地 点：武汉光电国家实验室A101
报告人：Prof.Kon Max Wong, McMaster University, Canada 加拿大麦克马斯特大学

邀请人：Prof. Li Xun 李洵教授

报告人简介：

Kon Max Wong (黄干), 加拿大皇家科学院院士，加拿大工程院院士，IEEE终身院士，英国电气工程师学院院士，英国皇家统计学会会士，英国物理学会会士。黄教授于1969年，毕业于英国伦敦大学，获电气工程学士学位，从而就职于英国Plessey通讯研究公司。1970年重返伦敦大学帝国理工学院从事研究生学习和研究，获哲学博士学位。继又重进 Plessey公司，任研发工程师，从事数字信号处理与信号传输工作。 1976年，黄教授移居加拿大，任教于新斯科舍科技大学 (Technical University of Nova Scotia）电气工程系。1981年，他迁往安大略省麦克马斯特大学（McMaster University），现任该校国家科研讲座教授，并于1986-1987，1988-1994及2003-2008担任该校电气与计算机工程系主任。于1997-99年期间，亦曾任香港中文大学电子工程系名誉客座教授。1995年，黄教授荣获英国伦敦大学特别颁发理工学博士学位。1989年获英国电气工程师学院最佳海外论文奖，2006及2008年获IEEE信号处理青年作者最佳论文奖。研究范围包括信号处理通信理论，在所从事领域内发表240多篇文章。

Biography:

Kon Max Wong received his BSc(Eng), DIC, PhD, and DSc(Eng) degrees, all in electrical engineering, from the University of London, England, in 1969, 1972, 1974 and 1995, respectively. He started working at the Transmission Division of Plessey Telecommunications Research Ltd., England, in 1969. In October 1970 he was on leave from Plessey pursuing postgraduate studies and research at Imperial College of Science and Technology, London. In 1972, he rejoined Plessey as a research engineer and worked on digital signal processing and signal transmission. In 1976, he joined the Department of Electrical Engineering at the Technical University of Nova Scotia, Canada, and in 1981, moved to McMasterUniversity, Hamilton, Canada, where he has been a Professor since 1985 and served as Chairman of the Department of Electrical and Computer Engineering in 1986–87, 1988–94 and 2003−08. Professor Wong was on leave as Visiting Professor at the Department of Electronic Engineering of the ChineseUniversity of Hong Kong from 1997 to 1999. At present, he holds the Canada Research Chair in Signal Processing at McMasterUniversity. His research interest is in signal processing and communication theory and has published over 240 papers in the area.

Professor Wong was the recipient of the IEE Overseas Premium for the best paper in 1989, and is also the co-author of the papers that received the IEEE Signal Processing Society “ Best Young Author” awards of 2006 and 2008. He is a Fellow of IEEE, a Fellow of the Institution of Electrical Engineers, a Fellow of the Royal Statistical Society, and a Fellow of the Institute of Physics. More recently, he has also been elected as Fellow of the CanadianAcademy of Engineering as well as Fellow of the Royal Society of Canada. He was an Associate Editor of the IEEE Transaction on Signal Processing, 1996–98 and served as Chair of the Sensor Array and Multi-channel Signal Processing Technical Committee of the IEEE Signal Processing Society in 2002–04. Professor Wong was the recipient of the Alexander Von Humboldt International Research Award in 2010 and of the McMaster Engineering Research Achievement Award in 2011.

报告摘要：

信号处理经常需要选择一种信号特征，以作比较信号间的相似度。能量谱密度便是信号处理中通常选择的特征之一。然而，能量谱密度矩阵具有特别的结构约束，该等矩阵是在信号空间中描述一种流形。所以，要测度能量谱密度矩阵间之距离，我们认为流形上的黎曼距离，比之受广泛使用的欧基里德距离，更为适用。考察过功率谱密度流形的几何特性后，我们推算出流形上两个功率谱密度矩阵间的闭式黎曼距离。为利用信号处理中的先验信息，还可以推算出黎曼距离的最优权重。该黎曼距离可以应用在以下的信号处理领域：1）稳健的波束形成， 2）睡眠状态的脑电图信号分类，3）声纳信号检测。在上述领域中，应用该黎曼距离所得的结果，相比其他方法准确率有大幅度的提升。

Abstract:

The power spectral density (PSD) of a signal is often used as a feature for signal processing, for which a distance measure is often necessary to compare the similarity between the signal features. We reason that PSD matrices have structural constraints and describe a manifold in the signal space. Thus, the widely used Euclidean distance may not be appropriate. A more suitable measure is the Riemannian distance on the manifold. Here, we examine the geometry of the PSD manifold and develop closed-form Riemannian distances between two PSD matrices on the manifold. To make use of prior information in signal processing, optimum weighting of the Riemannian distance can be developed. Examples of employing this new measure in signal processing are presented: 1) Robust beamforming and, 2) Classification of EEG signals in the determination of a patient’s sleep state, 3) Detection of sonar signals. In all cases, the results are highly encouraging, having accuracies greatly improved from those using other measures.