报告题目：Exact Sparse Signal Recovery via Orthogonal MatchingPursuit with Prior Information

报告人：温金明教授（暨南大学）

报告时间：2018年12月7日（星期五），下午15：30-17：00

报告地点：大学城校区工学一号馆201

报告摘要：

Exact recovery ofK-sparse signalsx∈ Rⁿfrom linearmeasurementsy = Ax, whereA∈ R^m×nis a sensing matrix, arises from many applications. The orthogonal matchingpursuit (OMP) algorithm is a widely used algorithm for reconstructing thexbased onyandAdue to its excellent recoveryperformance and high efficiency. A fundamental question inthe performance analysis of OMP is the characterizations ofthe probability that it can exactly recoverxfor random matrixAand the minimalmto guarantee a satisfactory recoveryperformance. Although in many practical applications, inaddition to the sparsity,xusually also has some additionalproperties (for example, the nonzero entries ofxindependentlyand identically follow the Gaussian distribution, andxhasexponential decaying property), as far as we know, none ofexisting analysis uses these properties to answer the abovequestion. In this talk, we first show that the prior distributioninformation ofxcan be used to provide an upper bound on|x|2 1/|x|2 2. Then, we explore this upper bound to develop abetter lower bound on the probability of exact recovery withOMP inKiterations. Furthermore, we develop a lower boundon m to guarantee that the exact recovery probability ofKiterations of OMP is not lower than a given probability. Wefurther show that, ifKis sufficiently small compared withn, whenKapproaches infinity,m≈2Kln(n), m≈Kandm≈1.6Kln(n) are enough to ensure that OMP hasa satisfactory recovery performance for recovering anyK-sparsex,K-sparsexwith exponential decaying propertyandK-sparsexwhose nonzero entries independently andidentically follow the Gaussian distribution, respectively. Thissignificantly improves Troppet. al.’s result which requiresm≈ 4Kln(n/δ).

报告人简介：

温金明，2015年6月毕业于加拿大麦吉尔大学数学与统计学院，获哲学博士学位。从2015年3月到2018年9月，温教授先后在法国科学院里昂并行计算实验室、加拿大阿尔伯塔大学、多伦多大学从事博士后研究工作。

从2018年9月至今，他是暨南大学网络空间安全学院的教授。他的研究方向主要是整数信号和稀疏信号恢复的算法设计与理论分析。他以第一作者在IEEE Communications Magazine（2篇）、Applied and Computational Harmonic Analysis (中科院数学一区期刊，2篇)、IEEE Transactions on Information Theory（2篇）、IEEE Transactions on Signal Processing（2篇）、IEEE Transactions on Wireless Communications（2篇）、IEEE Transactions on Communications等顶级期刊和会议发表25篇（含三篇ESI高被引论文）,以通讯作者和合作者身份发表期刊和会议发表14篇。目前他担任IEEE Access（中科院二区）期刊的编辑。

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