Optimal Measurements in Phase Retrieval: From Stability to Geometry      

主讲人：许志强（中国科学院数学与系统科学研究院）

摘要：Phase retrieval aims to recover a signal from the magnitudes of linear measurements. In this talk, we study the stability of phase retrieval through a condition number defined in terms of the bi-Lipschitz constants of the measurement map, and discuss the problem of designing measurement frames with optimal stability. We present universal lower bounds for the condition number and explain their asymptotic sharpness for Gaussian measurements. We then focus on real phase retrieval in dimension two, where the optimal frame problem admits a surprising connection with the classical problem of maximizing the perimeter of a planar polygon with prescribed diameter. This geometric viewpoint leads to a characterization of several optimal configurations and, in particular, shows that harmonic frames are optimal for an odd number of measurements but not for an even number.This is joint work with Yu Xia, Zili Xu and Xinyue Zhang.

主讲人简介：许志强，中国科学院数学与系统科学研究院研究员，冯康首席研究员（2021-2023). 研究领域包括逼近论、计算调和分析、离散数学等，尤其对采样理论、压缩感知、球面布点以及相位恢复等领域感兴趣。一方面，他将纯粹数学中的研究方法引入到计算调和分析，系统发展了相位恢复的代数簇方法，从而对一些困难问题得到实质性进展；另一方面，将逼近论中样祥条函数和代数理论相结，从而解决了多个猜想和公开问题。应邀于2023年在荷兰举行的SIAM Conference on Applied Algebraic Geometry做一小时大会邀请报告，应邀于华为罗马广场高端论坛做学术演讲。现担任IEEE Trans. Information Theory，数学学报（英文版），J. Comp Math.等国际期刊编委。   

邀请人：刘海霞

时间：2026年10月27日上午10:00-11:30

地点： 腾讯会议室：753504280