Stable Phase Retrieval in Infinite-Dimensional Spaces

发布时间：2022-06-21 作者：浏览次数：

Speaker:	成诚	DateTime:	2022-6-28（星期二）上午10:10-11:10
Brief Introduction to Speaker: 成诚，研究员，现任职于中山大学数学学院，毕业于中佛罗里达大学数学系，指导老师是孙颀彧教授和李欣教授，并在美国杜克大学跟Ingrid Daubechies做博士后。她的主要研究方向为应用调和分析，特别是信号处理中的采样理论以及图信号分布式算法中的数学理论，目前已有多篇论文发表在Applied and Computational Harmonic Analysis, Journal of Fourier Analysis and Applications, IEEE Transaction on Signal Processing and IEEE Signal Processing letters.		Place:	六号楼二楼报告厅 M201
Abstract:In finite-dimensional spaces, frames that allow phase retrieval are stable, with a finite stability constant; yet when one considers nested hierarchies of finite-dimensional approximation spaces these constants tend to infinity as the dimension grows, possibly suffering a “curse of dimensionality”, i.e. growth may be exponential in the dimension. In this talk, we will consider the locally stable phase retrieval for frames in infinite-dimensional or finite-but large-dimensional Banach spaces. To study the local stability of phase retrievable signals, we introduce the notion of “locally stable and conditionally connected” (LSCC) measurement scheme associated with frames. We then characterize the phase retrieval stability of the signal by two measures that are commonly used to quantify the connectivity of the graph: the Cheeger constant and the algebraic connectivity.

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