4 papers
Optimal Frames for Phase Retrieval from Edge Vectors of Optimal Polygons
Zhiqiang Xu, Zili Xu, Xinyue Zhang
This paper aims to characterize the optimal frame for phase retrieval, defined as the frame whose condition number for phase retrieval attains its minimal value. In the context of…
Generalized Interlacing Families: New Error Bounds for CUR Matrix Decompositions
Jian-Feng Cai, Zhiqiang Xu, Zili Xu
This paper introduces the concept of generalized interlacing families of polynomials, which extends the classical interlacing polynomial method to handle polynomials of varying deg…
Interlacing Polynomial Method for Matrix Approximation via Generalized Column and Row Selection
Jian-Feng Cai, Zhiqiang Xu, Zili Xu
This paper delves into the spectral norm aspect of the Generalized Column and Row Subset Selection (GCRSS) problem. Given a target matrix , th…
Stability in Phase Retrieval: Characterizing Condition Numbers and the Optimal Vector Set
Yu Xia, Zhiqiang Xu, Zili Xu
In this paper, we primarily focus on analyzing the stability property of phase retrieval by examining the bi-Lipschitz property of the map $Φ_{\boldsymbol{A}}(\boldsymbol{x})=|\bo…