1 citations · 1 across the 7 of their papers we have counts for
7 papers
The Minimum Number of Measurements for Almost-Everywhere Complex Phase Retrieval
Zhiqiang Xu
Let and let . We prove that if , then the intensity measurement map \[ \bf{x}\longmapsto \bigl( |\langle \bf{x},\bf{f}…
Optimal Condition Numbers in Low-Rank Positive Semidefinite Matrix Sensing
Mingxuan Sun, Zhiqiang Xu
In this paper we focus on the stability of positive semidefinite matrix sensing maps where , and $\operat…
Fourier Phase Retrieval for Finite Unions of Intervals
Yu Xia, Zhiqiang Xu
This paper investigates the one-dimensional Fourier phase retrieval problem for indicator functions of finite unions of intervals. Specifically, we study the recovery of a set $Ω=…
Instance optimality in phase retrieval
Yu Xia, Zhiqiang Xu
Compressed sensing has demonstrated that a general signal () can be estimated from few linear measurement…
On the Performance of Amplitude-Based Models for Low-Rank Matrix Recovery
Huanmin Ge, Zhiqiang Xu
In this paper, we focus on low-rank phase retrieval, which aims to reconstruct a matrix with from noi…
Finite Samples for Shallow Neural Networks
Yu Xia, Zhiqiang Xu
This paper investigates the ability of finite samples to identify two-layer irreducible shallow networks with various nonlinear activation functions, including rectified linear uni…
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})=|\bol…