6 papers
PhaseLift for Coded Diffraction Patterns: Optimal Sampling Rate
Gao Huang, Song Li
Recovering a complex-valued signal from coded diffraction patterns, namely the Fourier intensities obtained after modulating the signal with a collection of masks, is a fundamental…
Low-Rank Matrix Recovery via Heavy-Tailed Quadratic Sampling
Gao Huang, Song Li
The problem of recovering an (approximately) low-rank Hermitian matrix of rank from quadratic sampling matrices of the form $\{\pmb{a}_k…
Focused Width in Adversarial Fake Detection: A Separation
Gao Huang
We study the adversarial fake detection model introduced by Mendelson, Paouris and Vershynin. In this model, a genuine sample is , while a fake sample i…
Low-Rank Toeplitz Matrix Restoration: Descent Cone Analysis and Structured Random Matrix
Gao Huang, Song Li
This note demonstrates that we can stably recover all symmetric Toeplitz matrices of rank at most from a number of rank-one subgaussian mea…
Geometric Characteristics and Stable Guarantees for Phaseless Operators and Structured Matrix Restoration
Gao Huang, Song Li
In this paper, we first propose a unified framework for analyzing the stability of the phaseless operators for both amplitude and intensity measurement on an arbitrary geometric se…
Stable Phase Retrieval: Optimal Rates in Poisson and Heavy-tailed Models
Gao Huang, Song Li, Deanna Needell
We investigate stable recovery guarantees for phase retrieval under two realistic and challenging noise models: the Poisson model and the heavy-tailed model. Our analysis covers bo…