7 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…
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…
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…
Adversarial Phase Retrieval via Nonlinear Least Absolute Deviation
Gao Huang, Song Li, Hang Xu
We investigate the phase retrieval problem perturbed by dense bounded noise and sparse outliers that can change an adversarially chosen -fraction of the measurement vector. The…