Cai, T.T., Li, X. and Ma, Z. (2016) Optimal Rates of Convergence for Noisy Sparse Phase Retrieval via Thresholded Wirtinger Flow. The Annals of Statistics, 44, 2221-2251.
https://doi.org/10.1214/16-AOS1443

has been cited by the following article:

• TITLE: L1/2 -Regularized Quantile Method for Sparse Phase Retrieval

  AUTHORS: Si Shen, Jiayao Xiang, Huijuan Lv, Ailing Yan

  KEYWORDS: Sparse Phase Retrieval, Nonconvex Optimization, Alternating Direction Method of Multipliers, Quantile Regression Model, Robustness

  JOURNAL NAME: Open Journal of Applied Sciences, Vol.12 No.12, December 30, 2022

  ABSTRACT: The sparse phase retrieval aims to recover the sparse signal from quadratic measurements. However, the measurements are often affected by outliers and asymmetric distribution noise. This paper introduces a novel method that combines the quantile regression and the L1/2-regularizer. It is a non-convex, non-smooth, non-Lipschitz optimization problem. We propose an efficient algorithm based on the Alternating Direction Methods of Multiplier (ADMM) to solve the corresponding optimization problem. Numerous numerical experiments show that this method can recover sparse signals with fewer measurements and is robust to dense bounded noise and Laplace noise.