Author(s)

Si Shen^1*, Jiayao Xiang^2*, Huijuan Lv³, Ailing Yan^2#

¹College of Science, Minzu University of China, Beijing, China.
²School of Science, Hebei University of Technology, Tianjin, China.
³School of Insurance and Economics, University of International Business and Economics, Beijing, China.

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 L_1/2-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.

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

Shen, S. , Xiang, J. , Lv, H. and Yan, A. (2022) L_1/2 -Regularized Quantile Method for Sparse Phase Retrieval. Open Journal of Applied Sciences, 12, 2135-2151. doi: 10.4236/ojapps.2022.1212147.