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.