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Dhifallah, O. and Lu, Y.M. (2017) Fundamental Limits of PhaseMax for Phase Retrieval: A Replica Analysis. 2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), Curacao, 10-13 December 2017, 1-5.
https://doi.org/10.1109/CAMSAP.2017.8313210

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.