Work

Median-Truncated Nonconvex Approach for Phase Retrieval With Outliers

Year: 2018

Type: article

Abstract: This paper investigates the phase retrieval problem, which aims to recover a signal from the magnitudes of its linear measurements. We develop statistically and computationally efficient algorithms for the situation when the measurements are corrupted by sparse outliers that can take arbitrary values. We propose a novel approach to robustify the gradient descent algorithm by using the sample median as a guide for pruning spurious samples in initialization and local search. Adopting a Poisson loss and a reshaped quadratic loss, respectively, we obtain two algorithms termedmedian-truncated Wirtinger flowandmedian-reshaped Wirtinger flow, both of which provably recover the signal from a near-optimal number of measurements when the measurement vectors are composed of independent and identically distributed Gaussian entries, up to a logarithmic factor, even when a constant fraction of the measurements is adversarially corrupted. We further show that both algorithms are stable in the presence of additional dense bounded noise. Our analysis is accomplished by developing non-trivial concentration results of median-related quantities, which may be of independent interest. We provide numerical experiments to demonstrate the effectiveness of our approach.

Source: IEEE Transactions on Information Theory

DOI: 10.1109/tit.2018.2847695

Authors: Huishuai Zhang, Yuejie Chi, Yingbin Liang

Institutions: Microsoft Research Asia (China), Carnegie Mellon University, The Ohio State University

Language: English

Topic: Sparse and Compressive Sensing Techniques

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green