Robust phase retrieval via median-truncated smoothed amplitude flow

Abstract

ABSTRACT Phase retrieval (PR) is an inverse problem about recovering a signal from phaseless linear measurements, which arises in various fields. In practical scenarios, partial measurements can be inevitably corrupted by outliers that can take arbitrary values. To handle this, we propose the median-SAF method which is the smoothed amplitude flow (SAF) method equipped with the median truncation strategy. We find that median-SAF has some inherent advantages in suppressing outliers. Theoretical analysis ensures that median-SAF converges linearly to the original signal via the gradient algorithm from an delicate initial estimate with high probability. Substantial numerical tests empirically illustrate that the proposed method is superior to other state-of-the-art methods in terms of the recovery rate and the performance on suppressing outliers.