Polarization based phase retrieval for time-frequency structured measurements

Abstract

We consider phaseless measurements in the case when the measurement frame is a Gabor frame, that is, the frame coefficients are of the form of masked Fourier coefficients where the masks are time shifts of the Gabor window. This makes measurements meaningful for applications, but at the same time preserves the flexibility of the frame-theoretic approach. We are going to present a recovery algorithm which requires a sufficiently small number of measurements; it is based on the idea of polarization, which is proposed by Alexeev, Bandeira, Fickus and Mixon [1], [4].