Date:	Tue, May 6, 2014
Time:	11:15
Place:	Research I Seminar Room

Abstract: In many areas of imaging science it is difficult to capture the phase of linear measurements and it is often needed to reconstruct a signal from intensity measurements only. This problem is called phase retrieval. I am going to give an overview of the state of art results in this area and then focus on the polarization approach to the problem, first proposed by Alexeev, Bandeira, Fickus and Mixon. In particular I am going to consider the case when the measurement frame is a Gabor frame, that is, the case of time-frequency structured measurements. The main motivation is that in this case, 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. The most efficient existing algorithms, such as PhaseLift, work with randomly generated Gaussian frames. I am going to present the recovery algorithm with sufficiently small number of measurements required, working with time-frequency structured measurements which is based on the idea of polarization.