Date:	Wed, November 19, 2014
Time:	15:45
Place:	TBA

Abstract: In many areas of imaging science it is often needed to reconstruct a signal from intensity measurements only. This problem is called phase retrieval. We are 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. As a preliminary result, we are going to present the recovery algorithm with sufficiently small number of measurements required, which is working with time-frequency structured measurements. The algorithm is based on the idea of polarization, first proposed by Alexeev, Bandeira, Fickus and Mixon.

The plan of the further research includes investigation of the properties of Gabor frames, such as projective uniformity. This property gives us the control on the number of small frame coefficients. It enables us to prove the stability of the algorithm in the presence of noise, but also is of independent interest for Gabor analysis. As a part of the PhD project, we also aim to develop a modification of the PhaseLift algorithm and non-convex optimization methods to obtain stable recovery from time-frequency structured measurements.