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Polarization Based Phase Retrieval for Time-Frequency Structured Measurements

Palina Salanevich
Jacobs University


In many areas of imaging science, such as diffraction imaging, astronomical imaging, microscopy, etc., optical detectors can often only record the squared modulus of the Fraunhofer or Fresnel diffraction pattern of the radiation that is scattered from an object. In such settings, it is not possible to measure the phase of the optical wave reaching the detector. So, it is necessary 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. The most efficient existing algorithms, such as PhaseLift, work with randomly generated Gaussian frames. I am going to present the recovery algorithm with a 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.

Tuesday, April 21, 2015
11:00AM AP&M 2402