##### Department of Mathematics,

University of California San Diego

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### Center for Computational Mathematics Seminar

## Palina Salanevich

#### Jacobs University

## Polarization Based Phase Retrieval for Time-Frequency Structured Measurements

##### Abstract:

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 diff raction pattern of the radiation that is scattered from an object. In such setting, it is not possible to measure the phase of the optical wave reaching the detector. So, it is 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. 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.

Host: Rayan Saab

### April 21, 2015

### 11:00 AM

### AP&M 2402

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