# Mark Iwen : Fast Phase Retrieval for High-Dimensions

Phase retrieval problems appear in many imaging applications in which only the magnitude of (e.g., Fourier) transform coefficients of a given signal can be measured. In such settings one desires to learn the original signal (up to a global phase factor) using only such magnitude information. In this talk we discuss methods to rapidly re-learn such lost phase information by using the magnitudes of well-designed combinations of the original transform coefficients. In particular, we develop a fast phase retrieval method which is near-linear time, making it computationally feasible for large dimensional signals. Both theoretical and experimental results demonstrate the method's speed, accuracy, and robustness. We then use this new phase retrieval method to help establish the first known sublinear-time compressive phase retrieval algorithm capable of recovering a given $s$-sparse signal ${\bf x} \in \mathbbm{C}^d$ (up to an unknown phase factor) in just $\mathcal{O}(s \log^5 s \cdot \log d)$-time using only $\mathcal{O}(s \log^4 s \cdot \log d)$ magnitude measurements. This is joint work with Aditya Viswanathan and Yang Wang.

**Category**: Applied Math and Analysis**Duration**: 01:34:50**Date**: January 12, 2015 at 4:25 PM**Views**: 108-
**Tags:**seminar, Applied Math And Analysis Seminar

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