Data Dialogue
Thursday, February 25, 2016, 11:45am, Gross 330
Rima Alaifari (ETH Zurich)
Phase retrieval in the setting of (semi-)continuous frames

Abstract:

In this talk we first consider the following problem of phase retrieval in L2: Given a collection of real-valued bandlimited functions that constitutes a semi-discrete frame, we ask whether any real-valued function f can be uniquely recovered from the magnitudes of its convolutions with the frame elements. We find that under some mild assumptions this is indeed the case. Furthermore, it suffices to know the unsigned measurements on suitably fine lattices to uniquely determine f (up to a global sign factor). In the second half of the talk we present a generalized framework for phase retrieval in Banach spaces and for measurements from continuous frames. Our main result states that when the Banach space is infinite dimensional, phase retrieval is unstable even for continuous frames. Therefore, in the setting of a discrete frame, no oversampling of the frame can improve on the stability of the phase retrieval problem.

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