Injectivity of Gabor phase retrieval from lattice measurements

18.11.2020 14:00 - 15:30

Lukas Liehr (University of Vienna)

In this talk, we discuss novel uniqueness results for the Gabor phase retrieval problem. In particular, we are interested which classes of square-integrable functions can be uniquely reconstructed from lattice samples of their spectrogram. After giving a concise introduction to the relevant notions of Gabor phase retrieval, we will show that compactly supported functions, as well as functions in shift-invariant spaces with Gaussian generator, are determined up to a global phase from lattice measurements of their spectrogram. The considered signals can be real- or complex-valued. The results are based on a combination of certain Müntz-type theorems related to density properties of discrete translates as well as uniqueness theorems for Paley-Wiener and shift-invariant spaces. Finally, we discuss the sharpness of the presented uniqueness theorems.

Link:

https://us02web.zoom.us/j/81874457687?pwd=NjRzTjdEYzZub0pIUEpoQ0JLYjJCdz09

Meeting ID: 818 7445 7687

Passcode: 969502

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Organiser:
J. L. Romero, M. Ehler