Gabor phase retrieval via semidefinite programming

21.11.2023 11:30 - 13:00

Martin Rathmair (University of Vienna)

Given X a function space consisting of complex-valued functions, the corresponding phase retrieval problem is to reconstruct F ∈ X from phase-less observations, that is from (samples of) its modulus |F|. Among other difficulties, the lack of convexity makes such a problem a challenging task.
We discuss the case where X is the image of L2 under the short-time Fourier transform (STFT) with Gaussian window, i.e., reconstruction of the STFT from the spectrogram.
We propose a reconstruction scheme which is based on solving two convex problems and argue that the method accurately reconstructs F (up to a constant phase factor) provided that F is connected in a certain graph-theoretic sense (note that the problem at hand requires some sort of connectivity to be well-posed).

This is joint work with P. Jaming (U. Bordeaux)

K. Gröchenig and I. Shafkulovska
SR10 (2st floor)