Multi-window STFT phase retrieval

17.10.2022 15:00 - 16:30

Lukas Liehr (University of Vienna)

Short-time Fourier transform (STFT) phase retrieval refers to the reconstruction of a function f from its spectrogram, i.e., the magnitudes of its STFT. Recently established discretization barriers state that a unique reconstruction via spectrogram-sampling on lattices is unachievable in L2(R), irrespective of the window function g and the density of the lattice. We therefore initiate the study of multi-window STFT phase retrieval. The talk centers around the derivation of a new connection between phase retrieval via finite frames, multi-window STFT phase retrieval, as well as sampling in Fock space. With the help of an easy-to-check geometric condition, we then proceed by showing that spectrogram-sampling on lattices with 4 instead of a single window function yields unique recoverability of any square-integrable function. The result thereby overcomes the aforementioned discretization barriers and constitutes the first general uniqueness result for sampled STFT phase retrieval.

This is joint work with Philipp Grohs and Martin Rathmair.

Harmonic Analysis Seminar
SR6 (1st floor)