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math.FA2025
From completeness of discrete translates to phaseless sampling of the short-time Fourier transform
Philipp Grohs, Lukas Liehr, Irina Shafkulovska
We study the uniqueness problem in short-time Fourier transform phase retrieval by exploring a connection to the completeness problem of discrete translates. Specifically, we prove…
math.FA2024
Phase retrieval in Fock space and perturbation of Liouville sets
Philipp Grohs, Lukas Liehr, Martin Rathmair
We study the determination of functions in Fock space from samples of their absolute value, known as the phase retrieval problem in Fock space. An important finding in this researc…
math.FA2024
Multi-window STFT phase retrieval: lattice uniqueness
Philipp Grohs, Lukas Liehr, Martin Rathmair
Short-time Fourier transform (STFT) phase retrieval refers to the reconstruction of a function from its spectrogram, i.e., the magnitudes of its short-time Fourier transform $V…