Injectivity of Gabor phase retrieval from lattice measurements

DOI10.1016/j.acha.2022.09.001zbMath1504.94040arXiv2008.07238OpenAlexW3049411183WikidataQ122212490 ScholiaQ122212490MaRDI QIDQ2105110

Philipp Grohs, Lukas Liehr

Publication date: 8 December 2022

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.07238

zbMATH Keywords

Gabor transformshift-invariant spacesphase retrievallattice measurementsspectrogram sampling

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) General harmonic expansions, frames (42C15) Sampling theory in information and communication theory (94A20) Completeness of sets of functions in one variable harmonic analysis (42A65)

Related Items

Non-Uniqueness Theory in Sampled STFT Phase Retrieval ⋮ Injectivity of sampled Gabor phase retrieval in spaces with general integrability conditions ⋮ Stable Gabor phase retrieval in Gaussian shift-invariant spaces via biorthogonality ⋮ Sampling at twice the Nyquist rate in two frequency bins guarantees uniqueness in Gabor phase retrieval ⋮ Phase retrieval of bandlimited functions for the wavelet transform

Cites Work

• Unnamed Item
• Unnamed Item
• Reconstruction of bandlimited functions from unsigned samples
• The fractional Fourier transform and quadratic field magnetic resonance imaging
• Uniqueness results in an extension of Pauli's phase retrieval problem
• Phase-retrieval in shift-invariant spaces with Gaussian generator
• Foundations of time-frequency analysis
• Bounds on the Segal-Bargmann transform of \(L^p\) functions
• Sampling theorems for shift-invariant spaces, Gabor frames, and totally positive functions
• Phase retrieval from sampled Gabor transform magnitudes: counterexamples
• On foundational discretization barriers in STFT phase retrieval
• On Fourier transforms of measures with compact support
• On the closure of characters and the zeros of entire functions
• Uniqueness of STFT phase retrieval for bandlimited functions
• Sign retrieval in shift-invariant spaces with totally positive generator
• Nonuniform Sampling and Reconstruction in Shift-Invariant Spaces
• On Approximation by Shifts and a Theorem of Wiener
• Completeness in L2(ℝ) of almost integer translates
• A note on the phase retrieval of holomorphic functions
• Phase Retrieval: Uniqueness and Stability
• Stable Gabor Phase Retrieval and Spectral Clustering
• Entire Functions and Muntz-Szasz Type Approximation
• The numerics of phase retrieval