Phase Retrieval from Gabor Measurements

Abstract

Compressed sensing investigates the recovery of sparse signals from linear measurements. But often, in a wide range of applications, one is given only the absolute values (squared) of the linear measurements. Recovering such signals (not necessarily sparse) is known as the phase retrieval problem. We consider this problem in the case when the measurements are time-frequency shifts of a suitably chosen generator, i.e. coming from a Gabor frame. We prove an easily checkable injectivity condition for recovery of any signal from all $N^2$ time-frequency shifts, and for recovery of sparse signals, when only some of those measurements are given.

References in corpus (1)

• Sparse Phase Retrieval from Short-Time Fourier Measurements

Cited by in corpus (5)

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• Stability estimates for phase retrieval from discrete Gabor measurements
• Time-Frequency Phase Retrieval for Audio -- The Effect of Transform Parameters
• On the connection between uniqueness from samples and stability in Gabor phase retrieval
• Arithmetic progressions and holomorphic phase retrieval