ﻻ يوجد ملخص باللغة العربية
We consider the problem of phase retrieval from magnitudes of short-time Fourier transform (STFT) measurements. It is well-known that signals are uniquely determined (up to global phase) by their STFT magnitude when the underlying window has an ambiguity function that is nowhere vanishing. It is less clear, however, what can be said in terms of unique phase-retrievability when the ambiguity function of the underlying window vanishes on some of the time-frequency plane. In this short note, we demonstrate that by considering signals in Paley-Wiener spaces, it is possible to prove new uniqueness results for STFT phase retrieval. Among those, we establish a first uniqueness theorem for STFT phase retrieval from magnitude-only samples in a real-valued setting.
We study the problem of phase retrieval in which one aims to recover a function $f$ from the magnitude of its wavelet transform $|mathcal{W}_psi f|$. We consider bandlimited functions and derive new uniqueness results for phase retrieval, where the w
In recent work [P. Grohs and M. Rathmair. Stable Gabor Phase Retrieval and Spectral Clustering. Communications on Pure and Applied Mathematics (2018)] the instabilities of the Gabor phase retrieval problem, i.e., the problem of reconstructing a funct
In a variety of fields, in particular those involving imaging and optics, we often measure signals whose phase is missing or has been irremediably distorted. Phase retrieval attempts the recovery of the phase information of a signal from the magnitud
We consider the problem of reconstructing the missing phase information from spectrogram data $|mathcal{G} f|,$ with $$ mathcal{G}f(x,y)=int_mathbb{R} f(t) e^{-pi(t-x)^2}e^{-2pi i t y}dt, $$ the Gabor transform of a signal $fin L^2(mathbb{R})$. More
We give some details about the stationary phase lemma. We first prove a special case where the high order terms are derived explicitly. Based on that, we prove a more general case by using Morse lemma.