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Date
2023-02Type
- Report
ETH Bibliography
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Abstract
We study the problem of recovering a signal from magnitudes of its wavelet frame coefficients when the analyzing wavelet is real-valued. We show that every real-valued signal can be uniquely recovered, up to global sign, from its multi-wavelet frame coefficients {|Wϕif(αmβn,αm)|:i∈{1,2,3},m,n∈Z} for every $\alpha>1,\beta>0$ with $\beta\ln(\alpha)\leq 4\pi/(1+4p)$, $p>0$, when the three wavelets $\phi_i$ are suitable linear combinations of the Poisson wavelet $P_p$ of order $p$ and its Hilbert transform $\mathscr{H}P_p$. For complex-valued signals we find that this is not possible for any choice of the parameters $\alpha>1,\beta>0$ and for any window. In contrast to the existing literature on wavelet sign retrieval, our uniqueness results do not require any bandlimiting constraints or other a priori knowledge on the real-valued signals to guarantee their unique recovery from the absolute values of their wavelet coefficients. Show more
Publication status
publishedExternal links
Journal / series
SAM Research ReportVolume
Publisher
Seminar for Applied Mathematics, ETH ZurichSubject
Phase retrieval; Wavelet transform; Cauchy wavelet; Poisson wavelet; Weighted Bergman space; Wavelet frame; Sampling theoremOrganisational unit
09603 - Alaifari, Rima / Alaifari, Rima
Funding
184698 - Mathematical analysis of the phase retrieval problem (SNF)
Related publications and datasets
Is previous version of: https://doi.org/10.3929/ethz-b-000683236
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