Efficient Computation of the Zeros of the Bargmann Transform Under Additive White Noise

Luis Alberto Escudero, Naomi Feldheim, Günther Koliander, José Luis Romero

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Abstract

We study the computation of the zero set of the Bargmann transform of a signal contaminated with complex white noise, or, equivalently, the computation of the zeros of its short-time Fourier transform with Gaussian window. We introduce the adaptive minimal grid neighbors algorithm (AMN), a variant of a method that has recently appeared in the signal processing literature, and prove that with high probability it computes the desired zero set. More precisely, given samples of the Bargmann transform of a signal on a finite grid with spacing δ, AMN is shown to compute the desired zero set up to a factor of δ in the Wasserstein error metric, with failure probability O(δ4log2(1/δ)). We also provide numerical tests and comparison with other algorithms.

Original languageEnglish
Pages (from-to)279-312
Number of pages34
JournalFoundations of Computational Mathematics
Volume24
Issue number1
DOIs
StatePublished - Feb 2024

Bibliographical note

Publisher Copyright:
© The Author(s) 2022.

Funding

L. A. E., G. K., and J. L. R. gratefully acknowledge support from the Austrian Science Fund (FWF): Y 1199 and P 29462. N. F. gratefully acknowledges support from the Israel Science Foundation (ISF) grant no. 1327/19.

FundersFunder number
Austrian Science FundP 29462, Y 1199
Israel Science Foundation1327/19

    Keywords

    • 30H20
    • 60G15
    • 60G55
    • 60G70
    • 62M30
    • 65R10
    • Bargmann transform
    • Computation
    • Random analytic function
    • Short-time Fourier transform
    • Wasserstein metric
    • Zero set

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