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

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

doi:10.1007/s10208-022-09593-5

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

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

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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(δ⁴log ²(1 / δ)). We also provide numerical tests and comparison with other algorithms.

Original language	English
Journal	Foundations of Computational Mathematics
DOIs	https://doi.org/10.1007/s10208-022-09593-5
State	Published - 2022

Bibliographical note

Funding Information:
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.

Publisher Copyright:
© 2022, The Author(s).

Keywords

Bargmann transform
Computation
Random analytic function
Short-time Fourier transform
Wasserstein metric
Zero set

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10.1007/s10208-022-09593-5

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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(δ4log 2(1 / δ)). We also provide numerical tests and comparison with other algorithms.",

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

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Keywords

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