Super-Resolution via Prony-Type Polynomials

MCML Authors

Anna Veselovska

Dr.

→ Group Massimo Fornasier
 Applied Numerical Analysis

Abstract

The problem of hidden periodicity in three dimensions is to recover frequency vectors ω1, …, ωN ∈ [0, 2π)3 using finitely many samples of the exponential f(n)=∑Nj=1ajexp(−i⟨ωj,n⟩), where a1, …, aN ∈ ℂ0 and n ∈ ℤ3. Inspired by the approaches developed in [11], [30], we consider specifically constructed polynomials, which are called Prony-type polynomials, and show that the frequency vectors ω1, …, ωN can be recovered via a set of common zeros of such polynomials. By employing Cantor tuple functions, we position the method of Prony-type polynomials within the spectrum of sampling requirements between the methods proposed in [21], [22]. While the Prony-type polynomial method demands more samples than the approach in [22], numerical experiments indicate that it exhibits greater stability in the presence of noisy data.

inproceedings

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SampTA 2025

15th International Conference on Sampling Theory and Applications. Vienna, Austria, Jul 28-Aug 01, 2025. To be published. Preprint available.

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Authors

A. Veselovska • J. Prestin

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Links

DOI

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Research Area

 A2 | Mathematical Foundations