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Design of variable densities for least-squares approximations

Abstract : We study the problem of interpolating a signal using samples at coordinates drawn for a probability density over the domain of definition of the signal, with the assumption that it can be approximated in a known linear subspace. Our goal is to minimize the number of samples needed to ensure a well-conditioned estimation of the signal. We show that the problem of optimizing the probability density is convex, and that applying the Frank-Wolf algorithm yields a simple and interpretable optimization procedure. Examples of optimizations are given with polynomials, trigonometric polynomials and Fourier-Bessel functions for wavefield interpolation.
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Submitted on : Friday, March 23, 2018 - 2:26:29 PM
Last modification on : Monday, October 17, 2022 - 1:34:13 PM



Gilles Chardon. Design of variable densities for least-squares approximations. 2017 International Conference on Sampling Theory and Applications (SampTA), Jul 2017, Tallin, Estonia. ⟨10.1109/SAMPTA.2017.8024445⟩. ⟨hal-01741782⟩



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