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.
Document type :
Conference papers
Complete list of metadatas

https://hal-centralesupelec.archives-ouvertes.fr/hal-01741782
Contributor : Gilles Chardon <>
Submitted on : Friday, March 23, 2018 - 2:26:29 PM
Last modification on : Monday, April 16, 2018 - 4:07:45 PM

Identifiers

Citation

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⟩

Share

Metrics

Record views

79