https://hal-centralesupelec.archives-ouvertes.fr/hal-01741782Chardon, GillesGillesChardonL2S - Laboratoire des signaux et systèmes - UP11 - Université Paris-Sud - Paris 11 - CentraleSupélec - CNRS - Centre National de la Recherche ScientifiqueDesign of variable densities for least-squares approximationsHAL CCSD2017[INFO.INFO-TS] Computer Science [cs]/Signal and Image ProcessingChardon, Gilles2018-03-23 14:26:292022-10-17 13:34:132018-03-23 14:26:29enConference papers10.1109/SAMPTA.2017.80244451We 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.