Exact reconstruction of the nonnegative measures using model sets

Article type: Research Article

Authors: Matei, Basarab

Affiliations: Université Paris 13, Sorbonne Paris Cité, LIPN, CNRS (UMR7030), Villetaneuse, 93430, France. E-mail: matei@lipn.univ-paris13.fr

Abstract: In this paper we are concerned with the reconstruction of a class of measures on the square from the sampling of its Fourier coefficients on some sparse set of points. We show that the exact reconstruction of a weighted Dirac sum measure is still possible when one knows a finite number of non-adaptive linear measurements of the spectrum. Surprisingly, these measurements are defined on a model set, i.e. quasicrystal.

Keywords: Fourier analysis, irregular sampling theory

DOI: 10.3233/ASY-151353

Journal: Asymptotic Analysis, vol. 97, no. 3-4, pp. 291-299, 2016