In this talk we present a random sampling approach for multi-variate signals spanned by the integer shifts of a set of generating functions with distinct frequency profiles. We show that taking the samples over a random periodic non-uniform set produces a sampling set with high probability, provided that the density of the sampling pattern exceeds the number of frequency profiles by a logarithmic factor.
The result includes, in particular, the case of Paley-Wiener spaces with multi-band spectra. While in this well-studied setting delicate constructions provide sampling strategies that meet the information theoretic benchmark of Shannon and Landau, the sampling pattern that we consider provides, at the price of a logarithmic oversampling factor, a simple alternative that is accompanied by favorable a priori stability margins (snug frames). Notably, the results obtained for this case are independent of the ambient dimension.
This is a joint work with Jorge Antezana (Autonomous University of Madrid) and José Luis Romero (University of Vienna).