"Random periodic sampling patterns for shift-invariant spaces"Carbajal, DianaThis talk presents a random sampling strategy for multi-variate signals spanned by the integer shifts of generating functions with distinct frequency profiles. We show that taking the samples over a random non-uniform periodic 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). This is a joint work with Jorge Antezana and José Luis Romero. |
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