Random periodic sampling patterns for shift-invariant spaces

Add to your list(s) Download to your calendar using vCal

• Diana Carbajal (University of Vienna)
• Thursday 18 July 2024, 12:15-12:35
• Seminar Room 1, Newton Institute.

If you have a question about this talk, please contact nobody.

DREW01 - Multivariate approximation, discretization, and sampling recovery

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).

This talk is part of the Isaac Newton Institute Seminar Series series.

This talk is included in these lists:

• All CMS events
• Featured lists
• INI info aggregator
• Isaac Newton Institute Seminar Series
• School of Physical Sciences
• Seminar Room 1, Newton Institute
• bld31

Note that ex-directory lists are not shown.