Irregular and multi--channel sampling of operators

TL;DR

This paper extends classical sampling theorems to bandlimited operators, exploring irregular sampling and multi-channel sampling to recover operators from non-uniform and multiple outputs.

Contribution

It introduces operator sampling frameworks for irregular and multi-channel cases, broadening the applicability of sampling theory to more complex operator classes.

Findings

Irregular operator sampling allows non-uniform sampling sets.

Multi-channel operator sampling enables complete operator reconstruction.

The methods generalize classical sampling to operator settings.

Abstract

The classical sampling theorem for bandlimited functions has recently been generalized to apply to so-called bandlimited operators, that is, to operators with band-limited Kohn-Nirenberg symbols. Here, we discuss operator sampling versions of two of the most central extensions to the classical sampling theorem. In irregular operator sampling, the sampling set is not periodic with uniform distance. In multi-channel operator sampling, we obtain complete information on an operator by multiple operator sampling outputs.