Random average sampling and reconstruction in shift-invariant subspaces of mixed Lebesgue spaces

TL;DR

This paper investigates the reconstruction of signals in mixed Lebesgue spaces from random average samples, deriving probabilistic inequalities and explicit formulas, with numerical validation demonstrating the effectiveness of the approach.

Contribution

It introduces new probabilistic sampling inequalities and explicit reconstruction formulas for signals in shift-invariant subspaces of mixed Lebesgue spaces, supported by numerical simulations.

Findings

Probabilistic inequalities improve with larger sample sizes.

Explicit reconstruction formulas are derived for specific signal subsets.

Numerical simulations confirm the theoretical results.

Abstract

In this paper, the problem of reconstruction of signals in mixed Lebesgue spaces from their random average samples has been studied. Probabilistic sampling inequalities for certain subsets of shift-invariant spaces have been derived. It is shown that the probabilities increase to one when the sample size increases. Further, explicit reconstruction formulae for signals in these subsets have been obtained for which the numerical simulations have also been performed.