Robustness of average sampling and reconstruction of shift-invariant signals in mixed Lebesgue spaces

Abstract

The robustness of sampling scheme ensures that the exact samples are not crucial to recover the signal under considered and some errors can be tolerated. This paper addresses that two kinds of nonuniform average sampling schemes are robust for finitely generated shift-invariant signals in mixed Lebesgue spaces. The results show that the mixed shift-invariant signals can be reconstructed stably from two classes of nonuniform average samples, respectively, when the generators and sampling functionals are disturbed slightly.