Fourier and Hankel bandlimited signal recovery

摘要

In this paper, we study the recovery problem of a bandlimited signal with missing data. More precisely, given a Fourier bandlimited signal f with bandwidth W and unknown on a bounded measurable set T, then by using the theory of prolate spheroidal wave functions, we prove that f can be stably recovered, no matter how large the Lebesgue measure of T. Moreover,we generalize these results to the case of Hankel bandlimited signals.