Sampling and Average Sampling in Quasi Shift-Invariant Spaces. (26th July 2020) - Kumar, Anuj; Sampath, Sivananthan
Abstract: In this paper, we study the sampling and average sampling problem in a quasi shift-invariant space V X ( φ ), where X is a discrete subset of R and φ is a continuously differentiable positive definite function satisfying certain decay conditions. We show that any f belonging to V X ( φ ) can be uniquely and stably reconstructed from its samples f ( y k ) : k ∈ Z as well as from its average samples provided sampling points y k : k ∈ Z are close enough. Further, iterative reconstruction algorithms for reconstruction of a function f belonging to V X ( φ ) from its samples f ( y k ) : k ∈ Z as well as from its average samples are also provided.