Remarks on the Voronoi method in Paley–Wiener space

Abstract

In Voronoi method, the reconstruction functions χn are not well-behaved, i.e., not continuous, which affect the convergence rate of this algorithm. In this paper, first, we obtain well-behaved reconstruction functions in place of χn; second, when the sampling set {xn:n∈Z} is denser, we obtain a faster convergent reconstruction iterative algorithm using analog to the mth order B-spline reconstruction functions φn(f)(x).