Single and multichannel sampling of bilevel polygons using exponential splines

In this paper we present a novel approach for sampling and reconstructing any K-sided convex and bilevel polygon with the use of exponential splines. It will be shown that with K+1 projections we are able to perfectly reconstruct a K-sided bilevel polygon from its samples. We will also investigate the multichannel sampling scenario, consisting of a bank of E-spline filters, each with a different delay parameter compared to the reference signal. We show how by retrieving the delay parameters, we can symmetrically sample and reconstruct a given bilevel polygon using exponential splines.