Quasi-interpolation on the Body Centered Cubic Lattice

Abstract

This paper introduces a quasi-interpolation method for reconstruction of data sampled on the Body Centered Cubic (BCC) lattice. The reconstructions based on this quasi-interpolation achieve the optimal approximation order offered by the shifts of the quintic box spline on the BCC lattice. We also present a local FIR filter that is used to filter the data for quasi-interpolation. We document the improved quality and fidelity of reconstructions after employing the introduced quasi-interpolation method. Finally the resulting quasi-interpolation on the BCC sampled data are compared to the corresponding quasi-interpolation method on the Cartesian sampled data.