On the choice of Kernel for signal interpolation on the sphere using reproducing kernel Hilbert spaces

Abstract

In this paper, we present a mathematical framework for the interpolation (approximation) of signals defined on the sphere using the notion of reproducing-kernel Hilbert spaces (RKHS) and evaluate the performance of different isotropic kernels. Using the reproducing kernel and kernel inclusion properties of RKHS, we first present the formulation for the interpolation (approximation) of a signal on the sphere from its measurements. Later, we analyse the performance of different isotropic univariate kernels: Abel Poisson kernel, Von Mises-Fisher kernel, Legendre generating function and Lebedev kernel, by evaluating the signal interpolation accuracy.