Accurate Reconstruction of Finite Rate of Innovation Signals on the Sphere

Abstract

We propose a method for the accurate and robust reconstruction of the non-bandlimited finite rate of innovation signals on the sphere. For signals consisting of a finite number of Dirac functions on the sphere, we develop an annihilating filter based method for the accurate recovery of parameters of the Dirac functions using a finite number of observations of the bandlimited signal. In comparison to existing techniques, the proposed method enables more accurate reconstruction primarily due to the better conditioning of systems involved in the recovery of parameters. In order to reconstruct K Diracs on the sphere, the proposed method requires samples of the signal bandlimited in the spherical harmonic ({\text{SH}}) domain at SH degree equal or greater than K + \sqrt {K + \frac{1}{4}} - \frac{1}{2}. In comparison to the existing state-of-the-art technique, the required bandlimit, and consequently the number of samples, of the proposed method is (approximately) the same. We also conduct numerical experiments to demonstrate that the proposed technique is more accurate than the existing methods by a factor of {10^7} or more for 2 \leq K \leq 20.