Conjugate gradient algorithm for extrapolation of sampled bandlimited signals on the 2-sphere

In this paper, we consider the problem of signal extrapolation for discrete (i.e., sampled) signals on the sphere. We propose conjugate gradient based algorithm for estimating a signal on the sphere from limited or incomplete measurements in a spatial domain. We prove that the proposed algorithm is guaranteed to converge and show that it has faster convergence compared to the Papoulis algorithm. The results also show that the incomplete measurements distributed in different non-connected spatial regions yield better extrapolation results, compared to the connected region case.