Iterative extrapolation algorithm for data reconstruction over sphere

Given limited or incomplete measurement data on a sphere, a new iterative algorithm is proposed on how to extrapolate signal over the whole sphere. The algorithm is based on a priori assumption that the Fourier decomposition of the signal on the sphere has finite degree of spherical harmonic coefficients, that is, the signal is mode limited. The algorithm is a simple iteration involving only the spherical harmonic decomposition. It is proven that the algorithm converges to the original signal over observation region and the convergence rate is lower bounded by the largest eigenvalue of an associated Fredholm integral equation.