Signal estimation from incomplete data on the sphere

An iterative algorithm is proposed to estimate a signal on the sphere from limited or incomplete measurements. 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 or low-pass in character. The iteration algorithm is to reduce the mean square error between the spherical harmonic coefficients of the estimated and that of the original signal. Convergence and its numerical properties are determined using spherical harmonic analysis. A practical example of antenna radiation pattern reconstruction is given with detailed analysis.