An Improved Iterative Algorithm for Band-Limited Signal Extrapolation on the Sphere

Abstract

We develop an algorithm for the extrapolation of band-limited signals on the sphere. The proposed algorithm improves the accuracy of the extrapolation of band-limited signal by using the information contained in the out-of-band harmonic coefficients of the signal to update the extrapolated signal at each iteration. The estimation of signals on the sphere from incomplete measurements finds applications in acoustics, cosmology and geophysics. The proposed algorithm does not only exploit the band-limited property of the signal, that is, force the harmonic coefficients outside the band-limit to zero, at each iteration as carried out in the existing algorithms but also uses the harmonic coefficients outside the harmonic domain to improve the accuracy of signal extrapolation. To demonstrate the improvement in the accuracy enabled by the proposed algorithm, we conduct numerical experiments and compare the results of the proposed algorithm with the existing iterative conjugate gradient method.