Fast extrapolation of band-limited signals on the 2-sphere

In this work, we develop a fast conjugate gradient based method for the extrapolation of band-limited signals. The problem of signal extrapolation on the sphere finds applications in many fields including acoustics, cosmology and geophysics. In comparison to the existing extrapolation methods of computationally complexity O(L6), the complexity of the proposed method is O(L3). We also provide analysis of the computational complexity of the proposed method and review the considerations which are required to be taken into account during the implementation of the proposed extrapolation method in practice. We finally conduct numerical experiments to analyse the extrapolation accuracy and demonstrate the convergence of the proposed method.