Nonparametric least squares regression for image reconstruction on the sphere

This paper addresses the problem of interpolating signals defined on a 2d sphere from non-uniform samples. We present an interpolation method based on locally weighted linear and nonlinear regression, which takes into account the differences in importance of neighboring samples for signal reconstruction. We show that for optimal kernel function variance, the proposed method performs interpolation more accurately than the nearest neighbor method, especially in noisy conditions. Moreover, this method does not have memory limitations which set the upper bound on the possible interpolation points number, like in the method presented in the work of Tosic and Frossard (2006).