Graph-based regularization for spherical signal interpolation

This paper addresses the problem of the interpolation of 2-d spherical signals from non-uniformly sampled and noisy data. We propose a graph-based regularization algorithm to improve the signal reconstructed by local interpolation methods such as nearest neighbour or kernel-based interpolation algorithms. We represent the signal as a function on a graph where weights are adapted to the particular geometry of the sphere. We then solve a total variation (TV) minimization problem with a modified version of Chambolle´s algorithm. Experimental results with noisy and uncomplete datasets show that the regularization algorithm is able to improve the result of local interpolation schemes in terms of reconstruction quality.