Revisiting metrics for evaluating the inhomogeneous anisotropic filters defined on the sphere

Abstract:

The inhomogeneous anisotropic filters are the most general form of filters defined on the sphere. Due to their adaptive nature on the sphere, it is difficult to define metrics for evaluating their performance. Currently, the metrics that assess the optimal filtering levels -- processing gain and processing loss -- work very well for homogeneous isotropic filters, but do not depict the gains made by the inhomogeneous anisotropic filters. In this study we analyse the problems associated with the current methods and develop metrics that make use of the matrix properties of the filtered and unfiltered covariance matrices to alleviate the identified problems. We take examples from processing GRACE/GRACE-FO data to illustrate the problem and its solution.