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Spherical radial-basis-based kernel interpolation abounds in image sciencesincluding geophysical image reconstruction, climate trends description andimage rendering due to its excellent spatial localization property and perfectapproximation performance. However, in dealing with noisy data, kernelinterpolation frequently behaves not so well due to the large condition numberof the kernel matrix and instability of the interpolation process. In thispaper, we introduce a weighted spectral filter approach to reduce the conditionnumber of the kernel matrix and then stabilize kernel interpolation. The mainbuilding blocks of the proposed method are the well developed sphericalpositive quadrature rules and high-pass spectral filters. Using a recentlydeveloped integral operator approach for spherical data analysis, wetheoretically demonstrate that the proposed weighted spectral filter approachsucceeds in breaking through the bottleneck of kernel interpolation, especiallyin fitting noisy data. We provide optimal approximation rates of the new methodto show that our approach does not compromise the predicting accuracy.Furthermore, we conduct both toy simulations and two real-world dataexperiments with synthetically added noise in geophysical image reconstructionand climate image processing to verify our theoretical assertions and show thefeasibility of the weighted spectral filter approach.

Weighted Spectral Filters for Kernel Interpolation on Spheres: Estimates of Prediction Accuracy for Noisy Data