Abstract
This article presents a method for approximating spherical functions from discrete data of a block-wise grid structure. The essential ingredients of the approach are scaling and wavelet functions within a biorthogonalisation process generated by locally supported zonal kernel functions. In consequence, geophysically and geodetically relevant problems involving rotationinvariant pseudodifferential operators become attackable. A multiresolution analysis is formulated enabling a fast wavelet transform similar to the algorithms known from classical tensor product wavelet theory.
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Freeden, W., Schreiner, M. Biorthogonal Locally Supported Wavelets on the Sphere Based on Zonal Kernel Functions. J Fourier Anal Appl 13, 693–709 (2007). https://doi.org/10.1007/s00041-006-6905-0
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DOI: https://doi.org/10.1007/s00041-006-6905-0