Wavelets and wavelet-like transforms on the sphere and their application to geophysical data inversion
arXiv:1109.1718 · doi:10.1117/12.892285
Abstract
Many flexible parameterizations exist to represent data on the sphere. In addition to the venerable spherical harmonics, we have the Slepian basis, harmonic splines, wavelets and wavelet-like Slepian frames. In this paper we focus on the latter two: spherical wavelets developed for geophysical applications on the cubed sphere, and the Slepian "tree", a new construction that combines a quadratic concentration measure with wavelet-like multiresolution. We discuss the basic features of these mathematical tools, and illustrate their applicability in parameterizing large-scale global geophysical (inverse) problems.
15 pages, 11 figures, submitted to the Proceedings of the SPIE 2011 conference Wavelets and Sparsity XIV
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