Wavelets and wavelet-like transforms on the sphere and their application to geophysical data inversion
Data Analysis, Statistics and Probability
2013-06-14 v1 Geophysics
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.
Keywords
Cite
@article{arxiv.1109.1718,
title = {Wavelets and wavelet-like transforms on the sphere and their application to geophysical data inversion},
author = {Frederik J. Simons and Ignace Loris and Eugene Brevdo and Ingrid C. Daubechies},
journal= {arXiv preprint arXiv:1109.1718},
year = {2013}
}
Comments
15 pages, 11 figures, submitted to the Proceedings of the SPIE 2011 conference Wavelets and Sparsity XIV