Wavelets and wavelet-like transforms on the sphere and their application to geophysical data inversion
Frederik Jozef Simons, Ignace Loris, Eugene Brevdo, Ingrid C. Daubechies · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2011
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.