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.
| Original language | English (US) |
|---|---|
| Title of host publication | Wavelets and Sparsity XIV |
| DOIs | |
| State | Published - Nov 2 2011 |
| Event | Wavelets and Sparsity XIV - San Diego, CA, United States Duration: Aug 21 2011 → Aug 24 2011 |
Publication series
| Name | Proceedings of SPIE - The International Society for Optical Engineering |
|---|---|
| Volume | 8138 |
| ISSN (Print) | 0277-786X |
Other
| Other | Wavelets and Sparsity XIV |
|---|---|
| Country | United States |
| City | San Diego, CA |
| Period | 8/21/11 → 8/24/11 |
All Science Journal Classification (ASJC) codes
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics
- Computer Science Applications
- Applied Mathematics
- Electrical and Electronic Engineering
Keywords
- frames
- geophysics
- inverse theory
- localization
- sparsity
- spherical harmonics
- wavelets
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Simons, F. J., Loris, I., Brevdo, E., & Daubechies, I. C. (2011). Wavelets and wavelet-like transforms on the sphere and their application to geophysical data inversion. In Wavelets and Sparsity XIV [81380X] (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 8138). https://doi.org/10.1117/12.892285