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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

11 Scopus citations

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 languageEnglish (US)
Title of host publicationWavelets and Sparsity XIV
DOIs
StatePublished - Nov 2 2011
EventWavelets and Sparsity XIV - San Diego, CA, United States
Duration: Aug 21 2011Aug 24 2011

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
Volume8138
ISSN (Print)0277-786X

Other

OtherWavelets and Sparsity XIV
CountryUnited States
CitySan Diego, CA
Period8/21/118/24/11

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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  • Cite this

    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