A spatiospectral localization approach for analyzing and representing vector-valued functions on spherical surfaces

Alain Plattner, Frederik Jozef Simons

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

2 Scopus citations

Abstract

We review the construction of three different Slepian bases on the sphere, and illustrate their theoretical behavior and practical use for solving ill-posed satellite inverse problems. The first basis is scalar, the second vectorial, and the third suitable for the vector representation of the harmonic potential fields on which we focus our analysis. When data are noisy and incompletely observed over contiguous domains covering parts of the sphere at satellite altitude, expanding the unknown solution in terms of a Slepian basis and seeking truncated expansions to achieve least-squares data fit has advantages over conventional approaches that include the ease with which the solutions can be computed, and a clear statistical understanding of the competing effects of solution bias and variance in modulating the mean squared error, as we illustrate with several new examples.

Original languageEnglish (US)
Title of host publicationWavelets and Sparsity XV
DOIs
StatePublished - Dec 9 2013
EventWavelets and Sparsity XV - San Diego, CA, United States
Duration: Aug 26 2013Aug 29 2013

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
Volume8858
ISSN (Print)0277-786X
ISSN (Electronic)1996-756X

Other

OtherWavelets and Sparsity XV
CountryUnited States
CitySan Diego, CA
Period8/26/138/29/13

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering

Keywords

  • Geomagnetism
  • Inverse theory
  • Satellite geodesy
  • Statistical methods
  • Vector spherical harmonics

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  • Cite this

    Plattner, A., & Simons, F. J. (2013). A spatiospectral localization approach for analyzing and representing vector-valued functions on spherical surfaces. In Wavelets and Sparsity XV [88580N] (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 8858). https://doi.org/10.1117/12.2024703