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

Alain Plattner; Frederik J. Simons

doi:10.1117/12.2024703

26 September 2013 A spatiospectral localization approach for analyzing and representing vector-valued functions on spherical surfaces

Alain Plattner, Frederik J. Simons

Author Affiliations +

Proceedings Volume 8858, Wavelets and Sparsity XV; 88580N (2013) https://doi.org/10.1117/12.2024703
Event: SPIE Optical Engineering + Applications, 2013, San Diego, California, United States

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.

Citation Download Citation

Alain Plattner and Frederik J. Simons "A spatiospectral localization approach for analyzing and representing vector-valued functions on spherical surfaces", Proc. SPIE 8858, Wavelets and Sparsity XV, 88580N (26 September 2013); https://doi.org/10.1117/12.2024703

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available