Splines and Wavelets on Geophysically Relevant Manifolds

2014/03/04 by Isaac Z. Pesenson, Isaac Pesenson, Pesenson, Isaac · 1 citation
Computer Science · Immunology and Microbiology · Mathematics · Medicine · #Biomarkers in Disease Mechanisms #Image and Signal Denoising Methods #Medical Imaging Techniques and Applications #math.FA

paper · pdf · doi:10.48550/arxiv.1403.0963

The final publication is available at http://www.springerlink.com

arxiv created 2014/03/04 · arxiv updated 2014/03/06

Abstract

Analysis on the unit sphere \mathbbS² found many applications in seismology, weather prediction, astrophysics, signal analysis, crystallography, computer vision, computerized tomography, neuroscience, and statistics. In the last two decades, the importance of these and other applications triggered the development of various tools such as splines and wavelet bases suitable for the unit spheres \mathbbS², >>\mathbbS³ and the rotation group SO(3). Present paper is a summary of some of results of the author and his collaborators on generalized (average) variational splines and localized frames (wavelets) on compact Riemannian manifolds. The results are illustrated by applications to Radon-type transforms on \mathbbS^d and SO(3).

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• Sampling, splines and frames on compact manifolds

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