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Splines and Wavelets on Geophysically Relevant Manifolds

In: Handbook of Geomathematics

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  • Isaac Pesenson

    (Temple University, The author was supported in part by the National Geospatial-Intelligence Agency University Research Initiative (NURI), grant HM1582-08-1-0019. Department of Mathematics)

Abstract

Analysis on the unit sphere 𝕊 2 $$\mathbb{S}^{2}$$ 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 𝕊 2 $$\mathbb{S}^{2}$$ , 𝕊 3 $$\mathbb{S}^{3}$$ 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 𝕊 d $$\mathbb{S}^{d}$$ and SO(3).

Suggested Citation

  • Isaac Pesenson, 2015. "Splines and Wavelets on Geophysically Relevant Manifolds," Springer Books, in: Willi Freeden & M. Zuhair Nashed & Thomas Sonar (ed.), Handbook of Geomathematics, edition 2, pages 2527-2562, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-54551-1_67
    DOI: 10.1007/978-3-642-54551-1_67
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