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Splines and Wavelets on Geophysically Relevant Manifolds

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Handbook of Geomathematics

Abstract

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

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Authors and Affiliations

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

    Isaac Pesenson

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  1. Isaac Pesenson
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Correspondence to Isaac Pesenson .

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Editors and Affiliations

  1. Geomathematics Group, University of Kaiserslautern, Kaiserslautern, Germany

    Willi Freeden

  2. Department of Mathematics, University of Central Florida, Orlando, Florida, USA

    M. Zuhair Nashed

  3. Computational Mathematics, Technische Universität Braunschweig, Braunschweig, Germany

    Thomas Sonar

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Pesenson, I. (2015). Splines and Wavelets on Geophysically Relevant Manifolds. In: Freeden, W., Nashed, M., Sonar, T. (eds) Handbook of Geomathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54551-1_67

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