Wavelets on the sphere

Pierre Vandergheynst, Yves Wiaux

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

In many application fields ranging from astrophysics and geophysics to neuroscience, computer vision, and computer graphics, data to be analyzed are defined as functions on the sphere. In all these situations, there are compelling rea- sons to design dedicated data analysis tools that are adapted to spherical geometry, for one cannot simply project the data in Euclidean geometry without having to deal with severe distortions. The wavelet transform has become a ubiquitous tool in signal processing mostly for its ability to exploit the multiscale nature of many data sets, and it is thus quite natural to generalize it to signals on the sphere. This generalization is not trivial, for the main ingredient of the wavelet theory, dilation, is not well defined on the sphere. Moreover, when turning to algorithms, one faces the problem that sampling data on the sphere is not an easy task either. In this chapter, we discuss recently developed results for the analysis and reconstruction of sig- nals on the sphere with wavelets, on the grounds of theory, implementation, and applications.
Original languageEnglish
Title of host publicationFour Short Courses in Harmonic Analysis
EditorsPeter Massoput, Brigit Forster-Heinlein
Place of PublicationBoston
PublisherBirkhäuser
Pages131-174
Number of pages44
ISBN (Print)978-0-8176-4890-9
Publication statusPublished - 2010

Publication series

NameApplied and Numerical Harmonic Analysis
ISSN (Print)2296-5009

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  • Cite this

    Vandergheynst, P., & Wiaux, Y. (2010). Wavelets on the sphere. In P. Massoput, & B. Forster-Heinlein (Eds.), Four Short Courses in Harmonic Analysis (pp. 131-174). (Applied and Numerical Harmonic Analysis). Birkhäuser.