Wavelet transform on manifolds: Old and new approaches
(2010) Applied and Computational Harmonic Analysis — Vol. 28, n° 2, p. 189-202 (2010)
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- Authors
Antoine, Jean-Pierre 
- Abstract
- Given a two-dimensional smooth manifold M and a bijective projection p from M on a fixed plane (or a subset of that plane), we explore systematically how a wavelet transform (WT) on M may be generated from a plane WT by the inverse projection p(-1). Examples where the projection maps the whole manifold onto a plane include the two-sphere, the upper sheet of the two-sheeted hyperboloid and the Paraboloid. When no such global projection is available, the construction may be performed locally, i.e., around a given point on M. We apply this procedure both to the continuous WT, already treated in the literature, and to the discrete WT. Finally, we discuss the case of a WT oil a graph, for instance, the graph defined by linking the elements of a discrete set of points on the manifold. (C) 2009 Elsevier Inc. All rights reserved.
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Citations
Antoine, J.-P., Rosca, D., & Vandergheynst, P. (2010). Wavelet transform on manifolds: Old and new approaches. Applied and Computational Harmonic Analysis, 28(2), 189-202. https://doi.org/10.1016/j.acha.2009.10.002 (Original work published 2010)