Antoine, Jean-PierreRosca, DanielaVandergheynst, Pierre2009-04-272009-04-272009-04-27201010.1016/j.acha.2009.10.002https://infoscience.epfl.ch/handle/20.500.14299/38139WOS:000275136900005Given a two-dimensional smooth manifold M and a bijective pro jection 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. 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 pro jection 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 on a graph, for instance, the graph defined by linking the elements of a discrete set of points on the manifold.waveletsharmonic analysisLTS2lts2text::journal::journal article::research article