Tight framelets and fast framelet filter bank transforms on manifolds

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)64-95
Journal / PublicationApplied and Computational Harmonic Analysis
Issue number1
Online published8 Feb 2018
Publication statusPublished - Jan 2020


Tight framelets on a smooth and compact Riemannian manifold M provide a tool of multiresolution analysis for data from geosciences, astrophysics, medical sciences, etc. This work investigates the construction, characterizations, and applications of tight framelets on such a manifold M. Characterizations of the tightness of a sequence of framelet systems for L(M) in both the continuous and semi-discrete settings are provided. Tight framelets associated with framelet filter banks on M can then be easily designed and fast framelet filter bank transforms on M are shown to be realizable with nearly linear computational complexity. Explicit construction of tight framelets on the sphere S2 as well as numerical examples are given.

Research Area(s)

  • Affine system, Compact Riemannian manifold, Fast spherical harmonic transform, FFT, Filter bank, Laplace-Beltrami operator, Quadrature rule, Tight framelets, Unitary extension principle