Approximations for Gabor and wavelet frames

Han, Deguang

doi:10.1090/S0002-9947-03-03047-2

Approximations for Gabor and wavelet frames
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by Deguang Han

Trans. Amer. Math. Soc. 355 (2003), 3329-3342

DOI: https://doi.org/10.1090/S0002-9947-03-03047-2

Published electronically: April 24, 2003

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Abstract:

Let $\psi$ be a frame vector under the action of a collection of unitary operators $\mathcal U$. Motivated by the recent work of Frank, Paulsen and Tiballi and some application aspects of Gabor and wavelet frames, we consider the existence and uniqueness of the best approximation by normalized tight frame vectors. We prove that for any frame induced by a projective unitary representation for a countable discrete group, the best normalized tight frame (NTF) approximation exists and is unique. Therefore it applies to Gabor frames (including Gabor frames for subspaces) and frames induced by translation groups. Similar results hold for semi-orthogonal wavelet frames.

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