Approximations for Gabor and wavelet frames

    Authors

    D. G. Han

    Comments

    Authors: contact us about adding a copy of your work at STARS@ucf.edu

    Abbreviated Journal Title

    Trans. Am. Math. Soc.

    Keywords

    Hilbert spaces; frames; unitary systems; approximation; Gabor family and; Gabor frames; wavelet frames; WEYL-HEISENBERG FRAMES; ALGEBRAS; SYSTEMS; Mathematics

    Abstract

    Let psi be a frame vector under the action of a collection of unitary operators 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.

    Journal Title

    Transactions of the American Mathematical Society

    Volume

    355

    Issue/Number

    8

    Publication Date

    1-1-2003

    Document Type

    Article

    Language

    English

    First Page

    3329

    Last Page

    3342

    WOS Identifier

    WOS:000182986900018

    ISSN

    0002-9947

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