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Proceedings Paper

Painless approximation of dual frames, with applications to shift-invariant systems
Author(s): Thomas Strohmer
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Paper Abstract

We analyze the relation between infinite-dimensional frame theory and finite-dimensional models for frames as they are used for numerical algorithms. Special emphasis in this paper is on perfect reconstruction oversampled filter banks, also known as shift-invariant frames. For certain finite- dimensional models it is shown that the corresponding finite dual frame provides indeed an approximation of the dual frame of the original infinite-dimensional dual frame. For filter banks on l2 (Z) we derive error estimates for the approximation of the synthesis filter bank when the analysis filter bank satisfies certain decay conditions. We show how one has to design the finite-dimensional model to preserve important structural properties of filter banks, such as polyphase representation. Finally an efficient regularization method is presented to solve the ill-posed problem arising when approximating the dual frame on L2(R) via truncated Gram matrix.

Paper Details

Date Published: 26 October 1999
PDF: 11 pages
Proc. SPIE 3813, Wavelet Applications in Signal and Image Processing VII, (26 October 1999); doi: 10.1117/12.366819
Show Author Affiliations
Thomas Strohmer, Univ. of California/Davis (United States)

Published in SPIE Proceedings Vol. 3813:
Wavelet Applications in Signal and Image Processing VII
Michael A. Unser; Akram Aldroubi; Andrew F. Laine, Editor(s)

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