Affine frames, quasi-affine frames, and their duals

Affine frames, quasi-affine frames, and their duals

The notion of quasi-affine frame was recently introduced by Ron and Shen [9] in order to achieve shift-invariance of the discrete wavelet transform. In this paper, we establish a duality-preservation theorem for quasi-affine frames. Furthermore, the preservation of frame bounds when changing an affi...

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Veröffentlicht in:Advances in computational mathematics 1998-01, Vol.8 (1-2), p.1-17
Hauptverfasser: Chui, Charles K, Shi Xianliang, Stöckler Joachim
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Computational mathematics
Discrete Wavelet Transform
Frames
Invariance
Operators
Wavelet transforms
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creator Chui, Charles K
Shi Xianliang
Stöckler Joachim
description The notion of quasi-affine frame was recently introduced by Ron and Shen [9] in order to achieve shift-invariance of the discrete wavelet transform. In this paper, we establish a duality-preservation theorem for quasi-affine frames. Furthermore, the preservation of frame bounds when changing an affine frame to a quasi-affine frame is shown to hold without the decay assumptions in [9]. Our consideration leads naturally to the study of certain sesquilinear operators which are defined by two affine systems. The translation-invariance of such operators is characterized in terms of certain intrinsic properties of the two affine systems.
doi_str_mv 10.1023/A:1018975725857
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subjects Computational mathematics
Discrete Wavelet Transform
Frames
Invariance
Operators
Wavelet transforms
title Affine frames, quasi-affine frames, and their duals
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