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Semiorthogonal Multiresolution Analysis Frames inHigher Dimensions

Semiorthogonal Multiresolution Analysis Frames inHigher Dimensions Benedetto and Li proposed the theory of frame multiresolution analysis (FMRA) in one dimension. This paper generalizes Benedetto and Li’s theory of FMRA to higher dimensions with arbitrary integral expansive matrix dilations, and gives two necessary and sufficient conditions to characterize (semiorthogonal) multiresolution analysis frames for L 2(ℝ n ). One of the two conditions is put on the frame scaling function and the low-pass and high-pass filters only. Multiresolution analysis Parseval frames are also characterized. The theory is implemented to a bidimensional example with the nonseparable quincunx dilation $\scriptsize\bigl(\begin{array}{c@{\ }c}1&-1\\1&1\end{array}\bigr)$ , along with its potential application in subband signal processing. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Semiorthogonal Multiresolution Analysis Frames inHigher Dimensions

Acta Applicandae Mathematicae , Volume 111 (3) – Aug 15, 2009

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References (26)

Publisher
Springer Journals
Copyright
Copyright © 2009 by Springer Science+Business Media B.V.
Subject
Mathematics; Mechanics; Statistical Physics, Dynamical Systems and Complexity; Theoretical, Mathematical and Computational Physics; Computer Science, general; Mathematics, general
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/s10440-009-9544-z
Publisher site
See Article on Publisher Site

Abstract

Benedetto and Li proposed the theory of frame multiresolution analysis (FMRA) in one dimension. This paper generalizes Benedetto and Li’s theory of FMRA to higher dimensions with arbitrary integral expansive matrix dilations, and gives two necessary and sufficient conditions to characterize (semiorthogonal) multiresolution analysis frames for L 2(ℝ n ). One of the two conditions is put on the frame scaling function and the low-pass and high-pass filters only. Multiresolution analysis Parseval frames are also characterized. The theory is implemented to a bidimensional example with the nonseparable quincunx dilation $\scriptsize\bigl(\begin{array}{c@{\ }c}1&-1\\1&1\end{array}\bigr)$ , along with its potential application in subband signal processing.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Aug 15, 2009

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