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Proceedings Paper

Unitary mappings and an equivalence relation between multiresolution analyses of L2(R)
Author(s): Manos Papadakis
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Paper Abstract

This paper provides classes of unitary operations of L2(R) contained in the commutant of the Shift operator, such that for any pair of multiresolution analyses of L2(R) there exists a unitary operator in one of these classes, which maps all the scaling functions of the first multiresolution analysis to scaling functions of the other. We also develop an equivalence relation between multiresolution analyses of L2(R). This relation called unitary equivalence is created by the action of a group of unitary operators contained in all the classes mentioned previously, in a way that the multiresolution structure and the Decomposition and Reconstruction algorithms remain invariant. A characterization of this relation in terms of the scaling functions is given. Distinct equivalence classes of multiresolution analyses are derived. Finally, we prove that B-splines give rise to non-equivalent examples.

Paper Details

Date Published: 1 September 1995
PDF: 12 pages
Proc. SPIE 2569, Wavelet Applications in Signal and Image Processing III, (1 September 1995); doi: 10.1117/12.217599
Show Author Affiliations
Manos Papadakis, Hellenic Military Academy (Greece)


Published in SPIE Proceedings Vol. 2569:
Wavelet Applications in Signal and Image Processing III
Andrew F. Laine; Michael A. Unser, Editor(s)

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