Equivalence relation between multiresolution analyses of L2(R)

Manos Papadakis; Theodoros Stavropoulos; Nicholas Kalouptsidis

doi:10.1117/12.205458

6 April 1995 Equivalence relation between multiresolution analyses of L²(R)

Manos Papadakis, Theodoros Stavropoulos, Nicholas Kalouptsidis

Proceedings Volume 2491, Wavelet Applications II; (1995) https://doi.org/10.1117/12.205458
Event: SPIE's 1995 Symposium on OE/Aerospace Sensing and Dual Use Photonics, 1995, Orlando, FL, United States

Abstract

This paper is concerned with the development of an equivalence relation between two multiresolution analyses of L²(R). The relation called unitary equivalence is created by the action of a unitary operator in a way that the multiresolution structure and the decomposition and reconstruction algorithms remain invariant. A characterization in terms of the scaling functions of the multiresolution analyses is given. Distinct equivalence classes of multiresolution analyses are derived. Finally, we prove that B-splines give rise to non- equivalent examples.

Citation Download Citation

Manos Papadakis, Theodoros Stavropoulos, and Nicholas Kalouptsidis "Equivalence relation between multiresolution analyses of L²(R)", Proc. SPIE 2491, Wavelet Applications II, (6 April 1995); https://doi.org/10.1117/12.205458

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