Partial parameterization of orthogonal wavelet matrix filters

Authors:
Mariantonia Cotronei;Matthias Holschneider
Affiliations:
DIMET, Universití Mediterranea di Reggio Calabria, Via Graziella loc. Feo di Vito, I-89122 Reggio Calabria, Italy;Institut für Mathematik, Universität Potsdam, Am Neuen Palais 10, D-14469, Potsdam, Germany
Venue:
Journal of Computational and Applied Mathematics
Year:
2013

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Abstract

In this paper we propose a procedure which allows the construction of a large family of FIR dxd matrix wavelet filters by exploiting the one-to-one correspondence between QMF systems and orthogonal operators which commute with the shifts by two. A characterization of the class of filters of full rank type that can be obtained with such procedure is given. In particular, we restrict our attention to a special construction based on the representation of SO(2d) in terms of the elements of its Lie algebra. Explicit expressions for the filters in the case d=2 are given, as a result of a local analysis of the parameterization obtained from perturbing the Haar system.