Wavelets for multichannel signals

Authors:
Silvia Bacchelli;Mariantonia Cotronei;Thomas Sauer
Affiliations:
Department of Mathematics, University of Bologna, Piazza di Porta S. Donato, 5, I-40127 Bologna, Italy;Department of Mathematics, University of Messina, Salita Sperone, 31, I-98166 Messina, Italy;Lehrstuhl für Numerische Mathematik, JustusLiebig-Universität Gieβen, HeinrichBuff-Ring 44, D-35392 Gieβen, Germany
Venue:
Advances in Applied Mathematics
Year:
2002

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Abstract

In this paper, we introduce and investigate multichannel wavelets, which are wavelets for vector fields, based on the concept of full rank subdivision operators. We prove that, like in the scalar and multiwavelet case, the existence of a scaling function with orthogonal integer translates guarantees the existence of a wavelet function, also with orthonormal integer translates. In this context, however, scaling functions as well as wavelets turn out to be matrix-valued functions.