Wavelets for multichannel signals |
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| Authors: | Silvia Bacchelli Mariantonia Cotronei Thomas Sauer |
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| Institution: | a Department of Mathematics, University of Bologna, Piazza di Porta S. Donato, 5, I-40127, Bologna, Italy;b Department of Mathematics, University of Messina, Salita Sperone, 31, I-98166, Messina, Italy;c Lehrstuhl für Numerische Mathematik, Justus–Liebig-Universität Gießen, Heinrich–Buff-Ring 44, D-35392, Gießen, Germany |
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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. |
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| Keywords: | Matrix wavelets Multichannel wavelets Multiwavelets Full rank subdivision Stationary subdivision |
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