Article ID Journal Published Year Pages File Type
838817 Nonlinear Analysis: Real World Applications 2009 9 Pages PDF
Abstract

In this paper, we study biorthogonal matrix-valued wavelets for analyzing matrix-valued signals based on matrix multiresolution analysis. Firstly, sufficient conditions for the existence of biorthogonal matrix-valued scaling function are established in terms of two-scale matrix symbols. Then we focus on the construction of biorthogonal matrix-valued wavelet. Two designs based on factorizations of biorthogonal two-scale matrix symbol are presented. In particular, explicit constructing formulations for biorthogonal matrix-valued wavelets are given. With these formulations, highpass filters {Gk}{Gk} and {G̃k} of biorthogonal matrix-valued wavelets can be given explicitly by lowpass filters {Hk}{Hk} and {H̃k} of their corresponding biorthogonal scaling functions. Finally, according to our designs, two examples of two-scale matrix filters are given.

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Physical Sciences and Engineering Engineering Engineering (General)
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