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Matrix-Valued and Quaternion Wavelets

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2 Author(s)
Ginzberg, P. ; Dept. of Math., Imperial Coll. London, London, UK ; Walden, A.T.

Wavelet transforms using matrix-valued wavelets (MVWs) can process the components of vector-valued signals jointly. We construct some novel families of non-trivial orthogonal n×n MVWs for n=2 and 4 having several vanishing moments. Some useful uniqueness and non-existence results for filters with certain lengths and numbers of vanishing moments are proved. The matrix-based method for n=4 is used for the construction of a non-trivial symmetric quaternion wavelet with compact support. This is an important addition to the literature where existing quaternion wavelet designs suffer from some critical problems.

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Signal Processing, IEEE Transactions on  (Volume:61 ,  Issue: 6 )