Ginzberg + Walden: Matrix-Valued and Quaternion Wavelets

P. Ginzberg and A. T. Walden, IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 61, NO. 6, MARCH 15, 2013, pp. 1357-1367. DOI:

Abstract — 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 nxn 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.

Index Terms — Matrix-valued wavelet, multichannel wavelet,
multiwavelet, quaternion wavelet, vector-valued wavelet.

Source: S. Sangwine,


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