P. Ginzberg and A. T. Walden, IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 61, NO. 6, MARCH 15, 2013, pp. 1357-1367. DOI: http://dx.doi.org/10.1109/TSP.2012.2235434
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, https://spiral.imperial.ac.uk/handle/10044/1/12537