Matrix-Valued and Quaternion Wavelets

  title={Matrix-Valued and Quaternion Wavelets},
  author={Paul Ginzberg and Andrew T. Walden},
  journal={IEEE Transactions on Signal Processing},
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… CONTINUE READING

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