Matrix-Valued and Quaternion Wavelets

@article{Ginzberg2013MatrixValuedAQ,
  title={Matrix-Valued and Quaternion Wavelets},
  author={Paul Ginzberg and Andrew T. Walden},
  journal={IEEE Transactions on Signal Processing},
  year={2013},
  volume={61},
  pages={1357-1367}
}
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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References

Publications referenced by this paper.
Showing 1-10 of 40 references

Construction of quaternion-valued wavelets,

  • M. Bahri
  • Matematika, vol
  • 2010
Highly Influential
6 Excerpts

A new class of full rank filters in the context of digital color image processing.

  • S. Agreste, A. Vocaturo
  • In Proceedings of the 10th European Congress of…
  • 2009
Highly Influential
20 Excerpts

m-band orthogonal vector-valued multiwavelets,

  • L. Cui, T. Zhang
  • J. Appl. Maths. and Comput.,
  • 2008
Highly Influential
19 Excerpts

Quaternion-valued smooth orthogonal wavelets with short support and symmetry,

  • L. Peng, J. Zhao
  • Qian et al. Editors),
  • 2004
Highly Influential
4 Excerpts

On existence of matrix-valued wavelets,

  • B. M. Yu
  • Advanced Materials Research,
  • 2011
1 Excerpt

A new class of full rank fi lters in the context of digital color image processing , ” in

  • M. Cotronei S. Bacchelli, T. Sauer
  • Proc . 10 th Eur . Congress of ISS , ser…
  • 2009

B

  • L. Cui
  • Zhai & T. Zhang, “Existence and design of…
  • 2009
2 Excerpts

Existence and design of biorthogonal matrix - valued wavelets

  • B. Zhai, T. Zhang
  • Nonlin . Anal . : Real World Appl .
  • 2009

Construction and properties of orthogonal matrix-valued wavelets and wavelet packets,

  • Q. Chen, Z. Shi
  • Chaos, Solitons & Fractals,
  • 2008
2 Excerpts

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