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A filter design technique for improving the directional selectivity of the first scale of the dual-tree complex wavelet transform

Bart Goossens (UGent) , Aleksandra Pizurica (UGent) and Wilfried Philips (UGent)
Author
Organization
Abstract
The dual-tree complex wavelet transform (DT-CWT) uses approximate Hilbert transform pairs of wavelet, which requires that the filters of each tree of the dual-tree structure should be delayed approximately one half sample from each other. However, the filters of the first (finest) scale of the transform do not obey this condition, resulting in a poor directional selectivity for the first scale. In this paper, we describe a design technique for first-scale infinite impulse response (IIR) wavelet filters, that solves this problem. Results demonstrate that a much better directional selectivity is obtained, which indicates a performance improvement for many applications that use the DT-CWT where the preservation of high-frequency information is important.
Keywords
IIR filters, wavelet transforms, trees (mathematics), Hilbert transforms

Citation

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MLA
Goossens, Bart, Aleksandra Pizurica, and Wilfried Philips. “A Filter Design Technique for Improving the Directional Selectivity of the First Scale of the Dual-tree Complex Wavelet Transform.” 2009 16TH IEEE INTERNATIONAL CONFERENCE ON IMAGE PROCESSING, VOLS 1-6. New York, NY, USA: IEEE, 2009. 3761–3764. Print.
APA
Goossens, B., Pizurica, A., & Philips, W. (2009). A filter design technique for improving the directional selectivity of the first scale of the dual-tree complex wavelet transform. 2009 16TH IEEE INTERNATIONAL CONFERENCE ON IMAGE PROCESSING, VOLS 1-6 (pp. 3761–3764). Presented at the 16th IEEE International conference on Image Processing (ICIP 2009), New York, NY, USA: IEEE.
Chicago author-date
Goossens, Bart, Aleksandra Pizurica, and Wilfried Philips. 2009. “A Filter Design Technique for Improving the Directional Selectivity of the First Scale of the Dual-tree Complex Wavelet Transform.” In 2009 16TH IEEE INTERNATIONAL CONFERENCE ON IMAGE PROCESSING, VOLS 1-6, 3761–3764. New York, NY, USA: IEEE.
Chicago author-date (all authors)
Goossens, Bart, Aleksandra Pizurica, and Wilfried Philips. 2009. “A Filter Design Technique for Improving the Directional Selectivity of the First Scale of the Dual-tree Complex Wavelet Transform.” In 2009 16TH IEEE INTERNATIONAL CONFERENCE ON IMAGE PROCESSING, VOLS 1-6, 3761–3764. New York, NY, USA: IEEE.
Vancouver
1.
Goossens B, Pizurica A, Philips W. A filter design technique for improving the directional selectivity of the first scale of the dual-tree complex wavelet transform. 2009 16TH IEEE INTERNATIONAL CONFERENCE ON IMAGE PROCESSING, VOLS 1-6. New York, NY, USA: IEEE; 2009. p. 3761–4.
IEEE
[1]
B. Goossens, A. Pizurica, and W. Philips, “A filter design technique for improving the directional selectivity of the first scale of the dual-tree complex wavelet transform,” in 2009 16TH IEEE INTERNATIONAL CONFERENCE ON IMAGE PROCESSING, VOLS 1-6, Cairo, Egypt, 2009, pp. 3761–3764.
@inproceedings{1002630,
  abstract     = {The dual-tree complex wavelet transform (DT-CWT) uses approximate Hilbert transform pairs of wavelet, which requires that the filters of each tree of the dual-tree structure should be delayed approximately one half sample from each other. However, the filters of the first (finest) scale of the transform do not obey this condition, resulting in a poor directional selectivity for the first scale. In this paper, we describe a design technique for first-scale infinite impulse response (IIR) wavelet filters, that solves this problem. Results demonstrate that a much better directional selectivity is obtained, which indicates a performance improvement for many applications that use the DT-CWT where the preservation of high-frequency information is important.},
  author       = {Goossens, Bart and Pizurica, Aleksandra and Philips, Wilfried},
  booktitle    = {2009 16TH IEEE INTERNATIONAL CONFERENCE ON IMAGE PROCESSING, VOLS 1-6},
  isbn         = {9781424456536},
  keywords     = {IIR filters,wavelet transforms,trees (mathematics),Hilbert transforms},
  language     = {eng},
  location     = {Cairo, Egypt},
  pages        = {3761--3764},
  publisher    = {IEEE},
  title        = {A filter design technique for improving the directional selectivity of the first scale of the dual-tree complex wavelet transform},
  url          = {http://dx.doi.org/10.1109/ICIP.2009.5414309},
  year         = {2009},
}

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