On the Dual-Tree Complex Wavelet Packet and -Band Transforms

Authors:
I. Bayram;I.W. Selesnick
Affiliations:
Dept. of Electr. & Comput. Eng., Polytech. Univ., Brooklyn, OH;-
Venue:
IEEE Transactions on Signal Processing
Year:
2008

Citing 0
Cited 3

Image and video denoising using adaptive dual-tree discrete wavelet packets

IEEE Transactions on Circuits and Systems for Video Technology
A new shift-invariance of discrete-time systems and its application to discrete wavelet transform analysis

IEEE Transactions on Signal Processing
Analytic wavelet packets: combining the dual-tree approach with wavelet packets for signal analysis and filtering

IEEE Transactions on Signal Processing

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Abstract

The two-band discrete wavelet transform (DWT) provides an octave-band analysis in the frequency domain, but this might not be ldquooptimalrdquo for a given signal. The discrete wavelet packet transform (DWPT) provides a dictionary of bases over which one can search for an optimal representation (without constraining the analysis to an octave-band one) for the signal at hand. However, it is well known that both the DWT and the DWPT are shift-varying. Also, when these transforms are extended to 2-D and higher dimensions using tensor products, they do not provide a geometrically oriented analysis. The dual-tree complex wavelet transform , introduced by Kingsbury, is approximately shift-invariant and provides directional analysis in 2-D and higher dimensions. In this paper, we propose a method to implement a dual-tree complex wavelet packet transform , extending the as the DWPT extends the DWT. To find the best complex wavelet packet frame for a given signal, we adapt the basis selection algorithm by Coifman and Wickerhauser, providing a solution to the basis selection problem for the . Lastly, we show how to extend the two-band to an -band (provided that ) using the same method.