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A new directional, low-redundancy, complex-wavelet transform

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3 Author(s)
Fernandes, F.C.A. ; Dept. of Electr. & Comput. Eng., Rice Univ., Houston, TX, USA ; van Spaendonck, Rutger L. ; Burrus, C.S.

Shift variance and poor directional selectivity, two major disadvantages of the discrete wavelet transform, have previously been circumvented either by using highly redundant, non-separable wavelet transforms or by using restrictive designs to obtain a pair of wavelet trees with a transform-domain redundancy of 4.0 in 2D. We demonstrate that excellent shift-invariance properties and directional selectivity may be obtained with a transform-domain redundancy of only 2.67 in 2D. We achieve this by projecting the wavelet coefficients from Selesnick's (Selesnick et al., 2000) almost-shift-invariant, double-density wavelet transform so as to separate approximately the positive and negative frequencies, thereby increasing directionality. Subsequent decimation and a novel inverse projection maintain the low redundancy while ensuring perfect reconstruction. Although our transform generates complex-valued coefficients allowing processing capabilities that are impossible with real-valued coefficients, it may be implemented with a fast algorithm that uses only real arithmetic. To demonstrate the efficacy of our new transform, we show that it achieves state-of-the-art performance in a seismic image-processing application

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Acoustics, Speech, and Signal Processing, 2001. Proceedings. (ICASSP '01). 2001 IEEE International Conference on  (Volume:6 )

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