The Design and Use of Steerable Filters
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ten lectures on wavelets
The design of approximate Hilbert transform pairs of wavelet bases
IEEE Transactions on Signal Processing
SDP Approximation of a Fractional Delay and the Design of Dual-Tree Complex Wavelet Transform
IEEE Transactions on Signal Processing
Image analysis using a dual-tree M-band wavelet transform
IEEE Transactions on Image Processing
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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.