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

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.