On Local Computation of Wavelet Coefficients in the Dual-tree CWT

The dual-tree complex wavelet (DT CWT) was introduced to overcome the disadvantages of the traditional fully decimated discrete wavelet transform (DWT), namely the shift-variance and the poor directional selectivity. Because of its desirable properties, the dual-tree has been successful in many image processing applications. However, its use in data compression has been hindered because of its redundancy. Our goal is to be able to predict the wavelet coefficients of one tree knowing those of the other tree. The proposed method is based on exploiting the orthogonality properties of one of the nicest dual-tree designs, the Q-shift complex wavelets.