Local computation and estimation of wavelet coefficients in the dual-tree complex wavelet transform

The dual-tree complex wavelet transform (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 properties. Because of its improvements in this regards, the dual-tree has been successfully demonstrated in many image processing applications such as denoising, motion estimation, image classification, and even compression despite its redundancy nature. Our goal is to be able to predict the wavelet coefficients of one tree knowing those of the other in the dual-tree complex wavelet transform. In other words, given a subset of real coefficients in the DTCWT, how can we compute or estimate accurately the imaginary coefficients in the same local neighborhood and vice versa? The proposed method is based on exploiting the orthogonality properties of one of the nicest dual-tree designs - the Q-shift complex wavelets.