Implementation and application of local computation of wavelet coefficients in the dual-tree complex wavelets

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 these aspects, the dual-tree has been widely used in many image processing applications such as denoising, motion estimation, image classification and even compression despite its redundant representation. In our previous work, we were able to accurately and locally estimate the wavelet coefficients of one tree in the DT CWT, given a subset of the other tree coefficients. Our method is based on exploiting the orthogonality properties of one of the nicest dual-tree designs - the Q-shift complex wavelets. In this paper, we demonstrate the implementation of multiple level of decomposition as well as the two dimensional realization with application to region of interest (ROI) imaging applications such as denoising.