The dual-tree complex wavelet transform: a new technique for shift invariance and directional filters

Abstract

As Kingsbury '97 + Computation time of Dual Tree WT is 2 m times that of FWT in m-D. Shift invariance with perfect reconstruction can be approximated with a real WT by doubling the sampling re ateachpoint in the tree, by eliminating the first downsampling step. Split teh data into two filter trees offset by one sample from each other. If the filters are chosen ot be odd length in one tree and even in the other, then these are equivalent to the real and imainary parts of a single tree using a complex wavelet. This allows efficient representation of compex wavelets with short filters.