Complex wavelet transform
The complex wavelet transform is a two-dimensional wavelet transform which provides multiresolution, sparse representation, and useful characterization of the structure of an image. Futher, it purveys a high degree of shift-invariance in its magnitude. However, a drawback to this transform is that it is four-times redundant compared to a separable discrete wavelet transform (DWT). Complex wavelet transform (CWT) is a complex-valued extension to the standard DWT.
The use of complex wavelets in image processing was originally set up in 1997 by Nick Kingsbury of Cambridge University.
The implementation of a dual-tree complex DWT of a signal is described on Matlab [1].