A Simple Construction for the M-Band Dual-Tree Complexwavelet Transform

The dual-tree complex wavelet transform (DT-CWT) which utilizes two 2-band discrete wavelet transforms (DWT) was recently extended to M-band by Chaux et al. In this paper, we provide a simple construction method for an M-band DT-CWT, with M = r^d where r, d isin Z. In particular, we show how to extend a given r-band DT-CWT to an r^d -band one. For convenience, the case where r = 2, d = 2 is considered. However, the scheme can be extended to general {r, d} pairs straightforwardly. The extension to 2-D which achieves a directional analysis is also provided