The dual-tree complex wavelet transform: A new efficient tool for image restoration and enhancement

A new implementation of the Discrete Wavelet Transform is presented for applications such as image restoration and enhancement. It employs a dual tree of wavelet filters to obtain the real and imaginary parts of the complex wavelet coefficients. This introduces limited redundancy (4 : 1 for 2-dimensional signals) and allows the transform to provide approximate shift invariance and directionally selective filters (properties lacking in the traditional wavelet transform) while preserving the usual properties of perfect reconstruction and computational efficiency. We show how the dual-tree complex wavelet transform can provide a good basis for multi-resolution image denoising and de-blurring.