A new complex-directional wavelet transform and its application to image denoising

This paper describes a new complex-directional expansive perfect reconstruction two-dimensional wavelet transform. Each complex wavelet is oriented along one of six possible directions, and the magnitude of each complex wavelet has a smooth bell-shape. The transform is based both on the complex dual-tree wavelet transform introduced by Kingsbury (see Phil. Trans. Royal Society London, A, September 1999 and Applied and Computational Harmonic Analysis, vol.10, no.3, p.234-53, 2001) and on the double-density DWT. It is designed so as to possess simultaneously the properties of the complex dual-tree DWT and the double-density DWT. The paper also describes a simple subband-dependent data-driven denoising algorithm for use with this transform. An example is shown to illustrate the performance of the denoising algorithm and the transform.