A new implementation of the hyperanalytic wavelet transform

The property of shift-invariance associated with a good directional selectivity are important for the application of a wavelet transform in many fields of image processing. Unfortunately, the 2D discrete wavelet transform is shift-variant and has a reduced directional selectivity. These disadvantages can be attenuated if a complex wavelet transform is used. In this paper, we propose a new implementation of such a wavelet transform, recently introduced, the hyperanalytic wavelet transform. It is quasi shift-invariant, it has a good directional selectivity, and a reduced degree of redundancy of 4 in 2D. The implementation proposed is very simple. The properties already mentioned are proved by simulation.