Design of Regular Wavelets Using a Three-Step Lifting Scheme

We propose structural multidimensional multichannel filter banks with desirable numbers of vanishing moments for the analysis and synthesis banks. For a two-channel filter bank, we use a three-step lifting scheme as opposed to the conventional two-step lifting method in order to provide more symmetry between the analysis and synthesis filters. We show that the resulting filters have more regularity, lower frame bounds ratio, and better frequency selectivity. We also extend our design to a general multichannel framework. Three steps of lifting scheme provides us a degree of freedom which we can benefit from toward a more flexible design.