Designing Hilbert-Pair of wavelets: Recent progress and future trends

The dual-tree complex wavelet transform is a recent development that overcomes some of the limitations, such as shift variancy, of the traditional critically sampled real wavelet transform. The transform is based on the use of a pair of filter banks whose corresponding wavelet functions are related through the Hilbert transform. The design of Hilbert-Pairs is more complicated than a single filter bank as there are more constraints that need to be satisfied. This area is still relatively new and there is much scope for innovation. This paper will first re-visit the design criteria to fix ideas. This is followed by a survey recent progress and discussion of some possible future directions.