Higher density dual-tree discrete wavelet transform

A new family of dual-tree based dyadic complex (approximate analytic) wavelet tight frames that is an extension of higher density discrete wavelet transform (DWT) introduced by Selesnick (in A Higher-density DWT, IEEE Transaction on Signal Processing) is proposed. Because the proposed wavelet frames are good combinations of the higher-density DWT and the dual tree complex wavelet transform, the corresponding new wavelet transform can be potentially applied to the applications when properties of both transforms are required simultaneously. The design problem to obtain finite impulse response filters satisfying the numerous constraints imposed by this new wavelet transform is addressed. The proposed wavelet frames are compactly supported, nearly shift-invariant, having vanishing moments and intermediate scales. Several explicit examples are discussed to illustrate the construction and properties of the wavelet frames.