A new class of almost symmetric orthogonal Hilbert pair of wavelets

•New class of Hilbert-pair of wavelets for the dual tree complex wavelet transform.•Wavelets are orthogonal but also virtually symmetric.•Present an efficient design procedure that give good analytic quality Hilbert pairs.

The dual-tree complex wavelet transform offers near shift invariance and a better directional selectivity compared to traditional discrete wavelet transforms. A new class of Hilbert-pair of wavelets that can be used in the dual-tree is presented in this work. These Hilbert-pairs are exactly orthogonal but are also almost symmetric. They therefore have the advantages found in both orthogonal and biorthogonal wavelets. Symmetry in the wavelets is of prime importance in many applications as it offers a better directional selectivity. An efficient and flexible design technique is proposed for the design of these new Hilbert-pairs. The proposed technique readily allows the designer to trade-off between the degree of symmetry and the analytic quality. The designed wavelet filters have good frequency response, flat group delay and achieve a good approximation to the half-sample delay condition which is required for good analytic quality.