Design of higher density dual-tree discrete wavelet transform with few degrees of freedom

We propose a method for the design of FIR filters that define higher density discrete wavelet transforms forming a dual tree. The design is based on a parameterization, using positive trigonometric polynomials, of the convex space of parameters characterizing the filters. Using only one or two degrees of freedom, we are able to design, via a search procedure, complex wavelets that are nearly analytic and have high regularity.