Design of two-channel linear phase biorthogonal wavelet filter banks via convex optimization

Filter banks can be designed via convex optimization techniques. We present a convex optimization based design method to design linear phase biorthogonal two-channel wavelet filter banks, with prescribed number of vanishing moments (VMs) or regularity. First we design an optimal low-pass filter (LPF) followed by the design of complementary optimal synthesis LPF. The optimization problem is formulated to minimize the convex combination of pass-band and stop-band errors, passband ripple and stop-band attenuation. The perfect reconstruction (PR) conditions are imposed as a set of linear equality constraints. The VM constraints are also incorporated in the design of the filters as a set of linear equality constraints. The wavelets are constructed from iterations of designed filter banks using the cascade algorithm. A few design examples are presented, which demonstrates that biorthogonal wavelets can be constructed using the proposed method. To the best of our knowledge, design of biorthogonal wavelet filter banks has not been addressed using convex optimization methods.