A SUFFICIENT AND NECESSARY CONDITION FOR CONSTRUCTION OF 3-BAND DUAL TREE COMPLEX WAVELET

Abstract

To desire expectable applications in image processing, the construction of 3-band dual tree complex wavelet is a meaningful and constructive topic. In this paper, a sufficient and necessary condition 2π/3-periodic of phase difference between the prime and dual filter banks is proposed. With this condition, it is proposed that the phase function θl(ω) of wavelet filters can be uniquely determined by the phase function θ0(ω) of the scaling filters. Imposed on a necessary constraint to θ0(ω), phase function θl(ω) can be obtained which results in the analytical of the 3-band dual tree complex wavelet. Furthermore, the complex filter banks are obtained using the wavelet matrix factorization approach. Then the dual tree 3-band complex wavelet is analytical that indicates approximately shift invariance property. In addition, it also has more direction selectivity because there are more sub-bands than dyadic wavelet transform is frequency domain.