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

作者：Shen Zheng Wei^*

来源：International Journal of Wavelets, Multiresolution and Information Processing, 2013, 11(3): 1350025.

DOI：10.1142/S0219691313500252

• Approximately shift invariance
• 3-band wavelet
• dual tree complex wavelet

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 2 pi/3-periodic of phase difference between the prime and dual filter banks is proposed. With this condition, it is proposed that the phase function theta(l) (omega) of wavelet filters can be uniquely determined by the phase function theta(0)(omega) of the scaling filters. Imposed on a necessary constraint to theta(0)(omega), phase function theta(l)(omega) 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.

• 出版日期2013-5