A new complex wavelet transform by using RI-spline wavelet

Abstract

We propose a new complex wavelet, the RI-spline wavelet, which is constructed using spline wavelets for dual-tree DWT. In the RI-spline wavelet, the real and imaginary components become an approximate Hilbert pair to each other. Then we propose a new dual-tree algorithm which uses an interpolation method for providing a half-sample-delay between the two filters of the trees. Finally, we experimentally show that the translation invariance, which can not be obtained by the ordinary DWT, is obtained by RI-spline wavelet.