Achieving complex discrete wavelet transform by lifting scheme using Meyer wavelet

The complex discrete wavelet transform (CDWT) can be carried out by using a complex mother wavelet that is designed based on the Meyer wavelet, and achieves perfect translation invariance. However, it is calculated by the parallel Multi-resolution algorithm (MRA) using the imaginary part and the real part of the complex mother wavelet and the calculation amount is more than double that of the traditional discrete wavelet transform (DWT). In order to reduce the calculation amount, using the lifting scheme instead of the MRA is considered, although the lifting scheme was only used in the case of the mother wavelet with a compact support. In this research, we design a lifting scheme filter of Meyer wavelet without compact support in order to achieve high-speed computation by application to the CDWT, and have obtained encouraging results.