How to turn Morlet wavelet into second generation wavelet? I have a very specific application which requires to use the complex Morlet wavelet (or Gabor wavelet, if that's the name you use). I currently use the convolution theorem to compute wavelets transforms, but I'm reading everywhere that direct wavelet transforms are more computer efficient, because of the lifting scheme.

On the other hand, I searched for lifting scheme, and it's so much of a different paradigm that I have no idea how to use it with my wavelet, or whether it's even possible.

My question is: is it possible to use the lifting scheme with the Morlet wavelet in 1D and 2D? If so, can you recommend some litterature explaining the algorithm?
The Lifting scheme is special algorithm that allows a very efficient computation of the discrete wavelet transform (DWT), via special filters (QMF) and down/up-samplers. In order to compute a DWT the wavelet has to fulfill orthogonality constraints under translation and dilation.

The Morlet wavelet does not fulfill these contraints. Thus, you cannot compute a DWT with it und consequently you cannot use the lifting scheme. The Morlet wavelet is only applicable for computing a continuous wavelet transform. If you need a fast approximation you can have a look here: Fast Gabor-Like Windowed Fourier and Continuous Wavelet Transforms