Lifting factorization and design based on stationary wavelet transform

The main advantage of the stationary wavelet transform is its translation invariance of the wavelet coefficients. In this paper, based on the polyphase representation of wavelet transform, a new structure is proposed to that the traditional stationary wavelet transform can be obtained with a finite number of alternating lifting and dual lifting steps starting from the Lazy wavelet, using the equivalent relation of position-swapping between up (down) sampler and filter. Moreover, one can increase the vanishing moments of stationary wavelet by designing proper (dual) lifting steps. It overcomes the drawback in former algorithm, which can only be used to design interpolating wavelets starting from odd-even splitting. Furthermore, we present that the asymptotically reduces the computational complexity of the standard algorithm by a factor two.