A lifting undecimated wavelet transform and its applications

In order to get a characterized wavelet with expected properties, a new wavelet is constructed by using the lifting scheme (LS). Taking the low-pass filter of cubic B-splines wavelet transform as an initial filter, and designing a lifting operator based on interpolating subdivision method, new wavelet is obtained through one lifting step. The wavelet inherits the property of low-pass filtering that the initial filter possessed, and also has ability to extract transient impulse from analyzed signal. By making an equivalent interchange manipulation to the LS framework, and removing decimators, a LS algorithm for undecimated wavelet transform (UWT) is proposed. Two engineering applications are reported in the paper, and the results show that the UWT can provide much more diagnostics information than the classical wavelet transform.