Basics
The basic idea of lifting is the following: If a pair of filters is complementary, that is it allows for perfect reconstruction, then for every filter the pair with allows for perfect reconstruction, too. Of course, this is also true for every pair of the form . The converse is also true: If the filterbanks and allow for perfect reconstruction, then there is a unique filter with .
Each such transform of the filterbank (or the respective operation in a wavelet transform) is called a lifting step. A sequence of lifting steps consists of alternating lifts, that is, once the lowpass is fixed and the highpass is changed and in the next step the highpass is fixed and the lowpass is changed. Successive steps of the same direction can be merged.
Read more about this topic: Lifting Scheme