Calculating transform
The input signal is split into odd and even samples using shifting and downsampling. The detail coefficients are then interpolated using the values of and the ''prediction operator'' on the even values: : The next stage (known as the ''updating operator'') alters the approximation coefficients using the detailed ones: : The functions prediction operator and updating operator effectively define the wavelet used for decomposition. For certain wavelets the lifting steps (interpolating and updating) are repeated several times before the result is produced. The idea can be expanded (as used in the DWT) to create aAdvantages
The SGWT has a number of advantages over the classical wavelet transform in that it is quicker to compute (by a factor of 2) and it can be used to generate a multiresolution analysis that does not fit a uniform grid. Using a priori information the grid can be designed to allow the best analysis of the signal to be made. The transform can be modified locally while preserving invertibility; it can even adapt to some extent to the transformed signal.References
* Wim Sweldens