An adaptive update lifting scheme with perfect reconstruction

The lifting scheme provides a general and flexible tool for the construction of wavelet decompositions and perfect reconstruction filter banks. We propose an adaptive version of this scheme which has the intriguing property that it allows perfect reconstruction without any overhead cost. We restrict ourselves to the update lifting step which affects the approximation signal only. The update lifting filter is assumed to depend pointwise on the norm of the associated gradient vector, in such a way that a large gradient induces a weak update filter. Thus, sharp transitions in a signal (eg, edges in an image) will not be smoothed to the same extent as regions which are more homogeneous