Adaptive wavelets for image compression using update lifting: quantisation and error analysis

Classical linear wavelet representations of images have the drawback that they are not optimally suited to represent edge information. To overcome this problem, nonlinear multiresolution decompositions have been designed that can take into account the characteristics of the input signal/image. In our previous work [20,22] we have introduced an adaptive lifting framework, that does not require bookkeeping but has the property that it processes edges and homogeneous image regions in a different fashion. The current paper discusses the effects of quantisation in such an adaptive wavelet decomposition, as such an analysis is essential for the application of these adaptive decompositions in image compression. We provide conditions for recovering the original decisions at the synthesis and show how to estimate the reconstructions error in terms of the quantisation error.