ADAPTIVE WAVELETS FOR IMAGE COMPRESSION USING UPDATE LIFTING: QUANTIZATION AND ERROR ANALYSIS

Abstract

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 to take into account the characteristics of the input signal/image. In our previous work20,22,23 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 quantization in such an adaptive wavelet decomposition. We provide conditions for recovering the original decisions at the synthesis and for relating the reconstruction error to the quantization error. Such an analysis is essential for the application of these adaptive decompositions in image compression.