Adaptive Wavelets for Image Compression Using Update Lifting-Quantization 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 or image. The adaptive update lifting framework is introduced that does not require bookkeeping but has the property that it processes edges and homogeneous image regions in different fashion. The effect of scalar uniform quantization in an adaptive multiresolution analysis based on lifting implementation is analyzed. Such an analysis is essential for the application of these adaptive decompositions in image compression. Conditions are provided for recovering the original decisions at the synthesis and show how to estimate the reconstruction error in terms of the quantization error.