Adaptive lifting schemes with perfect reconstruction

In this paper, we propose a framework for constructing adaptive wavelet decompositions using the lifting scheme. A major requirement is that perfect reconstruction is possible without any overhead cost. In this paper we restrict ourselves to the update lifting stage. It is assumed that the update lter utilises local gradient information to adapt itself to the signal in the sense that smaller gradients `evoke' stronger update lters. As a result, sharp transitions in a signal will not be smoothed to the same extent as regions which are more homogeneous. The approach taken in this paper di ers from other adaptive schemes found in the literature in the sense that that no bookkeeping is required in order to have perfect reconstruction. 2000 Mathematics Subject Classi cation: 42C40, 94A12