Adaptive lifting schemes with perfect reconstruction

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. We restrict ourselves to the update lifting stage. It is assumed that the update filter utilizes local gradient information to adapt itself to the signal in the sense that smaller gradients "evoke" stronger update filters. As a result, sharp transitions in a signal will not be smoothed to the same extent as regions that are more homogeneous. The approach taken in this paper differs from other adaptive schemes found in the literature in the sense that no bookkeeping is required in order to have perfect reconstruction.