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 filter utilises 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 which are more homogeneous. The approach taken in this paper differs from other adaptive schemes found in the literature in the sense that that no bookkeeping is required in order to have perfect reconstruction.

Wavelets and other special systems (msc 42C40), Signal theory (characterization, reconstruction, filtering, etc.) (msc 94A12)
CWI. Probability, Networks and Algorithms [PNA]
Signals and Images

Heijmans, H.J.A.M, & Piella, G. (2001). Adaptive lifting schemes with perfect reconstruction. CWI. Probability, Networks and Algorithms [PNA]. CWI.