Adaptive update lifting with a decision rule based on derivative filters

This letter treats a class of adaptive update-lifting schemes that do not require bookkeeping for perfect reconstruction. The choice of the update-lifting filter is triggered by a binary threshold criterion based on a generalized gradient that is chosen in such a way that it only smooths homogeneous regions. This criterion can be chosen so that it ignores portions of a signal that are polynomial up to a given order. The update-lifting filter modifies the signal in these polynomial regions but leaves other portions unaffected.