Adaptive update lifting with gradient criteria modeling high-order differences

This paper treats a class of adaptive update lifting schemes which do not require bookkeeping for perfect reconstruction. The choice of the update lifting filter is triggered by a binary threshold criterion based on a generalised gradient which is chosen in such a way that it only smoothes homogeneous regions. More precisely, the criterion can be chosen so that it ‘recognises’ signals that are polynomial up to a given order. The lifting filter updates the signal in these polynomial regions but leaves other parts unaffected.