Construction of adaptive wavelets using update lifting and quadratic decision criteria

This paper studies lifting schemes that are adaptive with respect to the gradient vector of the input signal and require no overhead information for perfect reconstruction. The choice of the update filter is triggered by a binary decision criterion based on a weighted ℓ
¹
-type seminorm of the gradient. Such an adaptive scheme has great potential for preserving the discontinuities in signals and images and providing a compact data representation, as illustrated by some simulation examples.