Gradient-driven update lifting for adaptive wavelets

摘要

Over the past few years, wavelets have become extremely popular in signal and image processing applications. The classical linear wavelet transform, however, performs a homogeneous smoothing of the signal contents which, in some cases, is not desirable. This has led to a growing interest in (nonlinear) wavelet representations that can preserve discontinuities, such as transitions and edges.In this paper, we present the construction of adaptive wavelets by means of an extension of the lifting scheme. The basic idea is to choose the update filters according to some decision criterion which depends on the local characteristics of the input signal. We show that these adaptive schemes yield lower entropies than schemes with fixed update filters, a property that is highly relevant in the context of compression. Moreover, we analyze the effect of a scalar uniform quantization and the stability in such adaptive wavelet decompositions.