Estimation of quantization noise for adaptive-prediction lifting schemes

The lifting scheme represents an easy way of implementing the wavelet transform and of constructing new content-adapted transforms. However, the adaptive version of lifting schemes can result in strongly non-isometric transforms. This can be a major limitation, since all most successful coding techniques rely on the distortion estimation in the transform domain. In this paper we focus on the problem of evaluating the reconstruction distortion (due to quantization noise) in the wavelet domain when a non-isometric adaptive-prediction lifting scheme is used. The problem arises since these transforms are nonlinear, and so common techniques for distortion evaluation cannot be used in this case. We circumvent the difficulty by computing an equivalent time-varying linear filter, for which it is possible to generalize the distortion computation technique. In addition to the theoretical formulation of the distortion estimation, in this paper we provide experimental results proving the reliability of this estimation, and the consequent improvement of RD performance, thanks to a more effective resource allocation which can be performed in the transform domain.