Many existing works related to lossy-to-lossless multiresolution image compression are based on the lifting concept. It is worth noting that a separable lifting scheme may not appear very efficient to cope with the 2D characteristics of edges which are neither horizontal nor vertical. In this paper, we propose to use 2D non-separable lifting schemes that still enable progressive reconstruction and exact decoding of images. Their relevant advantage is to yield a tractable optimization of all the involved decomposition operators. More precisely, we design the prediction operators by minimizing the variance of the detail coefficients. Concerning the update filters, we propose a new optimization criterion which aims at reducing the inherent aliasing artifacts. A theoretical analysis of the proposed method is conducted in terms of the adaptation criterion considered in the optimization of the update filter. Simulations carried out on still images and residual ones generated from stereo pairs show the benefits which can be drawn from the proposed optimization of the lifting operators. (C) 2011 Elsevier B.V. All rights reserved.