Design of signal-adapted multidimensional lifting scheme for lossy coding

This paper proposes a new method for the design of lifting filters to compute a multidimensional nonseparable wavelet transform. Our approach is stated in the general case, and is illustrated for the 2-D separable and for the quincunx images. Results are shown for the JPEG2000 database and for satellite images acquired on a quincunx sampling grid. The design of efficient quincunx filters is a difficult challenge which has already been addressed for specific cases. Our approach enables the design of less expensive filters adapted to the signal statistics to enhance the compression efficiency in a more general case. It is based on a two-step lifting scheme and joins the lifting theory with Wiener´s optimization. The prediction step is designed in order to minimize the variance of the signal, and the update step is designed in order to minimize a reconstruction error. Application for lossy compression shows the performances of the method.