Considering that quincunx lattice is a more e?cient spatial sampling scheme than square lattice, we investigate a new approach of image coding for quincunx sample arrangement. The key findings are: 1) adaptive directional lifting is particularly suited to decorrelate samples on quincunx lattice, and 2) quincunx samples can be processed by a 2D piecewise autoregressive model to reproduce the image of conventional square pixel grid, while preserving high frequency spatial features well. By incorporating these two techniques into the encoder and decoder respectively, we are able to improve the performance of JPEG 2000 image codec at low to modest bit rates. Since an image can be easily split into quincunx segments, this work has signi?cance for multiple description image/video coding as well.