In this paper we propose the lifting scheme of true 2D coifman wavele to reduce half computation compared with it directly be used to decomposition and reconstruction 2D data. True 2D coifman wavelet has many favourable properties such as perfect reconstruction

vanishing moments

diamond frequency response and dyadic fractions etc.

this makes this method competitive in image compression property preservation. Simply by changing normalizing factor

this lifting scheme can be used for lossy and lossless image compression and at the same time it keeps advantages of 1D wavelet lifting scheme at computation and border extension aspects. The characteristics of prediction and update operators in true 2D coifman wavelet lifting scheme provide guidance for constructing true 2D wavelet filter banks. Simulation results show that true 2D coifman wavelet filter bank has nicer compression property than another 2D wavelet filter bank constructed by the same 1D prototype wavelet filter bank.