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A technique using a lifting scheme is presented for constructing compactly supported wavelets whose coefficients are composed of free variables locating in an interval. An efficient approach-based wavelet for image compression is developed by selecting the coefficients of the 9-7 wavelet filter and associated lifting scheme. Furthermore, the rationalised coefficients wavelet filter that can be implemented with simple integer arithmetic is achieved and its characteristic is close to the well known original irrational coefficients 9-7 wavelet filters developed by A. Cohen et al. (Commun. Pure Appl. Maths., vol.45, no.1, p.485-560, 1992). To reduce the computational cost of image coding applications further, an acceleration technique is proposed for the lifting steps. Software and hardware simulations show that the new method has very low complexity, and simultaneously preserves the high quality of the compressed image.