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This paper presents an adaptive lifting scheme, which performs integer-to-integer wavelet transform, for lossless image compression. We optimize the coefficients of the predict filter in the lifting scheme to minimize the entropy of the detail coefficients. The optimized coefficients depend on the auto-correlation structure of the image. The presented lifting scheme adapts to both horizontal and vertical directions of the image. We obtain experimental results using different types of images. These results show that the presented adaptive transform is a competitive wavelet transform for lossless image compression.