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Reversible integer wavelet transforms are increasingly popular in lossless image compression, as evidenced by their use in the recently developed JPEG2000 image coding standard. In this paper, a projection-based technique is presented for decreasing the first-order entropy of transform coefficients and improving the lossless compression performance of reversible integer wavelet transforms. The projection technique is developed and used to predict a wavelet transform coefficient as a linear combination of other wavelet transform coefficients. It yields optimal fixed prediction steps for lifting-based wavelet transforms and unifies many wavelet-based lossless image compression results found in the literature. Additionally, the projection technique is used in an adaptive prediction scheme that varies the final prediction step of the lifting-based transform based on a modeling context. Compared to current fixed and adaptive lifting-based transforms, the projection technique produces improved reversible integer wavelet transforms with superior lossless compression performance. It also provides a generalized framework that explains and unifies many previous results in wavelet-based lossless image compression.