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CT or MRI medical imaging produce human body pictures in digital form. Since these imaging techniques produce prohibitive amounts of data, compression is necessary for storage and communication purposes. Many current compression schemes provide a very high compression rate but with considerable loss of quality. On the other hand, in some areas in medicine, it may be sufficient to maintain high image quality only in the region of interest, i.e., in diagnostically important regions. This paper discusses a hybrid model of lossless compression in the region of interest, with high-rate, motion-compensated, lossy compression in other regions. We evaluate our method on medical CT images, and show that it outperforms other common compression schemes, such as discrete cosine transform, vector quantization, and principal component analysis. In our experiments, we emphasize CT imaging of the human colon.