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Due to bandwidth and storage limitations, medical images must be compressed before transmission and storage. However, the compression reduces the image fidelity, especially when the images are compressed at low bit rates. The reconstructed images suffer from blocking artifacts and the image quality is severely degraded under high compression ratios. In this paper, we present a strategy to increase the compression ratio with low computational burden and excellent decoded quality. We regard the discrete cosine transform as a bandpass filter to decompose a sub-block into equal-sized bands. After a band-gathering operation, a high similarity property among the bands is found. By utilizing the similarity property, the bit rate of compression can be greatly reduced. Meanwhile, the characteristics of the original image are not sacrificed. Thus, it can avoid the misdiagnosis of diseases. Simulations were carried out on different kinds of medical images to demonstrate that the proposed method achieves better performance when compared to other existing transform coding schemes, such as JPEG, in terms of bit rate and quality. For the case of angiogram images, the peak signal-to-noise-ratio gain is 13.5 dB at the same bit rate of 0.15 bits per pixel when compared to the JPEG compression. As for the other kinds of medical images, their benefits are not so obvious as for angiogram images; however, the gains for them are still 4-8 dB at high compression ratios. Two doctors were invited to verify the decoded image quality; the diagnoses of all the test images were correct when the compression ratios were below 20.