Medical image compression plays a key role as hospitals move towards filmless imaging and go completely digital. Image compression will allow Picture Archiving and Communication Systems (PACS) to reduce the file sizes on their storage requirements while maintaining relevant diagnostic information. Lossy compression schemes are not used in medical image compression due to possible loss of useful clinical information and as operations like enhancement may lead to further degradations in the lossy compression. Medical imaging poses the great challenge of having compression algorithms that reduce the loss of fidelity as much as possible so as not to contribute to diagnostic errors and yet have high compression rates for reduced storage and transmission time. This paper outlines the comparison of compression methods such as Shape-Adaptive Wavelet Transform and Scaling Based ROI,JPEG2000 Max-Shift ROI Coding, JPEG2000 Scaling-Based ROI Coding, Discrete Cosine Transform, Discrete Wavelet Transform and Subband Block Hierarchical Partitioning on the basis of compression ratio and compression quality.