Since the progress of digital medical imaging techniques, it has been needed to compress the variety of medical images. In medical imaging, reversible compression of image's region of interest (ROI) which is diagnostically relevant is considered essential. Then, improving the global compression rate of the image can also be obtained by separately coding the ROI part and the remaining image (called background). For this purpose, the present work proposes an efficient reversible discrete cosine transform (RDCT) based embedded image coder designed for lossless ROI coding in very high compression ratio. Motivated by the wavelet structure of DCT, the proposed rearranged structure is well coupled with a lossless embedded zerotree wavelet coder (LEZW), while the background is highly compressed using the set partitioning in hierarchical trees (SPIHT) technique. Results coding shows that the performance of the proposed new coder is much superior to that of various state-of-art still image compression methods.