Many classes of images contain some spatial regions which are more imp
ortant than other regions. Compression methods which are capable of de
livering higher reconstruction quality for the important parts are att
ractive in this situation. For medical images, only a small portion of
the image might be diagnostically useful, but the cost of a wrong int
erpretation is high. Algorithms which deliver lossless compression wit
hin the regions of interest, and lossy compression elsewhere in the im
age, might be the key to providing efficient and accurate image coding
to the medical community. We present and compare several new algorith
ms for lossless region-of-interest (ROI) compression. One is based on
lossless coding with the S-transform, and two are based on lossy wavel
et zerotree coding together with either pixel-domain or transform-doma
in coding of the regional residual. We survey previous methods for reg
ion-based coding of medical images.