We propose a new algorithm for compression and enhancement of ultrasound images, motivated by the importance of efficient storage and transmission. Our scheme is based on separation of the input image into its Region-Of-Interest (ROI), which is important for medical diagnosis, and the remaining background. The ROI pixels are coded using Shape-adaptive transforms and a novel interpolation algorithm, in which pixels are added to the ROI mask in an adaptive manner such as to avoid spatial artifacts in the reconstructed image. Speckle reduction is further applied in order to enhance the image and improve its compressibility. Experiments with echo-cardiac and fetal images demonstrate that our method yields better reconstructed images in terms of preserving their diagnostically important regions of interest, compared with existing image compression algorithms.