The project proposes hybrid image compression model for efficient transmission of medical image using lossless and lossy coding for telemedicine application. Here, Fast- discrete curvelet transform with adaptive arithmetic coding will be used for loss less compression. Since storage space demands in hospitals are continually increasing the compression of the recorded medical images is the need of the hour. This would imply the need for a compression scheme that would give a very high compression ratio. Given a particular compression ratio, the quality of the image reconstructed using the AAC would be better. This project presents a method of employing both methods of compression in an intelligent manner to achieve better compression ratio and less error rate. This is also taken care of in the paper. And the regions of diagnostic importance are undisturbed in course of achieving energy efficiency. This method will be evaluated through parameters like mean square error, quality factor and compression ratio.