The use of computers for handling image data in the healthcare is growing The amount of data produced by modem image generating techniques, such as Computed Tomography (CT) and Magnetic Resonance (MR), is vast. The amount of data might be a problem from a storage point of view or when the data is sent over a network. To overcome these problems data compression techniques adapted to these applications are needed Many classes of images contain some spatial regions which are more important than other regions. Compression methods which are capable of achieving higher reconstruction quality of important parts of the image have been implemented For medical images, only a small portion of the image might be diagnostically useful but the cost of wrong interpretation is high. Algorithms which deliver lossless compression within the regions of interest (ROJ), and lossy compression elsewhere in the image, might be the key to providing efficient and accurate image coding to the medical community. In this thesis both of compression techniques (lossy and lossless) of medical images using the JPEG algorithm (DCT), will be discussed.