The image compression is a hot topic of research during these days. An uncompressed image data requires large amount of storage and high transmission bandwidth and hence requires compression. This project focuses on, the compression of medical images, particularly radiological images. The steps towards digital images in radiology raise the question that how to economically and suitably store, transmit and retrieve the volume of digital images with an acceptable quality for a given clinical application. Many techniques have been proposed for achieving data compression. In this paper two compression techniques JPEG and Wavelet Transform are used for comparison and analysis three types of computed tomography images are taken, based on the sequence of images in TIFF format of chest, brain and kidney. Objective evaluation is done on quality of the compressed images. The results show that Mean Square Error, Peak Signal to Noise Ratio, Compression Ratio and Compression Size are highly satisfactory for the images compressed w ith wavelet Transform. Thus the results of compression show that wavelet give better result than JPEG.