Image compression involves reducing the size of image data files, while retaining necessary information. Compression is a necessary and essential method for creating image files with manageable and transmittable sizes. There have been many types of compression algorithms developed. In this work a different methods of image compression were used in order to compress MRI (Magnetic Resonance Images) and to transmit these images by using serial port RS232. The compression of the medical images is very important for the purpose of telemedicine, so, by the compression technique, the size of the medical images will be reduced, then the time of image transmission will be reduced too, this feature is very necessary specially in emergencies cases. Also , the cost of communication (image transmission) will be reduced. The efficient compression method is the method that will acquire a higher compression ratio (Cr) , lower transmission time (tt) lower compression time (ct), and higher quality PSNR (Peak Signal to Noise Ratio) . The entropy (which represent the information of image) is very important parameter to test the efficiency of the compression method, increasing or decreasing of ( cr, tt, ct, PSNR) versus entropy will indicate to the efficiency of compression method. In this work, discrete cosine transform (DCT) and wavelet transform compression methods were used as lossy compression, and Huffman compression method was used a lone as a lossless compression. Huffman encoding was used as entropy encoding in both methods (DCT and wavelet) to show it's effect on compression ratio and the time of transmission and compression. Also a bitmap was added in wavelet compression method to show the effect of Run length encoding on the results of compression. Four methods of image compression (DCT-huffman, wavelet-huffman, wavelet-bitmap, huffman) were used in this thesis to show the most efficient method according to behavior of ( PSNR, ct, tt, cr ) parameters versus entropy. The efficiency of (compression and transmission) in wavelet bitmap method is the best.