The digital imaging techniques are used more and more in various diagnostic modalities, including computed tomography (CT), Digital Subtraction .A.ngiography (DSA), etc. As a result, a huge amount of digital images are being generated. Therefore, techniques to compress these images into a more compact form for storage and transmission become more important and anyone involved with the storage of medical images in a Picture Archiving and Communication System (PACS) should first apply compression (lossy or lossless depending on the characteristics of the digitized data) on them. There are image coding methods which reduces the storage size of an image b}' an amount of 1/10 without any visual degradation. But in some medical applications lossless coding of medical images is necessary. Multiresolution coding techniques have been used for lossy image and speech coding, in this thesis we developed multiresolution techniques for the lossless image compression. We observed that the use of multiresolution techniques in lossless compression is as advantages as in lossy compression schemes.