Breast Cancer is one of the leading causes of death for women. An early diagnosis is a requirement for reduction of the mortally rate from this disease. Modern imaging technology has created the capability of early detection of this. One of the most effective methods of early diagnosis is mammography. A mammography is a low dose X-ray imaging of the breast. Every year millions of mammograms are generated world-wide. Due to large size and high quality of the mammogram images, their transmission over computer networks can be difficult and image compression is necessary. On the other hand, these images are usually stored for a long period of time on the patient's digital file to keep track of the treatment. Archiving and retaining large amounts of data is expensive and requires compression methods. Image compression methods are Key Words Digital mammography, Image compression, Lossless, Context modelling.