Medical imaging is a quickly growing industry where the need for highly efficient lossless compression algorithms is necessary in order to reduce storage space and transmission rates for the large, high resolution, medical images. Due to the fact that medical imagining cannot utilize lossy compression, in the event that vital information may be lost, it is imperative that lossless compression be used. While several authors have investigated lossless compression of medical images, the Burrows-Wheeler Transformation with an Inversion Coder (BWIC) has not been examined. Our investigation shows that BWIC runs in linear time and yields better compression rates than well-known image coders, such as JPEG-LS and JPEG-2000.