The healthcare sector is currently undergoing a major transformation due to the recent advances in deep learning and artificial intelligence. Despite a significant breakthrough in medical imaging and diagnosis, there are still many open issues and undeveloped applications in the healthcare domain. In particular, transmission of a large volume of medical images proves to be a challenging and time-consuming problem, and yet no prior studies have investigated the use of deep neural networks towards this task. The purpose of this paper is to introduce and develop a deep-learning approach for the efficient transmission of medical images, with a particular interest in the progressive coding of bit-planes. We establish a connection between bit-pla...