With advances in imaging and communication systems, there is increased use of multi-dimensional images. Examples include multi-view image/video, hyperspectral image/video and dynamic volume imaging in CT/MRI/Ultrasound. These datasets consume even larger amounts of resources for transmission or storage compared to 2-D images. Hence, it is vital to have efficient compression methods for multi-dimensional images. In this dissertation, first, a JPEG2000 Part-2 compliant scheme is proposed for compressing multi-dimensional datasets for any dimension N>=3. Secondly, a novel view-compensated compression method is investigated for remote visualization of volumetric data. Experimental results indicate superior compression performance compared to state-of-the-art compression standards. Thirdly, a new scalable low complexity coder is designed that sacrifices some compression efficiency to get substantial gain in throughput. Potential use of the scalable low complexity coder is illustrated for two applications: Airborne video transmission and remote volume visualization.