This thesis presents a novel framework for four-dimensional medical data compression architecture. This framework is based on different procedures and algorithms that detect time and spatial redundancy in recorded MRI volumes. Motion in time is analyzed through motion estimation based on neural networks. Motion estimation is used to eliminate a large amount of temporal and frequency redundancies that exists in sequences of 3D data. Combination of segmentation, block matching and motion field prediction along with expert knowledge are incorporated to achieve better performance. Frequency analysis is done through an extension of wavelet transformations to three dimensions. For still volume objects different wavelet packets with different filter banks can be constructed, providing a wide range of frequency analysis. With combination of removing temporal and spatial redundancies, very high compression ratio is achived. The suggested data compression architecture can be implemented in telemedicine to improve the quality of service. It incorporates operations for frequency and time analysis of datasets, creating kernel shapes and models, and fitting of medical 4D datasets. Each part of the system architecture is implemented independently and can be used for other approaches such as entertainment applications and other new applications that use 4D data.