Reversible data compression by universal arithmetic coding

The paper considers the general approach to the reversible (lossless) digital data compression problem, which is based on universal arithmetic coding of data with unknown statistics. A model of a source with calculable sequence of states is used for data description. Within the approach, the tasks of obtaining specific compression methods and algorithms for particular data types are set up. The authors use computed tomography data (tomograms) as the object of the study and present two methods of lossless compression of tomograms. The first method encodes prediction errors of tomograms; the second method encodes components of discrete wavelet transform of tomograms. These methods are examined in details, effective compression algorithms are constructed, and individual estimates of bit rate are obtained for the algorithms. The bit rates of the constructed algorithms and the lossless compression algorithms of the JPEG 2000 standard are compared. The results demonstrate high quality of the constructed algorithms and indicate great potential of the approach in general.