Application of ridgelet in cubic data compression

Cubic data has two notable characteristics, the first being the large size of the datasets, requiring compression for storing or Internet transfer, the second is possible occurrence of many line or plane singularities which need to be preserved in compressed data. Ridgelet, a new analytic tool, has the ability to describe linear or super-plane singularities. The ridgelet transform can be described as the application of the wavelet transform to the coefficients of the Radon transform. In this paper, on the basis of this theory, two compression strategies for compression of cubic data are examined. The first strategy is the concept of 2D ridgelet compression applied to each slice of the cubic data and the second one is the concept of 3D ridgelet compression applied to the entire cubic data directly. In our strategies, the Radon transform is realized numerically by parallel projection (2D) or cone beam projection (3D), and the wavelet transform is realized by the lifting wavelet transform. These strategies have the following characteristics: embedded coding and strong robustness, all of which can be seen in the results of the numerical experiments.