Study On Cubic Data Compression Algorithm Based On Ridgelet Transform

As image is composed of pixel, cubic data is composed of voxel. The first characteristic of the cubic data is its enormous data amount, which is not convenient for storing and transmitting on the Internet. The second characteristic of the cubic data is that there are many line or plane singularities, which are the basic elements of the cubic data.Currently, the most popular choice for image compression is wavelet transform. The success of wavelets is mainly due to the good performance for piecewise smooth functions in one dimension. Unfortunately, this is not the case in higher dimensions. For describing the images which have linear or super-plane singularities, in 1998, Candes and Donoho proposed a new analytic tool—ridgelet. At present, there have been a few successful researches on compression using ridgelet. Up to now, these researches mainly concentrate on the case of 2-D.Simply speaking, the ridgelet transform is precisely the application of a wavelet transform to the domain of the Radon transform. So, in practical work, do the Radon transform (projection) at first, then do the wavelet transform in the Radon domain. In this thesis, on the basis of the ridgelet transform, two compression strategies are researched to the cubic data, including the CT serial images, echocardiographic serial images and so on. In these methods, the Radon transform is realized by parallel projection (2-D Radon transform) in the first strategy and cone beam projection (3-D Radon transform) in the second strategy, then doing wavelet transform, coefficients organizing, quantization and entropy coding. In the course of coefficients organizing, we use method of orientation sampling and forecast.Due to the ridgelet transform coefficients coding, the construction information of the cubic data are kept, and the compression ratio can be improved. Other hand, these strategies have following characteristics: gradually coding and robustness. Because of gradually coding, users can catch on the content of the cubic data at their first time, then to decide decoding to go on or not. In the storage or transmission of the cubic data, the loss coefficients can be compensated using adjacent valid orientations. The case of losing 1 byte data, the whole reconstruct data is null, will not happen.Comparatively speaking, each of above two strategies has its own strong point, the first one has better decoding quality, the second one has more compression ability. Seeing from our experiments'results, when the external values are almost equivalent, the compression ratio of our method is greater than those of JPEG method or method based on DWT.