Lossless image compression via predictive coding of discrete Radon projections

This paper investigates predictive coding methods to compress images represented in the Radon domain as a set of projections. Both the correlation within and between discrete Radon projections at similar angles can be exploited to achieve lossless compression. The discrete Radon projections investigated here are those used to define the Mojette transform first presented by Guédon et al. [Psychovisual image coding via an exact discrete Radon transform, in: T.W. Lance (Ed.), Proceedings of the Visual Communications AND Image Processing (VCIP), May 1995, Taipei, Taiwan, pp. 562–572]. This work is further to the preliminary investigation presented by Autrusseau et al. [Lossless compression based on a discrete and exact radon transform: a preliminary study, in: Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), vol. II, May 2006, Toulouse, France, pp. 425–428]. The 1D Mojette projections are re-arranged as two dimensional images, thus allowing the use of 2D image compression techniques onto the projections. Besides the compression capabilities, the Mojette transforms brings an interesting property: a tunable redundancy. As the Mojette transform is able to both compress and add redundancy, the proposed method can be viewed as a joint lossless source-channel coding technique for images. We present here the evolution of the compression ratio depending on the chosen redundancy.