Lossless image coding via one-dimensional grammar based codes

Lossless image coding is considered from an information theoretic point of view. Three new coding schemes are proposed. In the first coding scheme, an image is first scanned in a quadrant-by-quadrant manner and then encoded by using a one-dimensional grammar-based code which has been developed by Yang and Kieffer (2000) and is called the improved sequential algorithm (or simply the YK algorithm). In the second coding scheme, an image is first predicted by using a context template then scanned in a quadrant-by-quadrant manner, and finally encoded by using the YK algorithm. In the third coding scheme, an image is first scanned in a quadrant-by-quadrant manner and then encoded by using a modified YK algorithm, which also includes a 2D arithmetic code as an option to remove local 2D redundancy. Because of the nature of the YK algorithm and the scanning method, all three coding schemes can remove effectively global redundancy existing in images. Indeed, it is proved that all three coding schemes are universal and outperform asymptotically finite 2D block code and any finite context 2D arithmetic code as the image size gets larger and larger. For small images, however, the second coding scheme is slightly more effective in removing local redundancy occurring in images than does the first coding scheme, and the third one is the best among the three. Simulation results on bi-level images confirm our theoretic results: for images of size 512×512, our results are comparable with those afforded by JBIG1; for some images of size 1024×1024, our results are better than those afforded by JBIG1