Lossless image coding deals with the problem of representing an image with a minimum number of binary bits from which the original image can be fully recovered without any loss of information. Most lossless image coding algorithms reach the goal of efficient compression by taking care of the spatial correlations and statistical redundancy lying in images. Context based algorithms are the typical algorithms in lossless image coding. One key probelm in context based lossless bi-level image coding algorithms is the design of context templates. By using carefully designed context templates, we can effectively employ the information provided by surrounding pixels in an image. In almost all image processing applications, image data is accessed in a raster scanning manner and is treated as 1-D integer sequence rather than 2-D data. In this thesis, we present a quadrisection scanning method which is better than raster scanning in that more adjacent surrounding pixels are incorporated into context templates. Based on quadrisection scanning, we develop several context templates and propose several image coding schemes for both sequential and progressive lossless bi-level image compression. Our results show that our algorithms perform better than those raster scanning based algorithms, such as JBIG1 used in this thesis as a reference. Also, the application of 1-D grammar based codes in lossless image coding is discussed. 1-D grammar based codes outperform those LZ77/LZ78 based compression utility software for general data compression. It is also effective in lossless image coding. Several coding schemes for bi-level image compression via 1-D grammar codes are provided in this thesis, especially the parallel switching algorithm which combines the power of 1-D grammar based codes and context based algorithms. Most of our results are comparable to or better than those afforded by JBIG1.

Lossless image coding deals with the problem of representing an image with a minimum number of binary bits from which the original image can be fully recovered without any loss of information. Most lossless image coding algorithms reach the goal of efficient compression by taking care of the spatial correlations and statistical redundancy lying in images. Context based algorithms are the typical algorithms in lossless image coding. One key probelm in context based lossless bi-level image coding algorithms is the design of context templates. By using carefully designed context templates, we can effectively employ the information provided by surrounding pixels in an image. In almost all image processing applications, image data is accessed in a raster scanning manner and is treated as 1-D integer sequence rather than 2-D data. In this thesis, we present a quadrisection scanning method which is better than raster scanning in that more adjacent surrounding pixels are incorporated into context templates. Based on quadrisection scanning, we develop several context templates and propose several image coding schemes for both sequential and progressive lossless bi-level image compression. Our results show that our algorithms perform better than those raster scanning based algorithms, such as JBIG1 used in this thesis as a reference. Also, the application of 1-D grammar based codes in lossless image coding is discussed. 1-D grammar based codes outperform those LZ77/LZ78 based compression utility software for general data compression. It is also effective in lossless image coding. Several coding schemes for bi-level image compression via 1-D grammar codes are provided in this thesis, especially the parallel switching algorithm which combines the power of 1-D grammar based codes and context based algorithms. Most of our results are comparable to or better than those afforded by JBIG1.