New approach for applying high-order entropy coding to image data

Entropy coding is a well-known method for exploiting the statistical redundancy in order to compress image data. Information theory indicates that the coding efficiency can be improved by utilizing high-order entropy coding (HEC). However, due to the high complexity of the implementation and the difficulties in estimating the high-order statistics during the coding process, high-order entropy coding has not been widely used. Conditional coding of an Lth order Markov source requires 2KL code tables with 2K probabilities in each table. In this paper, we present a new approach called binary decomposed high-order entropy coding (BDHEC) that significantly reduces the complexity of implementation of HEC techniques. Furthermore, it increases the accuracy of estimating the statistical model and thus it also improves the effectiveness of HEC for practical applications. The novelty of this approach is that the K-bits, M equals 2K representation levels, grayscale image is decomposed into M binary sub-images, each corresponding to one representation level of M outcomes of pels. Since each sub-image has only two representation levels, K is reduced to 1, the smallest possible value. Thus, when high-order conditional entropy coding is applied to these sub- images instead of the original image, the implementation complexity is significantly reduced and the accuracy of estimating the statistical model is increased. Theoretical analysis and experimental results are presented, which verify the value of BDHEC.