Adaptive compression of images using high-order entropy coding

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. In this thesis, 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 = 2{dollar}sp{lcub}K{rcub}{dollar} representation levels, greyscale image is decomposed into M binary sub-images, each corresponding to one representation level of M. Therefore, 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. Our theoretical analysis and experimental results conclude that BDHEC approach is a simple, practical and effective coding technique good for both lossy and lossless image compression. We also proposed an enhanced BDHEC algorithm aimed to increase coding efficiency. In this new approach, an image having K-bits, or M = 2{dollar}sp{lcub}K{rcub}{dollar} grey levels is decomposed into M/2 sub-images. Each sub-image corresponds to 2 consecutive grey values. Two rounds of binary representation have to be used to represent the information contained in one double binary decomposed (DBD) sub-image. We indicate that this enhanced technique improved coding efficiency without increasing the complexity of implementation.