Liu Zhen, Karam Lina J
Qualcomm, Inc., San Diego, CA 92121-1714, USA.
IEEE Trans Image Process. 2005 Apr;14(4):411-22. doi: 10.1109/tip.2004.841199.
Context-based arithmetic coding has been widely adopted in image and video compression and is a key component of the new JPEG2000 image compression standard. In this paper, the contexts used in JPEG2000 are analyzed using the mutual information, which is closely related to the compression performance. We first show that, when combining the contexts, the mutual information between the contexts and the encoded data will decrease unless the conditional probability distributions of the combined contexts are the same. Given I, the initial number of contexts, and F, the final desired number of contexts, there are S(I, F) possible context classification schemes where S(I, F) is called the Stirling number of the second kind. The optimal classification scheme is the one that gives the maximum mutual information. Instead of using an exhaustive search, the optimal classification scheme can be obtained through a modified generalized Lloyd algorithm with the relative entropy as the distortion metric. For binary arithmetic coding, the search complexity can be reduced by using dynamic programming. Our experimental results show that the JPEG2000 contexts capture the correlations among the wavelet coefficients very well. At the same time, the number of contexts used as part of the standard can be reduced without loss in the coding performance.
基于上下文的算术编码已在图像和视频压缩中得到广泛应用，并且是新的JPEG2000图像压缩标准的关键组成部分。在本文中，使用与压缩性能密切相关的互信息对JPEG2000中使用的上下文进行了分析。我们首先表明，在组合上下文时，除非组合上下文的条件概率分布相同，否则上下文与编码数据之间的互信息将会减少。给定初始上下文数量I和最终所需上下文数量F，存在S(I, F)种可能的上下文分类方案，其中S(I, F)称为第二类斯特林数。最优分类方案是能给出最大互信息的方案。无需进行穷举搜索，通过使用以相对熵作为失真度量的改进广义劳埃德算法即可获得最优分类方案。对于二进制算术编码，可通过使用动态规划来降低搜索复杂度。我们的实验结果表明，JPEG2000上下文能很好地捕捉小波系数之间的相关性。同时，作为标准一部分使用的上下文数量可以减少而不会损失编码性能。
