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Zhen Liu

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Proceedings Article | 7 May 2003 Paper

Mutual information analysis of JPEG2000 contexts

Zhen Liu, Lina Karam

Proceedings Volume 5022, (2003) https://doi.org/10.1117/12.476620

KEYWORDS: JPEG2000, Image compression, Computer programming, Wavelets, Binary data, Discrete wavelet transforms, Distortion, Statistical modeling, Image quality standards, Quantization

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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 has a direct link with 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 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 the dynamic programming. Our experimental results show that the JPEG2000 contexts capture very well the correlations among the wavelet coefficients. At the same time, the number of contexts used as part of the standard can be reduced without loss in the coding performance.

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