Abstract
This paper reports an information-theoretic analysis of the dependencies that exist between curvelet coefficients. We show that strong dependencies exist in local intra-band micro-neighborhoods, and that the shape of these neighborhoods is highly anisotropic. With this respect, it is found that the two immediately adjacent neighbors that lie in a direction orthogonal to the orientation of the subband convey the most information about the coefficient. Moreover, taking into account a larger local neighborhood set than this brings only mild gains with respect to intra-band mutual information estimations. Furthermore, we point out that linear predictors do not represent sufficient statistics, if applied to the entire intra-band neighborhood of a coefficient. We conclude that intra-band dependencies are clearly the strongest, followed by their inter-orientation and inter-scale counterparts; in this respect, the more complex intra-band/inter-scale or intra-band/inter-orientation models bring only mild improvements over intra-band models. Finally, we exploit the coefficient dependencies in a curvelet-based image coding application and show that the scheme is comparable and in some cases even outperforms JPEG2000.
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Alecu, A., Munteanu, A., Pižurica, A., Cornelis, J., Schelkens, P. (2007). Analysis of the Statistical Dependencies in the Curvelet Domain and Applications in Image Compression. In: Blanc-Talon, J., Philips, W., Popescu, D., Scheunders, P. (eds) Advanced Concepts for Intelligent Vision Systems. ACIVS 2007. Lecture Notes in Computer Science, vol 4678. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74607-2_96
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DOI: https://doi.org/10.1007/978-3-540-74607-2_96
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74606-5
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