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Analysis of the Statistical Dependencies in the Curvelet Domain and Applications in Image Compression

  • Alin Alecu
  • Adrian Munteanu
  • Aleksandra Pižurica
  • Jan Cornelis
  • Peter Schelkens
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4678)

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.

Keywords

curvelet coefficient dependency mutual information compression 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Alin Alecu
    • 1
  • Adrian Munteanu
    • 1
  • Aleksandra Pižurica
    • 2
  • Jan Cornelis
    • 1
  • Peter Schelkens
    • 1
  1. 1.Dept. of Electronics and Informatics, Vrije Universiteit Brussel – Interdisciplinary Institute for Broadband Technology (IBBT), Pleinlaan 2, 1050 BrusselsBelgium
  2. 2.Dept. of Telecommunications and Information Processing, Ghent University, Sint-Pietersnieuwstraat 41, 9000 GentBelgium

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