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Analysis of the statistical dependencies in the curvelet domain and applications in image compression

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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
REPRESENTATIONS, compression, mutual information, curvelet, coefficient dependency, INFORMATION

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Chicago
Alecu, Alin, Adrian Munteanu, Aleksandra Pizurica, Jan Cornelis, and Peter Schelkens. 2007. “Analysis of the Statistical Dependencies in the Curvelet Domain and Applications in Image Compression.” In Lecture Notes in Computer Science, ed. JB Talon, W Philips, D Popescu, and P Scheunders, 4678:1061–1071. Berlin, Germany: Springer.
APA
Alecu, A., Munteanu, A., Pizurica, A., Cornelis, J., & Schelkens, P. (2007). Analysis of the statistical dependencies in the curvelet domain and applications in image compression. In J. Talon, W. Philips, D. Popescu, & P. Scheunders (Eds.), LECTURE NOTES IN COMPUTER SCIENCE (Vol. 4678, pp. 1061–1071). Presented at the 9th International Conference on Advanced Concepts for Intelligent Vision Systems, Berlin, Germany: Springer.
Vancouver
1.
Alecu A, Munteanu A, Pizurica A, Cornelis J, Schelkens P. Analysis of the statistical dependencies in the curvelet domain and applications in image compression. In: Talon J, Philips W, Popescu D, Scheunders P, editors. LECTURE NOTES IN COMPUTER SCIENCE. Berlin, Germany: Springer; 2007. p. 1061–71.
MLA
Alecu, Alin, Adrian Munteanu, Aleksandra Pizurica, et al. “Analysis of the Statistical Dependencies in the Curvelet Domain and Applications in Image Compression.” Lecture Notes in Computer Science. Ed. JB Talon et al. Vol. 4678. Berlin, Germany: Springer, 2007. 1061–1071. Print.
@inproceedings{424197,
  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.},
  author       = {Alecu, Alin and Munteanu, Adrian and Pizurica, Aleksandra and Cornelis, Jan and Schelkens, Peter},
  booktitle    = {LECTURE NOTES IN COMPUTER SCIENCE},
  editor       = {Talon, JB and Philips, W and Popescu, D and Scheunders, P},
  isbn         = {978-3-540-74606-5},
  issn         = {0302-9743},
  language     = {eng},
  location     = {Delft, The Netherlands},
  pages        = {1061--1071},
  publisher    = {Springer},
  title        = {Analysis of the statistical dependencies in the curvelet domain and applications in image compression},
  volume       = {4678},
  year         = {2007},
}

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