On the minimum entropy of a mixture of unimodal and symmetric distributions

IEEE Transactions on Information Theory

Volumn 54, Issue 7, 2008, Pages 3166-3174

  Chen, Ting Li ^a   Geman, Stuart ^b  

^a INSTITUTE OF STATISTICAL SCIENCE   (Taiwan)

^b BROWN UNIVERSITY   (United States)

Author keywords

Entropy coding; LOCO; Lossless image compression; Mixture distributions; Predictive coding; Symmetric distributions; Unimodal distributions

Indexed keywords

ENTROPY; ESTIMATION; MOBILE TELECOMMUNICATION SYSTEMS; PROGRAMMING THEORY;

(R ,S)-SYMMETRIC; COMMON SENSE; CONDITIONAL DISTRIBUTIONS; FINANCIAL DATA; MINIMUM ENTROPY; NATURAL SCENES; PROGRESSIVE ENCODING; ROTATION INVARIANT; SYMMETRIC DISTRIBUTIONS; UNIMODAL; UNIMODAL DISTRIBUTIONS;

IMAGE SEGMENTATION;

EID: 46749124769     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2008.924686     Document Type: Article

References (20)

1. A. Netravali and J. O. Limb, "Picture coding: A review," Proc. IEEE vol. 68, pp. 366-406, 1980.
2. L. A. Lehmann and A. Macovski, "Data compression of X-ray images by adaptive DPCM coding," in Proc. SPIE Digit. Radiol. Conf., Sep. 1981, pp. 314-317.
3. P. Howard and J. S. Vitter, "Error modeling for hierarchical lossless image compression," in Proc. IEEE Data Compress. Conf., Snowbird, UT, 1992, pp. 269-278.
4. G. Langdon and M. Manohar, "Centering of context-dependent components of prediction error distributions of images," SPIE Appl. Digit. Image Process. XVI, vol. 2028, pp. 26-32, 1993.
5. R. F. Engle, "Autoregressive conditional heteroscedasticity with estimates of the variance of united kingdom inflation," Econometrica vol. 50, pp. 987-1007, 1982.
6. T. P. Bollerslev, "A conditionally heteroskedastic time series model for security prices and rates of return data," Rev. Econom. Statist. vol. 69, pp. 542-547, 1987.
7. Balaban, Ercan, Ouenniche, Jamal, Politou, and Danae, "A note on return distribution of UK stock indices," Appl. Econom. Lett., vol. 12, pp. 573-576, 2005.
8. M. Weinberger, G. Seroussi, and G. Sapiro, "LOCO-I: A low complexity, context-based, lossless image compression algorithm," in Proc. IEEE Data Compress. Conf., Snowbird, UT, Mar.-Apr. 1996.
9. M. Weinberger, G. Seroussi, and G. Sapiro, The LOCO-I lossless image compression algorithm: Principles and standardization into JPEG-LS 1998, Hewlett-Packard Laboratories Technical Report No. HPL-98-193R1.
10. N. Farvardin and J. W. Modestino, "Adaptive buffer-instrumented entropy-coded quantizer performance for memoryless sources," IEEE Trans. Inf. Theory, vol. IT-32, pp. 9-22, 1986.
11. X. Wu, "Lossless compression of continuous-tone images via context selection, quantization, and modeling," IEEE Trans. Image Process. vol. IP-6, pp. 656-664, May 1997.
12. K. Popat, "Lossy compression of grayscale document images by adaptive-offset quantization," Proc. IS&T/SPIE Electron. Imag. 2001: Document Recognit. Retrieval VIII, Jan. 2001.
13. M. Janžura, T. Koski, and A. Otáhal, "Minimum entropy of error principle in estimation," Inf. Sci., vol. 79, pp. 123-144, 1994.
14. G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities. Cambridge, U.K.: Cambridge Univ. Press, 1934.
15. H. L. Weidemann and E. B. Stear, "Entropy analysis of parameter estimation," Inf. Control, vol. 14, pp. 493-506, 1969.
16. A. Otáhal, "Minimum entropy of error estimate for multi-dimensional parameter and finite-state-space observations," Kybernetika, vol. 31, pp. 331-335, 1995.
17. M. Janžura, T. Koski, and A. Otáhal, "Minimum entropy of error estimation for discrete random variables," IEEE Trans. Inf. Theory vol. IT-42, pp. 1193-1201, 1996.
18. T. M. Cover and J. A. Thomas, Elements of Information Theory, Second ed. New York: Wiley, 2006.
19. Digital Compression and Coding Of Continuous Tone Still Images - Requirements And Guidelines, ISO/IEC 10918-1, ITU Recommendation, 1993, T.81.
20. S. A. Martucci, "Reversible compression of HDTV images using median adaptive prediction and arithmetic coding," in Proc. IEEE Int. Symp. Circuits Syst., 1990, pp. 1310-1313.