Complex Daubechies wavelets: Properties and statistical image modelling

Signal Processing

Volumn 84, Issue 1, 2004, Pages 1-23

  Clonda, Diego ^a   Lina, J M ^a   Goulard, Bernard ^a  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

Author keywords

Complex wavelet; Hidden Markov models; Image processing; Statistical modelling

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; DATA REDUCTION; HIERARCHICAL SYSTEMS; POLYNOMIALS; STATISTICAL METHODS; TEXTURES;

COMPLEX WAVELETS; HIDDEN MARKOV MODELS (HMM);

IMAGE PROCESSING;

EID: 0344494103     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sigpro.2003.06.001     Document Type: Article

References (33)

1. Baum L.E., Petrie T., Soules G., Weiss N. A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains. Ann. Math. Statist. Soc. 41:1970;164-171.
2. Besag J. On the statistical analysis of dirty picture. J. Roy. Statist. Soc. Ser. B. 48:1986;259-302.
3. Burt P.J., Adelson E.H. The Laplacian pyramid as a compact image code. IEEE Trans. Comm. 31(4):1983;532-540.
4. H. Choi, R.G. Baraniuk, Image Segmentation using Wavelet-domain Classification, Rice-Preprint, April 1999.
5. D. Clonda, J.M. Lina, B. Goulard, Mixed memory model for image processing and modeling with complex Daubechies wavelets, wavelet applications in signal processing VII, SPIEE Conference, San Diego, 2000.
6. M.S. Crouse, R.D. Nowak, R.G. Baraniuk, Wavelet-based statistical signal processing using hidden Markov models, IEEE Trans. Signal Process. (Special Issue on Wavelets and Filter Banks) (April 1998).
7. Daubechies I. Ten Lectures on Wavelets. 1992;SIAM, Philadelphia, PA.
8. Daubechies I. A Wavelet Tour of Signal Processing. 1998;Academic Press, New York.
9. Dempster A., Laird N., Rubin D. Maximum likelihood from incomplete data via EM algorithm. J. Roy. Statist. Soc. B. 39:1977;1-38.
10. DeVore R., Jawerth B., Lucier B. Image compression through transform coding. IEEE Trans. Inform. Theory. 38:1992;719-746.
11. Donoho D., Johnstone I. Wavelet shrinkage. assymptopia? J. Roy. Statist. Soc. B. 39:1995;301.
12. Geman S., Geman D. Stochastic relaxation, Gibbs distribution and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Machine Intell. 6:1984;721-741.
13. Gidas B. A renormalization group approach to image processing problems. IEEE Trans. Pattern Anal. Machine Intell. 11:1989;164-180.
14. N.G. Kingsbury, Complex wavelets and shift invariance, Proceedings of the IEE Colloquium on Time-Scale and Time-Frequency Analysis and Applications, London, 29 February 2000.
15. Lawton W. Application of complex valued wavelet transforms to subband coding. IEEE Trans. Signal Process. 41:1993;3566-3568.
16. Lina J.-M. Image processing with complex Daubechies wavelets. J. Math. Imaging Vision. 7:1997;211-223.
17. Lina J.-M., Drouilly P. The importance of phase of the symmetric Daubechies wavelets representation of signals. Wavelet Appl. Signal Process. 3169:1996;67-79.
18. Lina J.-M., Mayrand M. Complex Daubechies wavelets. Appl. Comput. Harmonic Anal. 2:1995;219-229.
19. Lina J.-M., McGibbon B. Nonlinear shrinkage estimation with complex Daubechies wavelets. SPIE. 3169:1997;67-79.
20. Magarey J.F.A., Kingsbury N.G. Motion estimation using a complex-valued wavelet transform. IEEE Trans. Signal Process. (Special Issue on Wavelets and Filter Banks). 46(4):1998;1069-1084 Magarey J.F.A., Kingsbury N.G. Motion estimation using a complex-valued wavelet transform. IEEE Trans. Signal Process. (Special Issue on Wavelets and Filter Banks). 3169:1997;67-79.
21. Magarey J.F.A., Kingsbury N.G. Motion estimation using a complex-valued wavelet transform. IEEE Trans. Signal Process. (Special Issue on Wavelets and Filter Banks). 46(4):1998;1069-1084 Magarey J.F.A., Kingsbury N.G. Motion estimation using a complex-valued wavelet transform. IEEE Trans. Signal Process. (Special Issue on Wavelets and Filter Banks). 3169:1997;67-79.
22. Mallat S.G. A theory of multiresolution signal decomposition. the wavelet representation IEEE Trans. Pattern Anal. Machine Intell. 11:1989;674-693.
23. Mallat S.G. Multifrequency channel decomposition of images and wavelet models. IEEE Trans. Acoust. Speech Signal Process. 37:1989;2091-2110.
24. Mallat S.G. A Wavelet Tour of Signal Processing. 1998;Academic Press, New York.
25. Miller K.S. Complex Stochastic Processes. 1974;Addison-Wesley, Reading, MA.
26. Oppenheim A.V., Li J.S. The importance of phase in signals. Proc. IEEE. 69:1981;529-541.
27. Picinbono B. Second-order complex random vectors and normal distributions. IEEE Trans. Signal Process. 44:1996;2637.
28. J. Portilla, E. Simoncelli, Texture modeling and synthesis using joint statistics of complex wavelet coefficients, IEEE Workshop on Statistical and Computational Theories of Vision, June 1999.
29. Rabiner L. A tutorial on hidden Markov Models and selected applications in speech recognition. Proc. IEEE. 77(2):1989;257-286.
30. Ronen O., Rohlicek J., Ostendorf M. Parameter estimation of dependence tree models using the EM algorithm. IEEE Signal Process. Lett. 2:1995;157-159.
31. Shapiro J.M. Embedded image coding using zerotrees of wavelet coefficients. IEEE Trans. Signal Process. 41(12):1993;3445-3462.
32. E. Simoncelli, Statistical Models for Images: Compression, Restoration and Synthesis, 31st Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, 1997.
33. M.V. Wickerhauser, Adapted Wavelet Analysis from Theory to Software, AK Peters, Ltd., Wellesley, MA, 1994.