Wavelet-based image denoising using a Markov random field a priori model

IEEE Transactions on Image Processing

Volumn 6, Issue 4, 1997, Pages 549-565

  Malfait, Maurits ^a   Roose, Dirk ^b  

^a LUCENT TECHNOLOGIES   (United States)

^b UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

INTERFERENCE SUPPRESSION; MARKOV PROCESSES; MATHEMATICAL MODELS; PROBABILITY; RANDOM PROCESSES; SIGNAL TO NOISE RATIO; WAVELET TRANSFORMS;

IMAGE ACQUISITION TECHNIQUES; MARKOV RANDOM FIELD IMAGE MODEL; WAVELET SHRINKAGE TECHNIQUES;

IMAGE RECONSTRUCTION;

EID: 0031117537     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/83.563320     Document Type: Article

References (27)

1. M. G. Bello, "A combined Markov random field and wave-packet transform-based approach for image segmentation," IEEE Trans. Image Processing, vol. 3, pp. 834-846, Nov. 1994.
2. J. J. Benedetto and S. Li, "Subband coding and noise reduction in multiresolution analysis frames," in Mathematical Imaging: Wavelet Applications in Signal and Image Processing, SPIE Proc. Series, A. F. Laine and M. Unser, Eds., vol. 2303, pp. 154-165, 1994.
3. J. E. Besag, "Spatial interaction and the spatial analysis of lattice systems," J. Roy. Stat. Soc., Ser. B, vol. 36, pp. 192-236, 1974.
4. R. A. Carmona, "Wavelet identification of transients in noisy time series," in Mathematical Imaging: Wavelet Applications in Signal and Image Processing, SPIE Proc. Series, A. F. Laine and M. Unser, Eds., vol. 2034, pp. 392-400.
5. _, "Extrema reconstructions and spline smoothing: Variations on an algorithm of Mallat and Zhong," in Wavelets and Statistics, in Lecture Notes in Statistics. A. Antoniadis and G. Oppenheim, Eds., vol. 103, 1995, pp. 83-94.
6. P. Charbonnier, L. Blanc-Féraud, and M. Barlaud, "Noisy image restoration using multiresolution Markov random fields," J. Vis. Commun. Image Represent., vol. 3, pp. 338-346, 1992.
7. R. R. Coifman and F. Majid, "Adapted waveform analysis and denoising," in Progress in wavelet analysis and applications, Y. Meyer and S. Roques, Eds. Gif-sur-Yvette Cedex, France: Editions Frontieres, 1993, pp. 63-76.
8. I. Daubechies, Ten Lectures on Wavelets. Philadelphia, PA: SIAM: 1992.
9. D. L. Donoho and I. M. Johnstone, "Adapting to unknown smoothness via wavelet shrinkage. J. Amer. Stat. Assoc., to be published.
10. S. Geman and D. Geman, "Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images," IEEE Trans. Pattern Anal. Machine Intell., vol. 6, pp. 721-741, 1984.
11. I. M. Johnstone and B. W. Silverman, "Wavelet threshold estimators for data with correlated noise," Stanford Univ., CA, and Bristol Univ., U.K., 1994, preprint.
12. Z. Kato, M. Berthod, and J. Zerubia, "Parallel image classification using multiscale Markov random fields," in Proc. 1993 IEEE Int. Conf. Acoustics, Speech, and Signal Processing, pages V-137-V-140, 1993.
13. R. Kindermann and J. Snell, Markov Random Fields and Their Application. Providence, RI: American Math. Soc., 1980.
14. J. Lu, "Signal recovery and noise reduction with wavelets," Ph.D. dissertation, Thayer School Eng., Dartmouth College, Hanover, NH, 1993.
15. M. R. Luettgen, W. C. Karl, A. S. Willsky, and R. R. Tenney, "Multiscale representations of Markov random fields, IEEE Trans. Signal Processing, vol. 41, pp. 3377-3395, Dec. 1993.
16. M. Malfait and D. Roose, "Biomedical image denoising with wavelets and Bayesian geometrical constraints, in Proc. 16th IEEE EMBS Conf., N. F. Sheppard, M. Eden, and G. Kantor, Eds., Nov. 1994, vol. 2, pp. 1228-1229.
17. _, "Convergence of concurrent Markov chain Monte Carlo algorithms," Concurrency: Practice and Experience, vol. 8, pp. 167-189, 1996.
18. S. Mallat and W. L. Hwang, "Singularity detection and processing with wavelets," IEEE Trans. Inform. Theory, vol. 38, pp. 617-643, 1992.
19. S. G. Mallat, "A theory for multiresolution signal decomposition: The wavelet representation," IEEE Trans. Pattern Anal. Machine Intell., vol. 11, pp. 674-693, 1989.
20. S. G. Mallat, W. L. Hwang, and S. Zhong, "Wave2©," software package, New York Univ., 1992. Available for scholarly and research purposes: (ftp://cs.nyu.edu/pub/wave/wave2.tar.Z).
21. N. Metropolis et al., "Equation of state calculations by fast computing machines," J. Chem. Phys., vol. 21, pp. 1087-1092, 1953.
22. J.-L. Starck and A. Bijaoui, "Filtering and deconvolution by the wavelet transform," Signal Processing, vol. 35, pp. 195-211, 1994.
23. B. Vidakovic, "Nonlinear wavelet shrinkage with Bayes rules and Bayes factors," Duke Univ., Durham, NC, 1994, preprint.
24. N. Weyrich and G. T. Warhola, "De-noising using wavelets and cross validation," in Approximation Theory, Wavelets and Applications, NATO ASI Series C, S. P. Singh, Ed., vol. 454, pp. 523-532, 1995.
25. M. V. Wickerhauser, Adapted Wavelet Analysis from Theory to Software. Wellesley, MA: A. K. Peters, 1994.
26. G. Winkler, Image Analysis, Random Fields and Dynamic Monte Carlo Methods, Applications of Mathematics. New York: Springer-Verlag, 1995.
27. Y. Xu, J. B. Weaver, D. M. Healy, and J. Lu, "Wavelet transform domain filters: A spatially selective noise filtration technique," IEEE Trans. Image Processing, vol. 3, pp. 747-758, 1994.