Removal of correlated noise by modeling the signal of interest in the wavelet domain

IEEE Transactions on Image Processing

Volumn 18, Issue 6, 2009, Pages 1153-1165

  Goossens, Bart ^a   Pižurica, Aleksandra ^a   Philips, Wilfried ^a  

^a GHENT UNIVERSITY   (Belgium)

Author keywords

Correlated noise; Hidden Markov trees (HMT); Image denoising

Indexed keywords

COMBINED MODEL; CORRELATED NOISE; DENOISING METHODS; DIGITAL IMAGING DEVICES; HIDDEN MARKOV TREE MODEL; HIDDEN MARKOV TREES (HMT); IMAGE DENOISING; INTRASCALE MODELS; REDUNDANT WAVELET TRANSFORM; SIGNAL OF INTERESTS; SIGNIFICANCE MEASURES; UNCORRELATED NOISE; WAVELET COEFFICIENTS; WAVELET DOMAIN; WAVELET-BASED METHODS;

ACOUSTIC NOISE; COMPUTATIONAL COMPLEXITY; CONTROL SYSTEM ANALYSIS; DIGITAL DEVICES; IMAGE PROCESSING; WHITE NOISE;

WAVELET TRANSFORMS;

EID: 67349122907     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2009.2017169     Document Type: Article

References (44)

1. D. L. Donoho, "De-noising by soft-thresholding," IEEE Trans. Inf. Theory, vol. 41, no. 5, pp. 613-627, May 1995.
2. S. Chang, B. Yu, and M. Vetterli, "Spatially adaptive wavelet thresholding with context modeling for image denoising," IEEE Trans. Image Process., vol. 9, no. 9, pp. 1522-1531, Sep. 2000.
3. L. Şendur and I. W. Selesnick, "Bivariate shrinkage with local variance estimation," IEEE Signal Process. Lett., vol. 9, no. 12, pp. 438-441, Dec. 2002.
4. J. Portilla, V. Strela, M. Wainwright, and E. Simoncelli, "Image denoising using Gaussian scale mixtures in the wavelet domain," IEEE Trans. Image Process., vol. 12, no. 11, pp. 1338-1351, Nov. 2003.
5. A. Pižurica and W. Philips, "Estimating the probability of the presence of a signal of interest in multiresolution single- and multiband image denoising.," IEEE Trans. Image Process., vol. 15, no. 3, pp. 654-665, Mar. 2006.
6. F. Shi and I. W. Selesnick, "Multivariate Quasi-Laplacian mixture models for wavelet-based image denoising," in Proc. Int. Conf. Image Processing, 2006, pp. 2097-2100.
7. F. Luisier, T. Blu, and M. Unser, "A new SURE approach to image denoising: Interscale orthonormal wavelet thresholding," IEEE Trans. Image Process., vol. 16, no. 3, pp. 593-606, Mar. 2007.
8. I. M. Johnstone and B. W. Silverman, "Wavelet threshold estimators for data with correlated noise," J. Roy. Statist. Soc. B, vol. 59, no. 2, pp. 319-351, 1997.
9. M. Basseville, A. Benveniste, K. Chou, S. Golden, R. Nikoukhah, and A. Willsky, "Modeling and estimation of multiresolution stochastic processes," IEEE Trans. Inf. Theory, vol. 38, no. 2, pp. 766-784, Mar. 1992.
10. M. R. Banham and A. K. Katsaggelos, "Spatially adaptive wavelet-based multiscale image restoration," IEEE Trans. Image Process., vol. 5, no. 4, pp. 619-634, Apr. 1996.
11. M. Crouse, R. Nowak, and R. Baraniuk, "Wavelet-based statistical signal processing using hidden Markov models," IEEE. Trans. Signal Process. vol. 46, no. 4, pp. 886-902, Apr. 1998.
12. H. Choi, J. Romberg, R. Baraniuk, and N. G. Kingsbury, "Hidden Markov tree modeling of complex wavelet transforms," presented at the IEEE Conf. Acoustics, Speech, Signal Process. (ICASSP), 2000.
13. J. K. Romberg, H. Choi, and R. G. Baraniuk, "Bayesian tree structured image modeling using wavelet-domain hidden Markov models," IEEE Trans. Image Process., vol. 10, no. 7, pp. 1056-1068, Jul. 2001.
14. G. Fan and X. Xia, "Image denoising using local contextual hidden Markov model in the wavelet domain," IEEE Signal Process. Lett., vol. 8, no. 5, pp. 125-128, May 2001.
15. M. Malfait and D. Roose, "Wavelet-based image denoising using a Markov random field a priori model," IEEE Trans. Image Process., vol. 6, no. 4, pp. 549-565, Apr. 1997.
16. M. Jansen and A. Bultheel, "Empirical bayes approach to improve wavelet thresholding for image noise reduction," J. Amer. Statist. Assoc. vol. 96, no. 454, pp. 629-639, 2001.
17. A. Pižurica, W. Philips, I. Lemahieu, and M. Acheroy, "A joint inter- and intrascale statistical model for Bayesian wavelet based image denoising," IEEE Trans. Image Process., vol. 11, no. 5, pp. 545-557, May 2002.
18. J. Portilla and E. P. Simoncelli, "Adaptive wiener denoising using a Gaussian scale mixture model in the wavelet domain," in Proc. IEEE Int. Conf. Image Processing, 2001, vol. 2, pp. 37-40.
19. I. W. Selesnick, R. G. Baraniuk, and N. G. Kingsbury, "The dual-tree complex wavelet transform," IEEE Signal Process. Mag., vol. 22, no. 6, pp. 123-151, Nov. 2005.
20. N. G. Kingsbury, "Complex wavelets for shift invariant analysis and filtering of signals," J. Appl. Comput. Harmon. Anal., vol. 10, no. 3, pp. 234-253, May 2001.
21. J. L. Starck, E. J. Candès, and D. L. Donoho, "The curvelet transform for image denoising," IEEE Trans. Image Process., vol. 11, no. 6, pp. 670-684, Jun. 2000.
22. M. N. Do and M. Vetterli, "The contourlet transform: An efficient directional multiresolution image representation," IEEE Trans. Image Process., vol. 14, no. 12, pp. 2091-2106, Dec. 2005.
23. H. Baher, Analog and Digital Signal Processing. Chichester, U.K.: Wiley, 2001.
24. S. Kotz, T. Kozubowski, and K. Podgorski, The Laplace Distributions And Generalizations: A Revisit with Applications to Communications, Economics, Engineering, Finance. Boston, MA: Birkhauser, 2001.
25. A. Srivastava, X. Liu, and U. Grenander, "Universal analytical forms for modeling image probabilities," IEEE Trans. Pattern Anal. Mach. Intell., vol. 24, no. 9, pp. 1200-1214, Sep. 2002.
26. J. M. Fadili and L. Boubchir, "Analytical form for a Bayesian wavelet estimator of images using the Bessel K form densities," IEEE Trans. Image Process., vol. 14, no. 2, pp. 231-240, Feb. 2005.
27. I. W. Selesnick, "Laplace random vectors, Gaussian noise, and the generalized incomplete gamma function," in Proc. Int. Conf. Image Processing, 2006, pp. 2097-2100.
28. S. Mallat, "Multifrequency channel decomposition of images and wavelet models," IEEE Trans. Acoust., Speech, Signal Process., vol. 37, no. 12, pp. 2091-2110, Dec. 1989.
29. M. J. Wainwright and E. P. Simoncelli, "Scale mixtures of Gaussians and the statistics of natural images," in Advances in Neural Information Processing Systems. Cambridge, MA: MIT Press, 2000, vol. 12, pp. 855-861.
30. L. Boubchir, "Algorithme EM pour l'estimation des hyperparamètres du debruiteur Bayésien d'images basé sur l'a priori des Formes K de Bessel," in Proc. Journées d'Etudes Algéro-Françaises en Imagerie Médicale, Algeria, 2006, pp. 47-54.
31. L. Boubchir, "Bayesian Approaches for Image Denoising in Oriented and Non-Oriented Multiscale Sparse Transforms," Ph.D. dissertation, Univ. Caen, Caen, France, 2007.
32. J. M. Shapiro, "Embedded image coding using zerotrees of wavelet coefficients," IEEE Trans. Signal Process., vol. 41, no. 12, pp. 3445-3462, Dec. 1993.
33. L. R. Rabiner, "A tutorial on hidden Markov models and selected applications in speech recognition," Proc. IEEE, vol. 77, no. 2, pp. 257-286, Feb. 1989.
34. A. Dempster, N. Laird, and D. Rubin, "Maximum likelihood from incomplete data via the EM algorithm," J. Roy. Satist. Soc., vol. 39, no. 1, pp. 1-38, 1977.
35. J. J. Kivinen, E. B. Sudderth, and M. I. Jordan, "Image denoising with nonparametric hidden Markov trees," presented at the IEEE Int. Conf. Image Processing, San Antonio, TX, Sep. 2007.
36. G. Gamerman, Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference. New York: Chapman & Hall/CRC, 1997.
37. G. Fan and X.-G. Xia, "Improved hidden Markov models in the wavelet-domain," IEEE Trans. Signal Process., vol. 49, no. 1, pp. 115-120, Jan. 2001.
38. H. L. Van Trees, Detection, Estimation and Modulation Theory. New York: Wiley, 1968.
39. K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, "Image denoising by sparse 3-D transform-domain collaborative filtering," IEEE Trans. Image Process., vol. 16, no. 8, pp. 2080-2095, Aug. 2007.
40. S. G. Chang, B. Yu, and M. Vetterli, "Adaptive wavelet thresholding for image denoising and compression," IEEE Trans. Image Process., vol. 9, no. 9, pp. 1532-1546, Sep. 2000.
41. M. Elad and M. Aharon, "Image denoising via sparse and redundant representations over learned dictionaries," IEEE Trans. Image Process., vol. 15, no. 12, pp. 3736-3745, Dec. 2006.
42. A. Buades, B. Coll, and J. M. Morel, "A non local algorithm for image denoising," in Proc. Int. Conf. Computer Vision and Pattern Recognition, 2005, vol. 2, pp. 60-65.
43. C. Kervrann and J. Boulanger, "Optimal spatial adaptation for patch-based image denoising," IEEE Trans. Image Process., vol. 15, no. 10, pp. 2866-2878, Oct. 2006.
44. E. J. Candes, L. Demanet, D. L. Donoho, and L. Ying, "Fast discrete curvelet transforms," Multiscale Model. Simul., vol. 5, no. 3, pp. 861-899, 2006.