An EM Algorthim for Wavelet-Besed Image Restoration

IEEE Transactions on Image Processing

Volumn 12, Issue 8, 2003, Pages 906-916

  Figueiredo, Mário A T ^a   Nowak, Robert D ^b  

^a INSTITUTO SUPERIOR TÉCNICO   (Portugal)

^b Rice University   (United States)

Author keywords

Bayesian estimation; Expectation maximization algorithm; Image deconvolution; Image restoration; Penalized maximum likelihood; Wavelets

Indexed keywords

COMPUTATIONAL COMPLEXITY; FAST FOURIER TRANSFORMS; MAXIMUM LIKELIHOOD ESTIMATION; WAVELET TRANSFORMS;

BAYESIAN ESTIMATION;

IMAGE RECONSTRUCTION;

EID: 0142200827     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2003.814255     Document Type: Article

References (35)

1. H. Andrews and B. Hunt, Digital Image Restoration. Englewood Cliffs, NJ: Prentice-Hall, 1977.
2. A. Antoniadis and J. Fan, "Regularized wavelet approximations, " J. Amer. Statist. Assoc., vol. 96, pp. 939-967, 2001.
3. M. Banham and A. Katsaggelos, "Spatially adaptive wavelet-based multiscale image restoration," IEEE Trans. Image Processing, vol. 5, pp. 619-634, 1996.
4. M. Belge, M. E. Kilmer, and E. L. Miller, "Wavelet domain image restoration with adaptive edge-peserving regularity," IEEE Trans. Image Processing, vol. 9, pp. 597-608, 2000.
5. R. Coifman and D. Donoho, "Translation invariant de-noising," in Wavelets and Statistics, Lecture Notes in Statistics, A. Antoniadis and G. Oppenheim, Eds. New York: Springer-Verlag, 1995, vol. 103, pp. 125-150.
6. M. Crouse, R. Nowak, and R. Baraniuk, "Wavelet-based statistical signal processing using hidden Markov models," IEEE Trans. Signal Processing, vol. 46, pp. 886-902, 1998.
7. A. Dempster, N. Laird, and D. Rubin, "Maximum likelihood estimation from incomplete data via the EM algorithm," J. R. Statist. Soc. B, vol. 39, pp. 1-38, 1977.
8. P. de Rivaz and N. Kingsbury, "Bayesian image deconvolution and denoising using complex wavelets," in Proc. IEEE Int. Conf. Image Proc. - ICIP'2001, Thessaloniki, Greece, 2001.
9. D. Donoho, "Nonlinear solution of linear inverse problems by wavelet-vaguelette decompositions," J. Appl. Comput. Harmon. Anal., vol. 1, pp. 100-115, 1995.
10. D. L. Donoho and I. M. Johnstone, "Adapting to unknown smoothness via wavelet shrinkage," J. Amer. Statist. Assoc., vol. 90, no. 432, pp. 1200-1224, 1995.
11. J. Fessler and A. Hero, "Penalized maximum-likelihood image reconstruction using space-alternating generalized EM algorithms," IEEE Trans. Image Processing, vol. 4, pp. 1417-1429, 1995.
12. M. Figueiredo and J. Leitão, "Unsupervised image restoration and edge location using compound Gauss-Markov random fields and the MDL principle," IEEE Trans. Image Processing, vol. 6, pp. 1089-1102, 1997.
13. M. Figueiredo and R. Nowak, "Bayesian wavelet-based signal estimation using noninformative priors," in Proc. 32nd Asilomar Conf. on Signals, Systems, and Computers, Monterey, CA, 1998, pp. 1368-1373.
14. _, "Wavelet-based image estimation: an empirical Bayes approach using Jeffreys' noninformative prior," IEEE Trans. Image Processing, vol. 10, pp. 1322-1331, 2001.
15. H. Gazzah, P. Regalia, and J.-P. Delmas, "Asymptotic eigenvalue distribution of block Toeplitz matrices and application to blind SIMO channel identification," IEEE Trans. Inform. Theory, vol. 47, pp. 1243-1251, 2001.
16. A. Jain, Fundamentals of Digital Image Processing, Englewood Cliffs, NJ: Prentice-Hall, 1989.
17. A. Jalobeanu, N. Kingsbury, and J. Zerubia, "Image deconvolution using hidden Markov tree modeling of complex wavelet packets," in Proc. IEEE Int. Conf. Image Proc. - ICIP'2001, Thessaloniki, Greece, 2001.
18. J. Kalifa, S. Mallat, and B. Rouge, "Deconvolution by thresholding in mirror wavelet bases," IEEE Trans. Image Processing, to be published.
19. R. Lagendijk, J. Biemond, and D. Boekee, "Identification and restoration of noisy blurred images using the expectation-maximization algorithm," IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, pp. 1180-1191, 1990.
20. L. Landweber, "An iterative formula for Fredholm integral equations of the first kind," Amer. J. Math., vol. 73, pp. 615-624, 1951.
21. M. Lang, H. Guo, J. E. Odegard, C. S. Burrus, and R. O. Wells, "Noise reduction using an undecimated discrete wavelet transform," IEEE Signal Processing Lett., vol. 3, pp. 10-12, 1996.
22. J. Liu and P. Moulin, "Complexity-regularized image restoration," in Proc. IEEE Int. Conf. on Image Processing-ICIP'98, vol. 1, Chicago, IL, 1998, pp. 555-559.
23. S. Mallat, A Wavelet Tour of Signal Proc. San Diego, CA: Academic, 1998.
24. G. McLachlan and T. Krishnan, The EM Algorithm and Extensions. New York: Wiley, 1997.
25. M. Mihçak, I. Kozintsev, K. Ramchandran, and P. Moulin, "Low-complexity image denoising based on statistical modeling of wavelet coefficients," Signal Processing Lett., vol. 6, pp. 300-303, 1999.
26. P. Moulin and J. Liu, "Analysis of multiresolution image denoising schemes using generalized - Gaussian and complexity priors," IEEE Trans. Inform. Theory, vol. 45, pp. 909-919, 1999.
27. _, "Statistical imaging and complexity regularization," IEEE Trans. Inform. Theory, vol. 46, pp. 1881-1895, 2000.
28. F. Murtagh, J. Starck, and A. Bijaoui, Image Processing and Data Analysis. Cambridge, U.K.: Cambridge Univ. Press, 1998.
29. R. Neelamani, H. Choi, and R. Baraniuk, "Wavelet-based deconvolution for ill-conditioned systems," IEEE Trans. Image Processing, to be published.
30. R. Nowak and D. Kolaczyk, "A statistical multiscale framework for Poisson inverse problems," IEEE Trans. Inform. Theory, vol. 46, pp. 1811-1825, 2000.
31. L. Scharf, Statistical Signal Processing. Reading, MA: Addison-Wesley, 1991.
32. O. Strand, "Theory and methods related to the singular-function expansion and Landweber's iteration for integral equations of the first kind," SIAM J. Numer. Anal., vol. 11, pp. 798-825, 1974.
33. Y. Wan and R. Nowak, "A wavelet-based approach to joint image restoration and edge detection," Proc. SPIE, vol. 3813, 1999.
34. J. Z. G. Wang and G.-W. Pan, "Solution of inverse problem in image processing by wavelet expansion," IEEE Trans. Image Processing, vol. 4, pp. 579-593, 1995.
35. C. Wu, "On the convergence properties of the EM algorithm," Ann. Statist., vol. 11, pp. 95-103, 1983.