Solution of Inverse Problems in Image Processing by Wavelet Expansion

IEEE Transactions on Image Processing

Volumn 4, Issue 5, 1995, Pages 579-593

  Pan, Guang Wen ^c  

^a Tanner Research Inc   (United States)

^b RENSSELAER POLYTECHNIC INSTITUTE   (United States)

^c UNIVERSITY OF WISCONSIN MILWAUKEE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; IMAGE RECONSTRUCTION; INVERSE PROBLEMS; MATHEMATICAL OPERATORS; WAVELET TRANSFORMS;

LINEAR INVERSE PROBLEMS; WAVELET EXPANSION;

IMAGE PROCESSING;

EID: 0029306397     PISSN: 10577149     EISSN: 19410042     Source Type: Journal    
DOI: 10.1109/83.382493     Document Type: Article

References (41)

1. M. Bertero, T. A. Poggio, and V. Torre, “Ill-posed problems in early vision” IEEE Proc., vol. 76, pp. 869-889, Aug. 1988.
2. L. Shepp and Y. Vardi, “Maximum likelihood reconstruction in positron emission tomography” IEEE Trans. Med. Imag., vol. MI-1, pp. 113-122, 1982.
3. S. Geman and D. Geman, “Stochastic relaxation, Gibbs distribution, and the Bayesian restoration of images” IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-6, pp. 721-741, Nov. 1984.
4. W. Hackbusch, Multi-Grid Methods and Applications. New York: Springer-Verlag, 1985.
5. D. L. Donoho, “Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition” Tech. Rep., Statist. Dept., Stanford Univ., June 1992.
6. F.-C. Jeng and J. W. Woods, “Compound Gauss-Markov random fields for image estimation” IEEE Trans. Acoust., Speech, Signal Processing, vol. 39, pp. 914-929, Apr. 1991.
7. I. Daubechies, Ten Lectures on Wavelet. New York: SIAM Press, 1992.
8. S. Mallat, “A theory for multiresolution signal decomposition: The wavelet representation” IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-11, pp. 674-693, July 1989.
9. O. Rioul and M. Vetterli, “Wavelets and signal processing” IEEE Signal Processing Mag., pp. 14-38, Oct. 1991.
10. J. W. Woods and J. Kim, “Image identification and restoration in subband domain” in Proc. ICASSP ' ‘92, San Francisco, CA, Mar. 23-26, 1992, vol. III pp. 297-300.
11. R. L. Lagendijk and M. I. Sezan, “Multiresolution image restoration and identification: Further developments and application to real-life images” in Proc. 7th MDSP Workshop, Lake Placid, New York, 1991, p. 1.4.
12. G. Walter, Wavelets and Other Orthogonal Systems with Applications. Boca Raton, FL: CRC, 1994.
13. A. H. Tewfik and M. Kim, “Correlation structure of the discrete wavelet coefficients of fractional Brownian motions” IEEE Trans. Inform. Theory, vol. 38, pp. 904-909, Mar. 1992.
14. G. W. Wornell and A. V. Oppenheim, “Estimation of fractal signals from noisy measurements using wavelets” IEEE Trans. Signal Processing, vol. 40, pp. 611-623, Mar. 1992.
15. G. W. Wornell, “A Karhunen-Loeve-like expansion for 1/f processes via wavelets” IEEE Trans. Inform. Theory, vol. 36, pp. 859-861, July 1990.
16. J. Zhang and G. Walter, “A KL like expansion for wide-sense stationary processes via a wavelet like basis” IEEE Trans. Signal Processing, vol. 42, no. 7, pp. 1737-1745, July 1992.
17. M. Allam and J. Zhang, “Detection of anomalies in images by wavelet expansion” submitted to IEEE Trans. Image Processing.
18. C. K. Chui, An Introduction to Wavelets. New York: Academic, 1991.
19. Y. Meyer, Wavelets: Algorithms and Applications. New York: SIAM, 1993 (translated by R. D. Ryan).
20. J. Kovacevic and M. Vetterli, “Nonseparable multidimensional perfect reconstruction filter banks and wavelet basis for Rn” IEEE Trans. Inform. Theory, vol. 38, pp. 533-555, Mar. 1992.
21. G. Beylkin, R. R. Coifman, and V. Rokhlin, “Fast wavelet transforms and numerical algorithms I” Yale University Technical Report, YALEU/DCS/RR-696, Aug. 1989, Comm. Pure Appl. Math., vol. XLIV, pp. 141-183, 1991.
22. I. Daubechies, “Orthonormal bases of compactly supported wavelets” Commun. Pure Appl. Math., vol. 41, pp. 909-996, Nov. 1988.
23. G. Beylkin, “On the representation of operators in bases of compactly supported wavelets” preprint, to appear in SIAM J. Numerical Anal.
24. S. Mallat and W. L. Hwang, “Singularity detection processing with wavelets” IEEE Trans. Inform. Theory, vol. 38, pp. 617-643, Mar. 1992.
25. H. C. Andrew and B. R. Hunt, Digital Image Restoration. Englewood Cliffs, NJ: Prentice-Hall, 1977.
26. G. Demoment, “Image reconstruction and restoration: Overview of common estimation structures and problems” IEEE Trans. Acoust., Speech, Signal Processing, vol. 37, pp. 2024-2073, Dec. 1989.
27. F.-C. Jeng and J. W. Woods, “Compound Gauss-Markov random fields for image estimation” IEEE Trans. Signal Processing, vol. 39, pp. 683-697, Mar. 1991.
28. A. K. Katsaggelos, J. Biemond, R. W. Schafer, and R. M. Mersereau, “A regularized iterative image restoration algorithm” IEEE Trans. Acoust., Speech, Signal Processing, vol. 39, pp. 914-929, Apr. 1991.
29. A. M. Tekalp, H. Kaufman, and J. W. Woods, “Identification of image and blur parameters for the restoration and noncausal blurs” IEEE Trans. Acoust., Speech, Signal Processing, vol. 34, pp. 963-972, 1986.
30. R. L. Lagendijk, J. Biemond, and D. E. Boekee, “Identification and restoration of noisy and blurred image using the expectation- maximization algorithm” IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, pp. 1180-1191, July 1990.
31. J. Zhang, “The mean field theory for EM procedures in blind MRF image restoration” IEEE Trans. Image Processing., vol. 2, pp. 27-40, Jan. 1993.
32. J. Zhang and B. Chen, “Multi-grid algorithms for MRF’s” in Proc. 1993 Int. Symp. Inform. Theory, San Antonio, Texas, Jan. 1993, p. 92.
33. G. Wang, “Numerical techniques for electromagnetic modeling of high speed circuits” Ph.D. dissertation (in preparation), Univ. of Rhode Island.
34. R.L. Lagendijk and J. Biemond, Iterative Identification and Restoration of Images. Boston: Kluwer, 1991.
35. M. Bertero, C. DeMol, and E. R. Pike, “Linear inverse problems with discrete data: II. Stability and regularization” Inverse Problems, vol. 4, pp. 573-594, 1988.
36. A. N. Tikhonov and V. Y. Arsenin, Solution of Ill-Posed Problems. New York: Wiley, 1977.
37. A. M. Thompson, J. C. Brown, J. W. Kay, and D. M. Titterington, “A study of methods of choosing the smoothing parameter in image restoration by regularization” IEEE Trans. Pattern Anal. Machine Intell., vol. 13, pp. 703-714, July 1991.
38. N. P. Galatsanos and A. K. Katsaggelos, “Methods for choosing the regularization parameter and estimating the noise variance in image restoration and their relation” IEEE Trans. Image Processing, vol. 1, pp. 322-336, July 1992.
39. J. Zhang, “The application of the Gibbs-Bogoliubov-Feynman in mean field calculations for Markov random fields” in Proc. SPIE Visual Commun. Image Processing, Chicago, IL, Sept. 1994, pp. 982-993.
40. N. B. Karayiannis and A. N. Venetsanopoulos, “Regularization theory in image restoration—The stabilizing functional approach” IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, no. 7, pp. 1155-1179, July 1990.
41. M. G. Kang and A. K. Katsaggelos, “Regularized iterative image restoration based on an iterative updated convex smoothing functional” in Proc. Visual Comm. Image Proc. ' ‘93, SPIE, Boston, MA, Nov. 1993, vol. 2094, pp. 1364-1375.