Electronic Journal Technical Acoustics ISSN 1819-2408

M. Djebbouri, D. Djebouri, R. Naoum

Fourier and wavelets for blind image restoration

language: English

received 28.10.2002, published 21.01.2003

Download article (PDF, 400 kb, ZIP), use browser command "Save Target As..."
To read this document you need Adobe Acrobat © Reader software, which is simple to use and available at no cost. Use version 4.0 or higher. You can download software from Adobe site (http://www.adobe.com/).

ABSTRACT

This paper describes a technique for the blind deconvolution based on the wavelet domain deconvolution that comprises Fourier-domain followed by wavelet-domain noise suppression, in order to benefit from the advantages of each of them. The algorithm employs regularized Wiener filter, which allows it to operate even when the system is non-invertible. In fact, we model such image to be the result of a convolution of the original image with a point spread function (PSF). This PSF depends mainly on the image formation system. Unfortunately, it is often very difficult to model this PSF from the physical data, for this reason we consider the problem as a blind deconvolution. First, the identification of the blur is based on maximum likelihood and the solution is obtained iteratively by successive estimations of the PSF from the noisy blurred image. We propose a blind restoration by estimating the noise variance, the point spread function (PSF) and the original image from a blurred and noisy observation. Our method is based on regularized Wiener filter and RDWT (redundant discrete wavelet transform). We illustrate the results with simulations on some examples.

12 pages, 7 figures

Сitation: M. Djebbouri, D. Djebouri, R. Naoum. Fourier and wavelets for blind image restoration. Electronic Journal “Technical Acoustics”, http://www.ejta.org, 2003, 2.

REFERENCES

1. P. C. Hansen. Numerical aspects of deconvolutions, lectures notes. Department of Mathematical Modelling, Technical University of Denmark, 2000.
2. D. L. Donoho and I. M. Johnstone. Adapting to unknown smoothness ideal via wavelet shrinkage. J. Amer. Stat. Assoc., vol. 90, pp. 1200–1224, Dec. 1995.
3. D. L. Donoho. Nonlinear wavelet methods for recovery of signals, densities, and spectra from indirect and noisy data, in Different Perspectives on wavelets. Vol. 47 of Proc. Symp. Appl. Math., pp. 173–205, American Mathematical Society, 1993.
4. J. Kalifa, S. G. Mallat, and B. Rouge. Minimax solution of inverse problems and deconvolution by mirror wavelet thresholding. SPIE conference on Wavelet applications in signal and image processing VII, vol. 3813, (Denver, CO), pp. 42–57, Jul. 1999.
5. M. R. Banham and A. K. Katsaggelos. Spatially adaptive wavelet-based multiscale image restoration. IEEE Trans. Image Processing, vol. 5, pp. 619–634, April 1996.
6. R. Neelamani, H. Choi, and R. G. Baraniuk. Wavelet-based deconvolution for ill-conditioned systems. Dept of Rice University, Submitted to IEEE Trans on Image Processing February 2000.
7. S. Mallat. A Wavelet tour of signal processing. San Diego: Academic Press, 1998.
8. A. K. Katsaggelos and K. T. Lay. Maximum likelihood blur identification and image restoration using the EM algorithm. IEEE Transactions on Signal Processing, vol. 39, No. 3, March 1991.
9. A. K. Katsaggelos. Digital Image Restoration. New-York: Springer-Verlag, 1991.
10. M. Lang, H. Guo, J. E. Odegard, and C. S. Burrus. Noise reduction using an undecimated discrete wavelet transform. IEEE Sig. Proc. Letters, vol. 3, pp. 10–12, Jan. 1996.
11. D. C. Biggs and M. Andews. Acceleration of Iterative Restoration Algorithms. Applied Optics, vol. 36, No. 8, pp. 1766–1775, March 1997.
12. M. Djebbouri and D. Djrbbouri. A blind deconvolution for image restoration. Sememaire sur le traitement du signal et de l’image, Djelfa, Algerie, Novembre 1999.
13. A. Pruessber and D. P. O'Leary. Blind deconvolution using a regularized structured total least norm algorithm. Department of computer science and institute of advanced computer studies. University of Maryland, college Park, MD 20742, Sept. 2001.
14. M. Janseen and A. Bultheel. Multiple wavelet threshold estimation by generalized cross validation for images with correlated noise. IEEE transactions on image processing, 8(7), pp. 947–953, July 1999.
15. M. Janseen and A. Bultheel. Geometrical priors in a Bayesian approach to improve wavelet threshold procedures. Wavelet applications in signal and image processing VII, vol. 3813 of Spie proceedings, pp. 580–590, July 1999.

		Mohamed Djebbouri received the Master's degrees in Signal Processing from the University of Laval, Ste-Foy, Quebec, Canada, in 1990. From 1991 to 2002 he was to the Faculty of the Graduate School of Engineering Institute, Department of Electronic, Sidi Bel Abbes, Algeria, where he was a teaching member. His research there focused on Noise reduction techniques, Filter design, Image processing and Wavelets. e-mail: mdjebbouri(at)hotmail.com
		Djamel Djebouri received the Master’s degree in Signal Processing from the Djillali Liabes University of Sidi Bel Abbes, Algeria, in 2000. From 2000 to 2001, he was to the Faculty of the Graduate School of Engineering Institute of Exact Sciences, Technologies and Informatics Department of Sidi Bel Abbes, Algeria, where he was Assistant Professor. Since February 2002, he has been a Research Scientist with the Technical Space National Centre of Arzew, Oran, Algeria, where his currently involved in GPS receiver design. He is interested in different aspects of Digital Signal Processing including GPS receiver architecture and measurements, Acquisition and Tracking threshold reduction techniques for GPS receivers, Spread Spectrum techniques, Filter design, Noise reduction techniques, Optimization theory, and Wavelets.
		Rafah Naoum received the diploma of Electronic Engineering from the University of Science, and Technology, Oran, Algeria in 1983, the diploma in "Telecommunications Optics and Microwaves", the PhD degree in integrated optics" from University of Limoges, France and the these d'etat from the University Sidi Bel Abbes, Algeria, in 1984, 1987, 1999 respectively. Since 1987, he is at the Dept of Electronics, where he is Associate Professor in Electronic Department, University of Sidi Bel-Abbes. His research interests include photonic integration, photonic networking, optical communications and image processing.