OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 17, Iss. 7 — Jul. 1, 2000
  • pp: 1177–1184

Iterative statistical approach to blind image deconvolution

Edmund Y. Lam and Joseph W. Goodman  »View Author Affiliations


JOSA A, Vol. 17, Issue 7, pp. 1177-1184 (2000)
http://dx.doi.org/10.1364/JOSAA.17.001177


View Full Text Article

Enhanced HTML    Acrobat PDF (816 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Image deblurring has long been modeled as a deconvolution problem. In the literature, the point-spread function (PSF) is often assumed to be known exactly. However, in practical situations such as image acquisition in cameras, we may have incomplete knowledge of the PSF. This deblurring problem is referred to as blind deconvolution. We employ a statistical point of view of the data and use a modified maximum a posteriori approach to identify the most probable object and blur given the observed image. To facilitate computation we use an iterative method, which is an extension of the traditional expectation–maximization method, instead of direct optimization. We derive separate formulas for the updates of the estimates in each iteration to enhance the deconvolution results, which are based on the specific nature of our a priori knowledge available about the object and the blur.

© 2000 Optical Society of America

OCIS Codes
(000.5490) General : Probability theory, stochastic processes, and statistics
(100.1830) Image processing : Deconvolution
(100.2000) Image processing : Digital image processing
(100.3020) Image processing : Image reconstruction-restoration
(110.5200) Imaging systems : Photography

History
Original Manuscript: April 19, 1999
Revised Manuscript: October 25, 1999
Manuscript Accepted: October 25, 1999
Published: July 1, 2000

Citation
Edmund Y. Lam and Joseph W. Goodman, "Iterative statistical approach to blind image deconvolution," J. Opt. Soc. Am. A 17, 1177-1184 (2000)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-17-7-1177


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).
  2. K. R. Castleman, Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1996).
  3. A. Gersho, R. Gray, Vector Quantization and Signal Compression (Kluwer Academic, Boston, Mass., 1992).
  4. E. Y. Lam, J. W. Goodman, “Discrete cosine transform domain restoration of defocused images,” Appl. Opt. 37, 6213–6218 (1998). [CrossRef]
  5. A. K. Katsaggelos, K.-T. Lay, “Maximum likelihood identification and restoration of images using the expectation-maximization algorithm,” in Digital Image Restoration, A. K. Katsaggelos, ed. (Springer-Verlag, New York, 1991), pp. 143–176.
  6. M. Cannon, “Blind deconvolution of spatially invariant image blurs with phase,” IEEE Trans. Acoust., Speech, Signal Process. 24, 58–63 (1976). [CrossRef]
  7. R. Bates, B. Quek, C. Parker, “Some implications of zero sheets for blind deconvolution and phase retrieval,” J. Opt. Soc. Am. A 7, 468–479 (1990). [CrossRef]
  8. D. Ghiglia, L. Romero, G. Mastin, “Systematic approach to two-dimensional blind deconvolution by zero-sheet separation,” J. Opt. Soc. Am. A 10, 1024–1036 (1993). [CrossRef]
  9. E. Y. Lam, J. W. Goodman, “Blind image deconvolution for symmetric blurs by polynomial factorization,” in 18th Congress of the International Commission for Optics: Optics for the Next Millennium, A. J. Glass, J. W. Goodman, M. Chang, A. H. Guenther, T. Asakura, eds., Proc. SPIE3749, 174–175 (1999). [CrossRef]
  10. G. Ayers, J. Dainty, “Iterative blind deconvolution method and its applications,” Opt. Lett. 13, 547–549 (1988). [CrossRef]
  11. Y.-L. You, M. Kaveh, “A regularization approach to joint blur identification and image restoration,” IEEE Trans. Image Process. 5, 416–428 (1996). [CrossRef] [PubMed]
  12. D. Kundur, D. Hatzinakos, “A novel blind deconvolution scheme for image restoration using recursive filtering,” IEEE Trans. Signal Process. 46, 375–390 (1998). [CrossRef]
  13. E. Y. Lam, J. W. Goodman, “Iterative blind image deconvolution in space and frequency domains,” in Sensors, Cameras, and Applications for Digital Photography, N. Sampat, T. Yeh, eds., Proc. SPIE3650, 70–77 (1999). [CrossRef]
  14. R. L. Lagendijk, A. M. Tekalp, J. Biemond, “Maximum likelihood image and blur identification: a unifying approach,” Opt. Eng. 29, 422–435 (1990). [CrossRef]
  15. K.-T. Lay, A. K. Katsaggelos, “Image identification and restoration based on the expectation-maximization algorithm,” Opt. Eng. 29, 436–446 (1990). [CrossRef]
  16. T. J. Hebert, K. Lu, “Expectation-maximization algorithms, null spaces, and MAP image restoration,” IEEE Trans. Image Process. 4, 1084–1095 (1995). [CrossRef] [PubMed]
  17. C. Bouman, K. Sauer, “A generalized Gaussian image model for edge-preserving MAP estimation,” IEEE Trans. Image Process. 2, 296–310 (1993). [CrossRef] [PubMed]
  18. S. Z. Li, “MAP image restoration and segmentation by constrained optimization,” IEEE Trans. Image Process. 7, 1730–1735 (1998). [CrossRef]
  19. L. Mugnier, J.-M. Conan, T. Fusco, V. Michau, “Joint maximum a posteriori estimation of object and PSF for turbulence degraded images,” in Bayesian Inference for Inverse Problems, A. Mohammad-Djafari, ed., Proc. SPIE3459, 50–61 (1998). [CrossRef]
  20. J. Markham, J.-A. Conchello, “Parametric blind deconvolution: a robust method for the simultaneous estimation of image and blur,” J. Opt. Soc. Am. A 16, 2377–2391 (1999). [CrossRef]
  21. G. J. McLachlan, T. Krishnan, The EM Algorithm and Extensions (Wiley, New York, 1997).
  22. A. Dempster, N. Laird, D. Rubin, “Maximum likelihood from incomplete data,” J. R. Statist. Soc. Ser. B 39, 1–38 (1977).
  23. R. J. Little, D. B. Rubin, Statistical Analysis with Missing Data (Wiley, New York, 1987).
  24. H. Andrews, B. Hunt, Digital Image Restoration (Prentice-Hall, Englewood Cliffs, N.J., 1977).
  25. A. Katsaggelos, Digital Image Restoration (Springer-Verlag, New York, 1991).
  26. A. K. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1989).
  27. K. Miller, “Least-squares methods for ill-posed problems with a prescribed bound,” SIAM J. Math. Anal. 1, 52–74 (1970). [CrossRef]
  28. T. Kailath, Linear Systems (Prentice-Hall, Englewood Cliffs, N.J., 1980).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4 Fig. 5
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited