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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics


  • Editor: Gregory W. Faris
  • Vol. 5, Iss. 11 — Aug. 25, 2010

Bayesian estimation of regularization and point spread function parameters for Wiener–Hunt deconvolution

François Orieux, Jean-François Giovannelli, and Thomas Rodet  »View Author Affiliations

JOSA A, Vol. 27, Issue 7, pp. 1593-1607 (2010)

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This paper tackles the problem of image deconvolution with joint estimation of point spread function (PSF) parameters and hyperparameters. Within a Bayesian framework, the solution is inferred via a global a posteriori law for unknown parameters and object. The estimate is chosen as the posterior mean, numerically calculated by means of a Monte Carlo Markov chain algorithm. The estimates are efficiently computed in the Fourier domain, and the effectiveness of the method is shown on simulated examples. Results show precise estimates for PSF parameters and hyperparameters as well as precise image estimates including restoration of high frequencies and spatial details, within a global and coherent approach.

© 2010 Optical Society of America

OCIS Codes
(100.1830) Image processing : Deconvolution
(100.3020) Image processing : Image reconstruction-restoration
(100.3190) Image processing : Inverse problems
(150.1488) Machine vision : Calibration

ToC Category:
Image Processing

Original Manuscript: October 21, 2009
Revised Manuscript: March 5, 2010
Manuscript Accepted: April 15, 2010
Published: June 9, 2010

Virtual Issues
Vol. 5, Iss. 11 Virtual Journal for Biomedical Optics

François Orieux, Jean-François Giovannelli, and Thomas Rodet, "Bayesian estimation of regularization and point spread function parameters for Wiener–Hunt deconvolution," J. Opt. Soc. Am. A 27, 1593-1607 (2010)

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  1. J.Idier, ed., Bayesian Approach to Inverse Problems (Wiley, 2008). [CrossRef]
  2. R. Molina, J. Mateos, and A. K. Katsaggelos, “Blind deconvolution using a variational approach to parameter, image, and blur estimation,” IEEE Trans. Image Process. 15, 3715–3727 (2006). [CrossRef] [PubMed]
  3. P.Campisi and K.Egiazarian, eds., Blind Image Deconvolution (CRC Press, 2007). [CrossRef]
  4. T. Rodet, F. Orieux, J.-F. Giovannelli, and A. Abergel, “Data inversion for over-resolved spectral imaging in astronomy,” IEEE J. Sel. Top. Signal Process. 2, 802–811 (2008). [CrossRef]
  5. A. Tikhonov and V. Arsenin, Solutions of Ill-Posed Problems (Winston, 1977).
  6. S. Twomey, “On the numerical solution of Fredholm integral equations of the first kind by the inversion of the linear system produced by quadrature,” J. Assoc. Comput. Mach. 10, 97–101 (1962). [CrossRef]
  7. A. Jalobeanu, L. Blanc-Féraud, and J. Zerubia, “Hyperparameter estimation for satellite image restoration by a MCMC maximum likelihood method,” Pattern Recogn. 35, 341–352 (2002). [CrossRef]
  8. J. A. O’Sullivan, “Roughness penalties on finite domains,” IEEE Trans. Image Process. 4, 1258–1268 (1995). [CrossRef] [PubMed]
  9. G. Demoment, “Image reconstruction and restoration: overview of common estimation structure and problems,” IEEE Trans. Acoust., Speech, Signal Process. ASSP-37, 2024–2036 (1989). [CrossRef]
  10. P. Pankajakshani, B. Zhang, L. Blanc-Féraud, Z. Kam, J.-C. Olivo-Marin, and J. Zerubia, “Blind deconvolution for thin-layered confocal imaging,” Appl. Opt. 48, 4437–4448 (2009). [CrossRef]
  11. E. Thiébaut and J.-M. Conan, “Strict a priori constraints for maximum likelihood blind deconvolution,” J. Opt. Soc. Am. A 12, 485–492 (1995). [CrossRef]
  12. N. Dobigeon, A. Hero, and J.-Y. Tourneret, “Hierarchical Bayesian sparse image reconstruction with application to MRFM,” IEEE Trans. Image Process. (2009).
  13. B. Zhang, J. Zerubia, and J.-C. Olivo-Marin, “Gaussian approximations of fluorescence microscope point-spread function models,” Appl. Opt. 46, 1819–1829 (2007). [CrossRef] [PubMed]
  14. L. Mugnier, T. Fusco, and J.-M. Conan, “MISTRAL: a myopic edge-preserving image restoration method, with application to astronomical adaptive-optics-corrected long-exposure images,” J. Opt. Soc. Am. A 21, 1841–1854 (2004). [CrossRef]
  15. E. Thiébaut, “MiRA: an effective imaging algorithm for optical interferometry,” Proc. SPIE 7013, 70131-I (2008). [CrossRef]
  16. T. Fusco, J.-P. Véran, J.-M. Conan, and L. M. Mugnier, “Myopic deconvolution method for adaptive optics images of stellar fields,” Astron. Astrophys. Suppl. Ser. 134, 193 (1999). [CrossRef]
  17. J.-M. Conan, L. Mugnier, T. Fusco, V. Michau, and G. Rousset, “Myopic deconvolution of adaptive optics images by use of object and point-spread function power spectra,” Appl. Opt. 37, 4614–4622 (1998). [CrossRef]
  18. A. C. Likas and N. P. Galatsanos, “A variational approach for Bayesian blind image deconvolution,” IEEE Trans. Image Process. 52, 2222–2233 (2004).
  19. T. Bishop, R. Molina, and J. Hopgood, “Blind restoration of blurred photographs via AR modelling and MCMC,” in Proceedings of 15th IEEE International Conference on Image Processing, 2008, ICIP 2008 (IEEE Signal Processing Society, 2008). [CrossRef]
  20. E. Y. Lam and J. W. Goodman, “Iterative statistical approach to blind image deconvolution,” J. Opt. Soc. Am. A 17, 1177–1184 (2000). [CrossRef]
  21. Z. Xu and E. Y. Lam, “Maximum a posteriori blind image deconvolution with Huber–Markov random-field regularization,” Opt. Lett. 34, 1453–1455 (2009). [CrossRef] [PubMed]
  22. M. Cannon, “Blind deconvolution of spatially invariant image blurs with phase,” IEEE Trans. Acoust., Speech, Signal Process. 24, 58–63 (1976). [CrossRef]
  23. A. Jalobeanu, L. Blanc-Feraud, and J. Zerubia, “Estimation of blur and noise parameters in remote sensing,” in Proceedings of 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2002) (IEEE Signal Processing Society, 2002), Vol. 4, pp. 3580–3583.
  24. F. Chen and J. Ma, “An empirical identification method of Gaussian blur parameter for image deblurring,” IEEE Trans. Signal Process. (2009).
  25. C. P. Robert and G. Casella, Monte-Carlo Statistical Methods, Springer Texts in Statistics (Springer, 2000).
  26. B. R. Hunt, “A matrix theory proof of the discrete convolution theorem,” IEEE Trans. Autom. Control AC-19, 285–288 (1971).
  27. M. Calder and R. A. Davis, “Introduction to Whittle (1953) ‘The analysis of multiple stationary time series’,” Breakthroughs in Statistics 3, 141–148 (1997). [CrossRef]
  28. P. J. Brockwell and R. A. Davis, Time Series: Theory and Methods (Springer-Verlag, 1991). [CrossRef]
  29. B. R. Hunt, “Deconvolution of linear systems by constrained regression and its relationship to the Wiener theory,” IEEE Trans. Autom. Control AC-17, 703–705 (1972). [CrossRef]
  30. K. Mardia, J. Kent, and J. Bibby, Multivariate Analysis (Academic, 1992), Chap. 2, pp. 36–43.
  31. C. A. Bouman and K. D. Sauer, “A generalized Gaussian image model for edge-preserving MAP estimation,” IEEE Trans. Image Process. 2, 296–310 (1993). [CrossRef] [PubMed]
  32. D. MacKay, Information Theory, Inference, and Learning Algorithms (Cambridge Univ. Press, 2003).
  33. R. E. Kass and L. Wasserman, “The selection of prior distributions by formal rules,” J. Am. Stat. Assoc. 91, 1343–1370 (1996). [CrossRef]
  34. E. T. Jaynes, Probability Theory: The Logic of Science (Cambridge Univ. Press, 2003). [CrossRef]
  35. S. Lang, Real and Functional Analysis (Springer, 1993). [CrossRef]
  36. P. Brémaud, Markov Chains. Gibbs Fields, Monte Carlo Simulation, and Queues, Texts in Applied Mathematics 31 (Springer, 1999).
  37. S. Geman and D. Geman, “Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images,” IEEE Trans. Pattern Anal. Mach. Intell. 6, 721–741 (1984). [CrossRef]
  38. P. Lalanne, D. Prévost, and P. Chavel, “Stochastic artificial retinas: algorithm, optoelectronic circuits, and implementation,” Appl. Opt. 40, 3861–3876 (2001) [CrossRef]
  39. H. R. Künsch, “Robust priors for smoothing and image restoration,” Ann. Inst. Stat. Math. 46, 1–19 (1994). [CrossRef]
  40. P. Charbonnier, L. Blanc-Féraud, G. Aubert, and M. Barlaud, “Deterministic edge-preserving regularization in computed imaging,” IEEE Trans. Image Process. 6, 298–311 (1997). [CrossRef] [PubMed]
  41. J.-F. Giovannelli, “Unsupervised Bayesian convex deconvolution based on a field with an explicit partition function,” IEEE Trans. Image Process. 17, 16–26 (2008). [CrossRef] [PubMed]
  42. D. Geman and C. Yang, “Nonlinear image recovery with half-quadratic regularization,” IEEE Trans. Image Process. 4, 932–946 (1995). [CrossRef] [PubMed]
  43. X. Descombes, R. Morris, J. Zerubia, and M. Berthod, “Estimation of Markov random field prior parameters using Markov chain Monte Carlo maximum likelihood,” IEEE Trans. Image Process. 8, 954–963 (1999). [CrossRef]
  44. G. E. P. Box and G. C. Tiao, Bayesian Inference in Statistical Analysis (Addison-Wesley, 1972).

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