IMAGE DECONVOLUTION USING A STOCHASTIC DIFFERENTIAL EQUATION APPROACH

X. Descombes, M. Lebellego, E. Zhizhina

Abstract

We consider the problem of image deconvolution. We foccus on a Bayesian approach which consists of maximizing an energy obtained by a Markov Random Field modeling. MRFs are classically optimized by a MCMC sampler embeded into a simulated annealing scheme. In a previous work, we have shown that, in the context of image denoising, a diffusion process can outperform the MCMC approach in term of computational time. Herein, we extend this approach to the case of deconvolution. We first study the case where the kernel is known. Then, we address the myopic and blind deconvolutions.

References

  1. Andrews, H. and Hunt, B. (1977). Digital image restoration. Prentice Hall, Englewood Cliffs, NJ.
  2. Descombes, X. and Zhizhina, E. (2004). Applications of gibbs fields methods to image processing problems. Problems of Information Transmission, 40(3):279- 295.
  3. Geman, S. and Geman, D. (1984). Stochastic relaxation, Gibbs distribution and the Bayeian restoration of images. IEEE Trans. on Pattern Analysis and Machine Intelligence, 6(6):721-741.
  4. Geman, S. and Reynolds, G. (1992). Constrained restoration and recovery of discontinuities. IEEE Trans. on Pattern Analysis and Machine Intelligence, 14(3):367-383.
  5. Kloeden, P. and Platen, E. (1992). Numerical Solution of Stochastic Differential Equations. Springer Verlag, Berlin, Heidelberg.
  6. Mignotte, M. (2006). A segmentation-based regularization term for image restoration. IEEE Trans. on Image Processing, 15(7):1973-1984.
  7. Molina, R., Katsaggelos, A., Mateos, J., Hermoso, A., and Segall, A. (2000). Restoration of severely blurred high range images using stochastic and deterministic relaxation algorithms in compound Gauss-Markov random fields. Pattern Recognition, 33(4):555-571.
Download


Paper Citation


in Harvard Style

Descombes X., Lebellego M. and Zhizhina E. (2007). IMAGE DECONVOLUTION USING A STOCHASTIC DIFFERENTIAL EQUATION APPROACH . In Proceedings of the Second International Conference on Computer Vision Theory and Applications - Volume 3: Bayesian Approach for Inverse Problems in Computer Vision, (VISAPP 2007) ISBN 978-972-8865-75-7, pages 157-164. DOI: 10.5220/0002064701570164


in Bibtex Style

@conference{bayesian approach for inverse problems in computer vision07,
author={X. Descombes and M. Lebellego and E. Zhizhina},
title={IMAGE DECONVOLUTION USING A STOCHASTIC DIFFERENTIAL EQUATION APPROACH},
booktitle={Proceedings of the Second International Conference on Computer Vision Theory and Applications - Volume 3: Bayesian Approach for Inverse Problems in Computer Vision, (VISAPP 2007)},
year={2007},
pages={157-164},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0002064701570164},
isbn={978-972-8865-75-7},
}


in EndNote Style

TY - CONF
JO - Proceedings of the Second International Conference on Computer Vision Theory and Applications - Volume 3: Bayesian Approach for Inverse Problems in Computer Vision, (VISAPP 2007)
TI - IMAGE DECONVOLUTION USING A STOCHASTIC DIFFERENTIAL EQUATION APPROACH
SN - 978-972-8865-75-7
AU - Descombes X.
AU - Lebellego M.
AU - Zhizhina E.
PY - 2007
SP - 157
EP - 164
DO - 10.5220/0002064701570164