# ROBUST VARIATIONAL BAYESIAN KERNEL BASED BLIND IMAGE DECONVOLUTION

### Dimitris Tzikas, Aristidis Likas, Nikolaos Galatsanos

#### 2007

#### Abstract

In this paper we present a new Bayesian model for the blind image deconvolution (BID) problem. The main novelties of this model are two. First, a sparse kernel based representation of the point spread function (PSF) that allows for the first time estimation of both PSF shape and support. Second, a non Gaussian heavy tail prior for the model noise to make it robust to large errors encountered in BID when little prior knowledge is available about both image and PSF. Sparseness and robustness are achieved by introducing Student-t priors both for the PSF and the noise. A Variational methodology is proposed to solve this Bayesian model. Numerical experiments are presented both with real and simulated data that demonstrate the advantages of this model as compared to previous Gaussian based ones.

#### References

- Bishop, C. M. (2006). Pattern Recognition and Machine Learning. Springer.
- D.Kundur and D.Hatzinakos (1996). Blind image deconvolution. IEEE Signal Processing Mag., 13(3):43-64.
- Galatsanos, N. P., Mesarovic, V. Z., Molina, R., Katsaggelos, A. K., and Mateos, J. (2002). Hyperparameter estimation in image restoration problems with partiallyknown blurs. Optical Eng., 41(8):1845-1854.
- Jeffs, B. D. and Christou, J. C. (1998). Blind Bayesian restoration of adaptive optics telescope images using generalized Gaussian markov random field models. In Bonaccini, D. and Tyson, R. K., editors, in Proc.

#### Paper Citation

#### in Harvard Style

Tzikas D., Likas A. and Galatsanos N. (2007). **ROBUST VARIATIONAL BAYESIAN KERNEL BASED BLIND IMAGE DECONVOLUTION** . 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 143-150. DOI: 10.5220/0002063601430150

#### in Bibtex Style

@conference{bayesian approach for inverse problems in computer vision07,

author={Dimitris Tzikas and Aristidis Likas and Nikolaos Galatsanos},

title={ROBUST VARIATIONAL BAYESIAN KERNEL BASED BLIND IMAGE DECONVOLUTION},

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={143-150},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0002063601430150},

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 - ROBUST VARIATIONAL BAYESIAN KERNEL BASED BLIND IMAGE DECONVOLUTION

SN - 978-972-8865-75-7

AU - Tzikas D.

AU - Likas A.

AU - Galatsanos N.

PY - 2007

SP - 143

EP - 150

DO - 10.5220/0002063601430150