# A MINIMUM ENTROPY IMAGE DENOISING ALGORITHM - Minimizing Conditional Entropy in a New Adaptive Weighted K-th Nearest Neighbor Framework for Image Denoising

### Cesario Vincenzo Angelino, Eric Debreuve, Michel Barlaud

#### Abstract

In this paper we address the image restoration problem in the variational framework. The focus is set on denoising applications. Natural image statistics are consistent with a Markov random field (MRF) model for the image structure. Thus in a restoration process attention must be paid to the spatial correlation between adjacent pixels.The proposed approach minimizes the conditional entropy of a pixel knowing its neighborhood. The estimation procedure of statistical properties of the image is carried out in a new adaptive weighted k-th nearest neighbor (AWkNN) framework. Experimental results show the interest of such an approach. Restoration quality is evaluated by means of the RMSE measure and the SSIM index, more adapted to the human visual system.

#### References

- Ahmad, I. A. and Lin, P. (1976). A nonparametric estimation of the entropy for absolutely continuous distributions. IEEE Transactions On Information Theory.
- Awate, S. P. and Whitaker, R. T. (2006). Unsupervised, information-theoretic, adaptive image filtering for image restoration. IEEE Trans. Pattern Anal. Mach. Intell., 28(3):364-376.
- Boltz, S., Debreuve, E., and Barlaud, M. (2007). Highdimensional statistical distance for region-of-interest tracking: Application to combining a soft geometric constraint with radiometry. In IEEE International Conference on Computer Vision and Pattern Recognition, Minneapolis, USA. CVPR'07.
- Carlsson, G., Ishkhanov, T., de Silva, V., and Zomorodian, A. (2007). On the local behavior of spaces of natural images. International Journal of Computer Vision.
- Comaniciu, D. and Meer, P. (May, 2002). Mean shift: A robust approach toward feature space analysis. IEEE Transactions On Pattern Analysis And Machine Intelligence, 24, NO.5:603-619.
- Cover, T. and Thomas, J. (1991). Elements of Information Theory. Wiley-Interscience.
- Dudani, S. (1976). The distance-weighted k-nearestneighbor rule. 6(4):325-327.
- Elgammal, A., Duraiswami, R., and Davis, L. S. (2003). Probabilistic tracking in joint feature-spatial spaces. pages 781-788, Madison, WI.
- Fukunaga, K. and Hostetler, L. D. (January, 1975). The estimation of the gradient of a density function, with applications in pattern recognition. IEEE Transactions On Information Theory, 21, NO.1:32-40.
- Geman, S. and Geman, D. (1990). Stochastic relaxation, gibbs distributions, and the bayesian restoration of images. pages 452-472.
- Huang, J. and Mumford, D. (1999). Statistics of natural images and models. pages 541-547.
- Lee, A. B., Pedersen, K. S., and Mumford, D. (2003). The nonlinear statistics of high-contrast patches in natural images. Int. J. Comput. Vision, 54(1-3):83-103.
- Scott, D. (1992). Multivariate Density Estimation: Theory, Practice, and Visualization. Wiley.
- Wang, Z., Bovik, A. C., Sheikh, H. R., and Simoncelli, E. P. (APRIL, 2004). Image quality assessment: From error visibility to structural similarity. IEEE Transactions On Image Processing, 13, NO.4:600-612.
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#### Paper Citation

#### in Harvard Style

Vincenzo Angelino C., Debreuve E. and Barlaud M. (2008). **A MINIMUM ENTROPY IMAGE DENOISING ALGORITHM - Minimizing Conditional Entropy in a New Adaptive Weighted K-th Nearest Neighbor Framework for Image Denoising** . In *Proceedings of the Third International Conference on Computer Vision Theory and Applications - Volume 1: BAIPCV, (VISIGRAPP 2008)* ISBN 978-989-8111-21-0, pages 577-582. DOI: 10.5220/0001092605770582

#### in Bibtex Style

@conference{baipcv08,

author={Cesario Vincenzo Angelino and Eric Debreuve and Michel Barlaud},

title={A MINIMUM ENTROPY IMAGE DENOISING ALGORITHM - Minimizing Conditional Entropy in a New Adaptive Weighted K-th Nearest Neighbor Framework for Image Denoising},

booktitle={Proceedings of the Third International Conference on Computer Vision Theory and Applications - Volume 1: BAIPCV, (VISIGRAPP 2008)},

year={2008},

pages={577-582},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001092605770582},

isbn={978-989-8111-21-0},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the Third International Conference on Computer Vision Theory and Applications - Volume 1: BAIPCV, (VISIGRAPP 2008)

TI - A MINIMUM ENTROPY IMAGE DENOISING ALGORITHM - Minimizing Conditional Entropy in a New Adaptive Weighted K-th Nearest Neighbor Framework for Image Denoising

SN - 978-989-8111-21-0

AU - Vincenzo Angelino C.

AU - Debreuve E.

AU - Barlaud M.

PY - 2008

SP - 577

EP - 582

DO - 10.5220/0001092605770582