OPTIMAL NONLINEAR IMAGE DENOISING METHODS IN HEAVY-TAILED NOISE ENVIRONMENTS

Hee-il Hahn

Abstract

The statistics for the neighbor differences between the particular pixels and their neighbors are introduced. They are incorporated into the filter to enhance images contaminated by additive Gaussian and impulsive noise. The derived denoising method corresponds to the maximum likelihood estimator for the heavy-tailed Gaussian distribution. The error norm corresponding to our estimator from the robust statistics is equivalent to Huber’s minimax norm. This estimator is also optimal in the respect of maximizing the efficacy under the above noise environment. It is mixed with the myriad filter to propose an amplitude-limited myriad filter. In order to reduce visually grainy output due to impulsive noise, Impulse-like signal detection is introduced so that it can be processed in different manner from the remaining pixels. Our approaches effectively remove both Gaussian and impulsive noise, not blurring edges severely.

References

  1. Rabie, T., 2005. Robust Estimation Approach for Blind Denoising. IEEE Trans. Image Process., vol. 14, No. 11, pp. 1755-1765.
  2. Black, M. J., Sapiro, G., Marimont, D. H., 2005. Robust Anisotropic Diffusion. IEEE Trans. Image Process., vol. 14, No. 11, pp.421-432.
  3. Huber, P., 1981. Robust Statistics, New York: Wily.
  4. Perona, P., Malik, J., 1990. Scale-Space and Edge Detection Using Anisotropic Diffusion. IEEE Trans. PAMI, vol. 12, No. 7, Jul., pp. 629-639.
  5. Hamza, A. B., Krim, H., 2001. Image Denoising: A Nonlinear Robust Statistical Approach. IEEE Trans. Signal Process., vol.49, No.12, pp.3045-3054.
  6. Garnett, R., Huegerich, T., Chui, C., He, W., 2005. A Universal Noise Removal Algorithm With an Impulse Detector. IEEE Trans. Image Process., vol. 14, No. 11, pp. 1747-1754.
  7. Gonzalez, J. G., Arce, G. R., 2001. Optimality of the Myriad Filter in Practical Impulsive-Noise Environments. IEEE Trans. Signal Process., vol.49, No.2, pp. 438-441.
  8. Zurbach, P., Gonzalez, J. G., Arce, G. R., 1996. Weighted Myriad Filters for Image Processing. ICIP96, pp. 726- 728.
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Paper Citation


in Harvard Style

Hahn H. (2007). OPTIMAL NONLINEAR IMAGE DENOISING METHODS IN HEAVY-TAILED NOISE ENVIRONMENTS . In Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 4: ICINCO, ISBN 978-972-8865-83-2, pages 424-429. DOI: 10.5220/0001650604240429


in Bibtex Style

@conference{icinco07,
author={Hee-il Hahn},
title={OPTIMAL NONLINEAR IMAGE DENOISING METHODS IN HEAVY-TAILED NOISE ENVIRONMENTS},
booktitle={Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 4: ICINCO,},
year={2007},
pages={424-429},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001650604240429},
isbn={978-972-8865-83-2},
}


in EndNote Style

TY - CONF
JO - Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 4: ICINCO,
TI - OPTIMAL NONLINEAR IMAGE DENOISING METHODS IN HEAVY-TAILED NOISE ENVIRONMENTS
SN - 978-972-8865-83-2
AU - Hahn H.
PY - 2007
SP - 424
EP - 429
DO - 10.5220/0001650604240429