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A Study on Statistical Approach for Nonlinear Image Denoising Algorithms

비선형 영상 잡음제거 알고리즘의 통계적 접근 방법에 관한 연구

  • Hahn, Hee-Il (Dept. of Information and Communications Engineering, Hankuk University of Foreign Studies)
  • 한희일 (한국외국어대학교 정보통신공학과)
  • Received : 2011.12.21
  • Accepted : 2012.02.10
  • Published : 2012.02.29

Abstract

In this paper robust nonlinear image denoising algorithms are introduced for the distribution which is Gaussian in the center and Laplacian in the tails. The distribution is known as the least favorable ${\epsilon}$-contaminated normal distribution that maximizes the asymptotic variance. The proposed filter proves to be the maximum likelihood estimator under the heavy-tailed Gaussian noise environments. It is optimal in the respect of maximizing the efficacy under the above noise environment. Another filter for reducing impulsive noise is proposed by mixing with the myriad filter to propose an amplitude-limited myriad filter. Extensive experiment is conducted with images corrupted with ${\alpha}$-stable noise to analyze the behavior and performance of the proposed filters.

근사분산을 최대화하는 least favorable한 ${\epsilon}$-contaminated 정규분포는, 중간 영역에서는 가우시안이나 그 외의 영역에서는 라플라시안 분포를 갖는다는 사실에 근거하여 본 논문에서는 이 확률분포 하에서 비선형 잡음제거 알고리즘을 유도하고 이의 성능을 확인한다. 제안 알고리즘은 위 잡음 환경에서 MLE(maximum likelihood estimator) 이며, efficacy를 최대화한다는 기준에서 최적임을 증명한다. 또한, 유도한 필터를 미리어드 필터와 결합함으로써 임펄스 잡음을 효과적으로 제거하기 위한 비선형 필터를 제안하고 이를 이론적으로 분석한 다음 ${\alpha}$-stable 확률분포를 갖는 잡음에 열화된 이미지를 이용하여 그 성능을 확인한다.

Keywords

References

  1. M. J. Black, G. Sapiro, D. H. Marimont, "Robust anisotropic diffusion," IEEE Trans. Image Process., vol. 7, no. 3, Mar., 1998.
  2. C. Tomasi and R. Manduchi, "Bilateranl filtering for gray and color images," in Proc. IEEE Int. Conf. Computer Vision, 1998, pp. 839-846.
  3. A. B. Hamza and H. Krim, "Image denoising: A nonlinear robust statistical approach", pp. 3045-3054, IEEE Trans. Signal Processing, vol.49, no.12, Dec., 2001. https://doi.org/10.1109/78.969512
  4. P. Huber, Robust Statistics. New York: Wily, 1981.
  5. T. Rabie, "Robust Estimation Approach for Blind Denoising", IEEE Trans. Image Process., vol. 14, No. 11, Nov., 2005.
  6. P. Perona and J. Malik, "Scale-space and edge detection using anisotropic Diffusion," IEEE Trans. PAMI, vol.12, no.7, Jul., 1990.
  7. J. G. Gonzaleez and G. R. Arce, "Optimality of the myriad filter in practical impulsive-noise environments," pp. 438-441, IEEE Trans. Signal Processing, vol.49, no.12, Feb., 2001. https://doi.org/10.1109/78.902126
  8. P. Zurbach, J. G. Gonzaleez and G. R. Arce, "Weighted myriad filter for image processing", pp. 726-728, ICIP1996.
  9. X. Wang, L. Zhao, P. Niu and Z. Fu, "Image Denoising Using Gaussian Scale Mixtures with Gaussian-Hermite PDF in Steerable Pyramid Domain," Journal of Mathematical Imaging and Vision, vol. 39, no 3, 245-258, Nov., 2010