This paper proposes a new algorithm to remove Gaussian noise. The new method introduces two filters. The first one is linear filter that modifies the noisy and noisy-free pixels uniformly and regardless of the pixel location. The second one is non-linear filter, a direction-based filter used to re-estimate the first output, particularly the values of the edge pixels. Simulation results indicate that the proposed method restores images corrupted at different degrees of Gaussian noise and demonstrates the best performance compared to other methods, particularly for highly corrupted images in terms of PSNR or visual quality.

1. P. Perona and J. Malik, "Scale -space and edge detection using anisotropic diffusion," IEEE Trans. Pattern Anal. Machine Intell. , Vol. 12, pp. 629–639, 1990
2. M. J. Black , Guillermo Sapiro, David Marimont, and David Heeger, 'Robust Anisotropic Diffusion', IEEE Trans. on Image Processing, Vol. 7, No. 3, pp. 4 21- 432,1998
3. M. J. Black , D. Fleet D. , and Y. Yacoob , 'Robustly estimating changes in image appearance', Computer Vision and Image Understand, Vol. 78, pp. 8 -31 2000
4. J. Tumblin and G. Turk, "LCIS: A Boundary Hierarchy for Detail-Preserving Contrast Reduction," in Proc. ACM SIGGRAPH 99. pp. 83-90, 1999. .
5. Y. You, W. Xu, A. Tannenbaum, and M. Kaveh, "Behavioral Analysis of Anisotropic Diffusion in Image Processing," IEEE Tran. Image Processing. Vol. 5,No. 11, pp. 1539-1553 ,1996.
6. J. B. Bednar and T. L. Watt, "Alpha-trimmed means and their relationship to median filters," IEEE Trans. on Acous. ,Speech and Signal Processing, vol. 32, pp. 145–153, 1987
7. Y. B. Rytsar and I. B. Ivanesko, "Application of (alpha, beta)-trimmed mean filtering for removal of additive noise from images," Proc. of SPIE, vol. 3238, 1997.
8. S. R. Peterson, Y. H. Lee, and S. A. Kassam, "Some statistical properties of alpha-trimmed mean and standard type M filters," IEEE Trans. On Signal Proc. , vol. 36, no. 5, pp. 707–713, 1988.
9. A. Taguchi, "An adaptive _ -trimmed mean filter with excellent detail preservation and evaluation of its performance," Elec. Comm. in Japan Part III, vol. 78, no. 10, pp. 46–56, 1995
10. L. Kaur, S. Gupta and R. C. Chauha. , "Image Denoising using Wavelet Thresholding , ICVGIP, 2002.
11. E. J. Candes, and D. L. Donoho,(1999) "Curvelets—A surprisingly effective nonadaptive representation for objects with edges," in Curves and Surfaces Fitting, L. L. Schumaker, Ed. et al. Nashville, TN: Vanderbilt Univ. Press.
12. R. Eslami and H. Radha (2003),"The Contourlet Transform for Image De-noising Using Cycle Spinning", IEEE Trans. Image Processing pp. 1982-1986.
13. C. Tomasi and R. Manduchi, "Bilateral filtering for gray and color images," IEEE Int. Conf. Computer Vision, pp. 839- 846, 1998.
14. S. Morillas, V. Gregori, and A. Sapena. Fuzzy bilateral filtering for color images. Lecture Notes in Computer Science, pages 138–145, 2006.
15. K. J. Overton and T. E. Weymouth. A noise reducing preprocessing algorithm. IEEE Proc. Comput. Sci. Conf. Pattern Recoginition and Image Processing, pp. 498–507, 1979.
16. S. Paris, P. Kornprobst, J. Tumblin, and F. Durand. A gentle introduction to bilateral filtering and its applications. SIGGRAPH, presentation, 2007.
17. B. Zhang and J. P. Allebach. Adaptive bilateral filter for sharpness enhancement and noise removal. IEEE Trans. Image Processing, Vol. 17,No. 5, pp. 664–678, 2008.
18. R. Garnett , Timothy Huegerich and Charles Chui, 'A Universal Noise Removal Algorithm with an Impulse Detector' IEEE Trans. on Image Processing, Vol. 14, No. 11, pp. 1747-1754, 2005.

De-noising Gaussian Noise Triangular Filter Non-linear Filter