Image Denoising via Fast and Fuzzy Non-local Means Algorithm

  • Lv, Junrui (School of Computer Science and Engineering, Panzhihua University) ;
  • Luo, Xuegang (School of Computer Science and Engineering, Panzhihua University)
  • Received : 2018.01.03
  • Accepted : 2019.07.29
  • Published : 2019.10.31


Non-local means (NLM) algorithm is an effective and successful denoising method, but it is computationally heavy. To deal with this obstacle, we propose a novel NLM algorithm with fuzzy metric (FM-NLM) for image denoising in this paper. A new feature metric of visual features with fuzzy metric is utilized to measure the similarity between image pixels in the presence of Gaussian noise. Similarity measures of luminance and structure information are calculated using a fuzzy metric. A smooth kernel is constructed with the proposed fuzzy metric instead of the Gaussian weighted L2 norm kernel. The fuzzy metric and smooth kernel computationally simplify the NLM algorithm and avoid the filter parameters. Meanwhile, the proposed FM-NLM using visual structure preferably preserves the original undistorted image structures. The performance of the improved method is visually and quantitatively comparable with or better than that of the current state-of-the-art NLM-based denoising algorithms.


Supported by : Innovation Foundation (Believe in Engineering) of Sichuan Province of China


  1. P. Milanfar, "A tour of modern image filtering: new insights and methods, both practical and theoretical," IEEE Signal Processing Magazine, vol. 30, no. 1, pp. 106-128, 2013.
  2. A. Buades, B. Coll, and J. M. Morel, "A review of image denoising algorithms, with a new one," Multiscale Modeling & Simulation, vol. 4, no. 2, pp. 490-530, 2005.
  3. X. G. Luo, J. R. Lu, H. J. Wang, and Q. Yang, "Fast nonlocal means image denoising algorithm using selective calculation," Journal of University of Electronic Science and Technology of China, vol. 44, no. 1, pp. 84-90, 2015.
  4. H. Li and C. Y. Suen, "A novel non-local means image denoising method based on grey theory," Pattern Recognition, vol. 49, pp. 237-248, 2016.
  5. V. May, Y. Keller, N. Sharon, and Y. Shkolnisky, "An algorithm for improving non-local means operators via low-rank approximation," IEEE Transactions on Image Processing, vol. 25, no. 3, pp. 1340-1353, 2016.
  6. J. V. Manjon, J. Carbonell-Caballero, J. J. Lull, G. Garcia-Marti, L. Marti-Bonmati, and M. Robles, "MRI denoising using non-local means," Medical Image Analysis, vol. 12, no. 4, pp. 514-523, 2008.
  7. P. Q. Yin, D. M. Lu, and Y. Yuan, "An improved non-local means image de-noising algorithm using Mahalanobis distance," Journal of Computer-Aided Design & Computer Graphics, vol. 28, no. 3, pp. 404-410, 2016.
  8. S. Morillas, V. Gregori, G. Peris-Fajarnes, and P. Latorre, "A fast impulsive noise color image filter using fuzzy metrics," Real-Time Imaging, vol. 11, no. 5-6, pp. 417-428, 2005.
  9. V. Gregori, S. Morillas, and A. Sapena, "Examples of fuzzy metrics and applications," Fuzzy Sets and Systems, vol. 170, no. 1, pp. 95-111, 2011.
  10. S. Grecova and S. Morillas, "Perceptual similarity between color images using fuzzy metrics," Journal of Visual Communication and Image Representation, vol. 34, no. 230-235, 2016.
  11. S. Morillas, V. Gregori, and A. Sapena, "Fuzzy bilateral filtering for color images," in Image Analysis and Recognition. Heidelberg: Springer, 2006, pp. 138-145.
  12. K. Zhang, X. Gao, D. Tao, and X. Li, "Single image super-resolution with non-local means and steering kernel regression," IEEE Transactions on Image Processing, vol. 21, no. 11, pp. 4544-4556, 2012.
  13. X. Chen, S. Bing Kang, J. Yang, and J. Yu, "Fast patch-based denoising using approximated patch geodesic paths," in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Portland, OR, 2013, pp. 1211-1218.
  14. K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, "Image denoising by sparse 3-D transform-domain collaborative filtering," IEEE Transactions on Image Processing, vol. 16, no. 8, pp. 2080-2095, 2007.
  15. Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, "Image quality assessment: from error visibility to structural similarity," IEEE Transactions on Image Processing, vol. 13, no. 4, pp. 600-612, 2004.