Advertisement

Fast Non-Local Mean Filter Algorithm Based on Recursive Calculation of Similarity Weights

  • V. N. KarnaukhovEmail author
  • M. G. Mozerov
MATHEMATICAL MODELS AND COMPUTATIONAL METHODS
  • 36 Downloads

Abstract—A theoretically derived technique for acceleration of the original non-local means image denoising algorithm based on calculation of recursive patch similarity weights is proposed. A significant amount of computation in the non-local means scheme is dedicated to estimation of the patch similarity between pixel neighborhoods. The proposed recursive weights calculation scheme adopts the classic recursive mean calculation scheme for a multidimensional shift-vector in order to lower the computational complexity of the original non-local means method, thus speeding up this algorithm more than tenfold. Note that the output of the proposed algorithm is exactly the same as that of the original non-local means method. Hence this algorithm belongs to the class of true fast algorithms, unlike methods approaching to a certain degree the resul of the original algorithm.

Keywords: image restoration fast algorithms non-local mean 

Notes

REFERENCES

  1. 1.
    L. P. Yaroslavsky, “Digital picture processing: An introduction,” Appl. Opt. 25, 3127 (1986).CrossRefGoogle Scholar
  2. 2.
    F. Catté, P.-L. Lions, J.-M. Morel, and T. Coll, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numerical Analysis 29 (1), 182–193 (1992).MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    H.-Y. Gao, “Wavelet shrinkage denoising using the non-negative garrote,” J. Comput. Graph. Stat. 7, 469–488 (1998).MathSciNetGoogle Scholar
  4. 4.
    D. L. Donoho, “De-noising by soft-thresholding,” IEEE Trans. Inf. Theory 41, 613–627 (1995).MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    M. Lindenbaum, M. Fischer, and A. Bruckstein, “On gabor’s contribution to image enhancement,” Pattern Recogn. 27 (1), 1–8 (1994).CrossRefGoogle Scholar
  6. 6.
    P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Analysis Machine Intelligence 12, 629–639 (1990).CrossRefGoogle Scholar
  7. 7.
    L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D: Nonlinear Phenomena 60, 259–268 (1992).MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    S. M. Smith and J. M. Brady, “Susan – a new approach to low level image processing,” Int. J. Comp. Vision 23, 45–78 (1997).CrossRefGoogle Scholar
  9. 9.
    C. Tomasi and R. Manduchi, “Bilateral filtering for gray and color images,” in Proc. Sixth Int. Conf. on Comput. Vision (ICCV), Bombay, India, Jan. 1998 (IEEE, New York, 1998), pp. 839–846.Google Scholar
  10. 10.
    A. Buades, B. Coll, and J.-M. Morel, “A non-local algorithm for image denoising,” in Proc. IEEE Comput. Soc. Conf. on Computer Vision and Pattern Recognition (CVPR), 2005 (IEEE, New York, 2005), Vol. 2, pp. 60–65.Google Scholar
  11. 11.
    K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-D transform-domain collaborative filtering,” IEEE Trans. Image Process. 16, 2080–2095 (2007).MathSciNetCrossRefGoogle Scholar
  12. 12.
    W. Zuo, L. Zhang, C. Song, and D. Zhang, “Texture enhanced image denoising via gradient histogram preservation,” in Proc. IEEE Conf. Comput. Vision & Pattern Recogn., Iune, 2013, (IEEE, New York, 2013), pp. 1203–1210.Google Scholar
  13. 13.
    G. Liu, H. Zhong, and L. Jiao, “Comparing noisy patches for image denoising: A double noise similarity model,” IEEE Trans. Image Processing 24, 862–872 (2015).MathSciNetCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2018

Authors and Affiliations

  1. 1.Kharkevich Institute for Information Transmission Problems, Russian Academy of SciencesMoscowRussia

Personalised recommendations