Non-local Sigma Filter

  • Nikolay Ponomarenko
  • Vladimir Lukin
  • Jaakko Astola
  • Karen EgiazarianEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9280)


This paper proposes a non-local modification of well-known sigma filter, Nonlocal Sigma filter (NSF), intended to suppress additive white Gaussian noise from images. Similarly to the Nonlocal Mean Filter (NLM), every output pixel value is computed as a nonlocal weighted average of pixels coming from similar patches to the patch around the current pixel. The main difference between the proposed NSF and NLM is in the following: there are pixels in NSF not used in a weighted averaging (if the difference between them and the central pixel value is above a predefined threshold value, and if the distance between patch neighborhood and the central patch neighborhood is greater than a second threshold value). The weights used to estimate the output pixel depend on the patch size as well as on a distance between considered and reference patches. The proposed filter is compared to its counter-parts, namely, the conventional sigma filter and the NLM filter. It is shown that NSF outperforms both of them in PSNR and visual quality metrics values, PSNR-HVS-M and MSSIM. In this paper, a novel filtering quality criterion that takes into account distortions introduced into processed images due to denoising is proposed. It is demonstrated that, according to this criterion, NSF has similar edge-detail preservation property as the conventional sigma filter but has better noise suppression ability.


Image denoising Non-local methods Similarity-based methods Sigma filter Human perception Visual quality metrics Image self-similarity 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Nikolay Ponomarenko
    • 1
  • Vladimir Lukin
    • 1
  • Jaakko Astola
    • 2
  • Karen Egiazarian
    • 2
    Email author
  1. 1.Department of Transmitters, Receivers and Signal ProcessingNational Aerospace UniversityKharkivUkraine
  2. 2.Department of Signal ProcessingTampere University of TechnologyTampereFinland

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