Circuits, Systems, and Signal Processing

, Volume 37, Issue 5, pp 2098–2116 | Cite as

Maximum Absolute Relative Differences Statistic for Removing Random-Valued Impulse Noise from Given Image

  • Mayank Tiwari
  • Bhupendra Gupta


In this work, we suggest a new impulse statistic and a new spatial gradient to design a trilateral filter for removal of mixture of Gaussian and impulse noise from a noisy image. The proposed impulse statistic is termed as maximum absolute relative differences statistic, and it is used to remove impulse noise. For Gaussian noise removal, we design modified spatial gradient-based bilateral filter ‘MSG-BF’. We also empirically show performance of the proposed algorithm for detection and removal of noisy pixels in comparison with directional absolute relative differences statistic and other methods. Also experimental results show that our method achieves better results in terms of quantitative measures of signal restoration and qualitative judgments of image quality.


Image restoration Noise detector Random-valued impulse noise Maximum absolute relative differences statistic 



We thank [6] for sharing their MATLAB code with us. We would also like to forward our thanks to anonymous referees, who spend their precious time in reviewing our work. We would like to acknowledge their contribution due to which there was significant improvement in the article. Also, we are grateful to the editor associated with this paper for their cooperation.


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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of MathematicsPDPM Indian Institute of Information Technology, Design and Manufacturing JabalpurJabalpurIndia

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