Sage Journals: Discover world-class research

Abstract

Salt and Pepper noise removal is an important image preprocessing task, it has two simultaneous demands: the suppression of impulses and the preservation of edges. To address this problem in gray scale images, we propose an efficient method which consists of introducing a Redescending M-Estimator within of the Median-Estimator scheme. The Redescending M-Estimator controls the magnitude of the Salt or Pepper impulses and deletes them when it is necessary; the remaining pixels in the neighborhood are processed by the Median-Estimator in order to obtain an estimation of a noise free pixel. The proposed scheme is applied on the entire image using sliding windows of size 5 $\times$ 5; the local information obtained by this window is used to calculate the thresholds and the parameters that characterize the influence functions tested in the Redescending M-Estimator. To improve the suppression ability of our proposal a pulse detector is used, it identifies when is necessary to submit each pixel to the denoising process. The effectiveness of our proposal is verified by quantitative and qualitative results.

Keywords

Salt and Pepper noise noise suppression grayscale images Redescending M-Estimator Median-Estimator

Get full access to this article

View all access options for this article.

References

Ahmed

and Das

, Removal of high-density salt-and-pepper noise in images with an iterative adaptive fuzzy filter using alpha-trimmed mean, IEEE Transactions on Fuzzy Systems 22 (2014), 1352–1358.

Ali

and Qadir

M.F.

, A modified m-estimator for the detection of outliers, Pakistan Journal of Statistics and Operation Research 1 (2005).

Andrews

D.F.

and Hampel

F.R.

, Robust Estimates of Location: Survey and Advances, Princeton University Press, 2015.

Astola

and Kuosmanen

, Fundamentals of Nonlinear Digital Filtering, CRC press, 1997.

Beaton

A.E.

and Tukey

J.W.

, The fitting of power series, meaning polynomials, illustrated on band-spectroscopic data, Technometrics 16 (1974), 147–185.

Bovik

A.C.

, The Essential Guide to Image Processing, Academic Press, 2009.

Chou

H.-H.

Hsu

L.-Y.

and Hu

H.-T.

, Turbulent-PSO-based fuzzy image filter with no-reference measures for high-density impulse noise, IEEE Transactions on Cybernetics 43 (2013), 296–307.

Frigui

and Krishnapuram

, A robust algorithm for automatic extraction of an unknown number of clusters from noisy data, Pattern Recognition Letters 17 (1996), 1223–1232.

Gao

and Liu

, An efficient three-stage approach for removing salt & pepper noise from digital images, Optik-International Journal for Light and Electron Optics 126 (2015), 467–471.

10.

Gayathri

and Srinivasan

, An efficient algorithm for image denoising using NLM and DBUTM estimation, in: TENCON 2014–2014 IEEE Region 10 Conference, IEEE, (2014), 1–6.

11.

Hampel

F.R.

Ronchetti

E.M.

Rousseeuw

P.J.

and Stahel

W.A.

, Robust Statistics: The Approach Based on Influence Functions, John Wiley & Sons, 2011.

12.

Hodges

J.L.

, Jr. and Lehmann

E.L.

, Estimates of location based on rank tests, The Annals of Mathematical Statistics (1963), 598–611.

13.

Huber

P.J.

, The basic types of estimates, Robust Statistics (1981), 43–72.

14.

Ibrahim

Neo

K.C.

Teoh

S.H.

T.F.

Chieh

D.C.J.

and Hassan

N.N.

, Impulse noise model and its variations, International Journal of Computer and Electrical Engineering 4 (2012), 647.

15.

Sun

and Luo

, A neuro-fuzzy network based impulse noise filtering for gray scale images, Neurocomputing 127 (2014), 190–199.

16.

Maronna

Martin

R.D.

and Yohai

, Robust Statistics, John Wiley & Sons, Chichester, ISBN, 2006.

17.

Meher

S.K.

and Singhawat

, An improved recursive and adaptive median filter for high density impulse noise, AEU-International Journal of Electronics and Communications 68 (2014), 1173–1179.

18.

Pitas

and Venetsanopoulos

A.N.

, Order statistics in digital image processing, Proceedings of the IEEE 80 (1992), 1893–1921.

19.

Sharma

and Chaurasia

, Removal of high density salt-and-pepper noise by recursive enhanced median filtering, in: Emerging Technology Trends in Electronics, Communication and Networking (ET2ECN), 2014 2nd International Conference on, IEEE, (2014), 1–4.

20.

Shevlyakov

Morgenthaler

and Shurygin

, Redescending M-Estimators, Journal of Statistical Planning and Inference 138 (2008), 2906–2917.

21.

Smolka

Andrzejczak

Nabialkowski

and Nelip

, Thresholded median filter for the impulsive noise removal in digital images, in: Information, Intelligence, Systems and Applications, IISA 2014, The 5th International Conference on, IEEE, (2014), 355–360.

22.

Statistics

, The Approach Based on Influence Functions, New York, 1986.

23.

Tukey

J.W.

, A survey of sampling from contaminated distributions, Contributions to Probability and Statistics 2 (1960), 448–485.

24.

Ullah

Qadir

M.F.

and Ali

, Insha’s Redescending M-Estimator for Robust Regression: A Comparative Study, Pakistan Journal of Statistics and Operation Research 2 (2006).

25.

Vijaykumar

Vanathi

Kanagasabapathy

and Ebenezer

, Robust statistics based algorithm to remove salt and pepper noise in images, International Journal of Information and Communication Engineering 5 (2009), 164–173.

26.

Zhang

and Wang

, A switching median–mean filter for removal of high-density impulse noise from digital images, Optik-International Journal for Light and Electron Optics 126 (2015), 956–961.