Robust Statistics Based Algorithm to Remove Salt and Pepper Noise in Images
In this paper, a robust statistics based filter to remove salt and pepper noise in digital images is presented. The function of the algorithm is to detect the corrupted pixels first since the impulse noise only affect certain pixels in the image and the remaining pixels are uncorrupted. The corrupted pixels are replaced by an estimated value using the proposed robust statistics based filter. The proposed method perform well in removing low to medium density impulse noise with detail preservation upto a noise density of 70% compared to standard median filter, weighted median filter, recursive weighted median filter, progressive switching median filter, signal dependent rank ordered mean filter, adaptive median filter and recently proposed decision based algorithm. The visual and quantitative results show the proposed algorithm outperforms in restoring the original image with superior preservation of edges and better suppression of impulse noise
[1] Pitas I. and Venetsanopoulos A. N., ÔÇÿNonlinear Digital Filters: Principles
and Applications-, Boston, MA: Kluwer Academic, 1990.
[2] Gonzalez R.C. and Woods R.E., ÔÇÿDigital Image Processing-, Addison-
Wesley Publishing Company,2002.
[3] Bovik A.C., ÔÇÿHandbook of Image and Video Processing-, Academic
Press, 2000.
[4] Pratt W. K., ÔÇÿDigital Image Processing-. New York Wiley, 1991.
[5] Astola J and P.Kuosmanen, Fundamentals of Nonlinear Digital
Filtering, CRC Press, 1997.
[6] Hung T.S., G.J Yang, and G.Y. Tang , ÔÇÿFast two dimensional median
filtering algorithm-, IEEE Transactions on Acoustics Speech and Signal
Processing , vol. 1 pp 13-18 , 1979.
[7] Srinivasan E. and Ebenezer D., ÔÇÿNew Nonlinear Filtering Strategies for
Eliminating Short and Long Tailed Noise in Images with Edge
Preservation Properties-, International Journal of Signal Processing,
Vol.4, No.3, pp. 175- 181, 2007.
[8] Brownrigg D.R.K., ÔÇÿThe weighted median filter,- Communication, ACM,
Vol. 27, No.8, pp. 807-818, 1984.
[9] Ko S.J. and Lee Y.H., ÔÇÿCenter weighted median filters and their
applications to image enhancement,- IEEE Trans. Circuits Systems, Vol.
38, No. 9, pp. 984 - 993, 1991.
[10] Arce G. and Paredes J., ÔÇÿRecursive Weighted Median Filters Admitting
Negative Weights and Their Optimization-, IEEE Trans. on Signal
Processing, Vol. 48, No. 3, pp. 768-779, 2000.
[11] Hwang H. and Haddad R. A., ÔÇÿAdaptive median filters: new and results-,
IEEE Trans. on Image Processing, Vol. 4, No.4,pp. 499-502, 1995.
[12] Abreu E., Lightstone M. and Mitra S.K., ÔÇÿA New Efficient Approach for
the Removal of Impulse Noise from Highly Corrupted Images-, IEEE
Trans. on Image Processing,Vol.5,No.6,pp. 1012-1025, 1996.
[13] Tao Chen, Kai-Kuang Ma and Li-Hui Chen (1999), ÔÇÿTri-State Median
Filter for Image Denoising-, IEEE Trans. on Image Processing, Vol. 8,
No.8, pp.1-3, 1999.
[14] Z. Wang and D. Zhang, "Progressive switching median filter for the
removal of impulse noise from highly corrupted imges", IEEE
Transactions on Circuits and Systems II, Vol.46 pp 78-80, 1999.
[15] Tao Chen and Hong Ren Wu, ÔÇÿSpace Variant Median Filters for the
Restoration of Impulse Noise Corrupted Images-, IEEE trans. on circuits
and systems II: analog and digital signal processing, Vol. 48, No. 8,
pp.784 -789, 2001.
[16] How-Lung Eng and Kai-Kuang Ma, ÔÇÿNoise Adaptive Soft-Switching
Median Filter-, IEEE Trans. On Image Processing, Vol. 10, No. 2, pp.
242 - 251, 2001.
[17] Yuan S.Q. and Tan Y.H., ÔÇÿDifference-type noise detector for adaptive
median filter-, Electronics letters, Vol. 42, No.8, pp. 454 - 455, 2006.
[18] Wenbin Luo, ÔÇÿAn Efficient Detail-Preserving Approach for Removing
Impulse Noise in Images-, IEEE signal processing letters, Vol. 13, No.7,
pp. 413 - 416, 2006.
[19] Deng Ze-Feng, Yin Zhou-Ping, and Xiong You-Lun, ÔÇÿHigh Probability
Impulse Noise-Removing Algorithm Based on Mathematical
Morphology-, IEEE signal processing Letters., Vol. 14, No.1, pp.31-
34.,2007.
[20] Srinivasan K. S. and Ebenezer D., ÔÇÿA New Fast and Efficient Decision-
Based Algorithm for Removal of High-Density Impulse Noises- IEEE
signal processing letters, Vol. 14, No. 3, pp.189 -192, 2007.
[21] Raymond H. Chan, Chung-Wa Ho, and Mila Nikolova, ÔÇÿSalt-and-Pepper
Noise Removal by Median-Type Noise Detectors and Detail-Preserving
Regularization-, IEEE Trans. on Image Processing, Vol.14, No.10,
pp.1479-1485, 2005.
[22] Rabie, "Robust Estimation Approach for Blind Denoising", IEEE Trans.
Image Processing, vol.14, no.11, pp.1755-1765, 2005.
[23] Kashyap R. and Eom K (1988), ÔÇÿRobust image modeling techniques
with an image restoration application-, IEEE Trans. Acoust., Speech,
Signal Processing , Vol. 36, No. 8, pp. 1313-1325, 1988.
[24] A. Hamza and H. Krim, "Image denoising: A nonlinear robust statistical
approach", IEEE Trans. Signal Process., vol. 49, no. 12, pp. 3045-3054,
Dec. 2001.
[25] Sardy S., Tseng P., and Brace A., ÔÇÿRobust Wavelet Denoising-, IEEE
Trans. Signal Processing., Vol. 49, No. 6, pp. 1146-1152, 2001.
[26] Ponomaryov V.I, Funes F. J. G, Pogrebnyak O.B, and De Rivera L. N.,
ÔÇÿDenoising robust image filter with retention of small-size details in
presence of complex noise mixture,- in Proc. SPIE Conf. Visual
Communications and Image Processing, Vol. 4671 II, San Jose, CA, pp.
877-887, 2002.
[27] Black M.J. and Rangarajan A. (1994), ÔÇÿThe outlier process: Unifying
line Processes and robust statistics-, IEEE Conf. Computer Vision and
Pattern Recognition. (Online). Available: citeseer.nj.nec.com/
black94outlier.html
[28] Black M.J., Guillermo Sapiro, David Marimont, and David Heeger
(1998), ÔÇÿRobust Anisotropic Diffusion-, IEEE Trans. on Image
Processing, Vol. 7, No.3, pp. 421- 432, 1998.
[29] Huber P.S., ÔÇÿRobust Statistics-, John Wiley,1981.
[30] Hampel F.R., Ronchetti E.M., Rousseeuw P.J. and Stahel W.A., ÔÇÿRobust
Statistics: The Approach Based on Influence Functions-, New York:
Wiley, 1986.
[31] Black M.J., ÔÇÿRobust Incremental Optical Flow-, PhD thesis, Yale
University, New Haven, CT, Research Report YALEU/ DCS/RR-923,
1992.
[32] Black M.J and A. Rangarajan, "On the unification of line processes,
outlier rejection, and robust statistics with applications to early vision,"
International Journal of Computer Vision, Vol.19 , pp. 57-91, 1996.
[1] Pitas I. and Venetsanopoulos A. N., ÔÇÿNonlinear Digital Filters: Principles
and Applications-, Boston, MA: Kluwer Academic, 1990.
[2] Gonzalez R.C. and Woods R.E., ÔÇÿDigital Image Processing-, Addison-
Wesley Publishing Company,2002.
[3] Bovik A.C., ÔÇÿHandbook of Image and Video Processing-, Academic
Press, 2000.
[4] Pratt W. K., ÔÇÿDigital Image Processing-. New York Wiley, 1991.
[5] Astola J and P.Kuosmanen, Fundamentals of Nonlinear Digital
Filtering, CRC Press, 1997.
[6] Hung T.S., G.J Yang, and G.Y. Tang , ÔÇÿFast two dimensional median
filtering algorithm-, IEEE Transactions on Acoustics Speech and Signal
Processing , vol. 1 pp 13-18 , 1979.
[7] Srinivasan E. and Ebenezer D., ÔÇÿNew Nonlinear Filtering Strategies for
Eliminating Short and Long Tailed Noise in Images with Edge
Preservation Properties-, International Journal of Signal Processing,
Vol.4, No.3, pp. 175- 181, 2007.
[8] Brownrigg D.R.K., ÔÇÿThe weighted median filter,- Communication, ACM,
Vol. 27, No.8, pp. 807-818, 1984.
[9] Ko S.J. and Lee Y.H., ÔÇÿCenter weighted median filters and their
applications to image enhancement,- IEEE Trans. Circuits Systems, Vol.
38, No. 9, pp. 984 - 993, 1991.
[10] Arce G. and Paredes J., ÔÇÿRecursive Weighted Median Filters Admitting
Negative Weights and Their Optimization-, IEEE Trans. on Signal
Processing, Vol. 48, No. 3, pp. 768-779, 2000.
[11] Hwang H. and Haddad R. A., ÔÇÿAdaptive median filters: new and results-,
IEEE Trans. on Image Processing, Vol. 4, No.4,pp. 499-502, 1995.
[12] Abreu E., Lightstone M. and Mitra S.K., ÔÇÿA New Efficient Approach for
the Removal of Impulse Noise from Highly Corrupted Images-, IEEE
Trans. on Image Processing,Vol.5,No.6,pp. 1012-1025, 1996.
[13] Tao Chen, Kai-Kuang Ma and Li-Hui Chen (1999), ÔÇÿTri-State Median
Filter for Image Denoising-, IEEE Trans. on Image Processing, Vol. 8,
No.8, pp.1-3, 1999.
[14] Z. Wang and D. Zhang, "Progressive switching median filter for the
removal of impulse noise from highly corrupted imges", IEEE
Transactions on Circuits and Systems II, Vol.46 pp 78-80, 1999.
[15] Tao Chen and Hong Ren Wu, ÔÇÿSpace Variant Median Filters for the
Restoration of Impulse Noise Corrupted Images-, IEEE trans. on circuits
and systems II: analog and digital signal processing, Vol. 48, No. 8,
pp.784 -789, 2001.
[16] How-Lung Eng and Kai-Kuang Ma, ÔÇÿNoise Adaptive Soft-Switching
Median Filter-, IEEE Trans. On Image Processing, Vol. 10, No. 2, pp.
242 - 251, 2001.
[17] Yuan S.Q. and Tan Y.H., ÔÇÿDifference-type noise detector for adaptive
median filter-, Electronics letters, Vol. 42, No.8, pp. 454 - 455, 2006.
[18] Wenbin Luo, ÔÇÿAn Efficient Detail-Preserving Approach for Removing
Impulse Noise in Images-, IEEE signal processing letters, Vol. 13, No.7,
pp. 413 - 416, 2006.
[19] Deng Ze-Feng, Yin Zhou-Ping, and Xiong You-Lun, ÔÇÿHigh Probability
Impulse Noise-Removing Algorithm Based on Mathematical
Morphology-, IEEE signal processing Letters., Vol. 14, No.1, pp.31-
34.,2007.
[20] Srinivasan K. S. and Ebenezer D., ÔÇÿA New Fast and Efficient Decision-
Based Algorithm for Removal of High-Density Impulse Noises- IEEE
signal processing letters, Vol. 14, No. 3, pp.189 -192, 2007.
[21] Raymond H. Chan, Chung-Wa Ho, and Mila Nikolova, ÔÇÿSalt-and-Pepper
Noise Removal by Median-Type Noise Detectors and Detail-Preserving
Regularization-, IEEE Trans. on Image Processing, Vol.14, No.10,
pp.1479-1485, 2005.
[22] Rabie, "Robust Estimation Approach for Blind Denoising", IEEE Trans.
Image Processing, vol.14, no.11, pp.1755-1765, 2005.
[23] Kashyap R. and Eom K (1988), ÔÇÿRobust image modeling techniques
with an image restoration application-, IEEE Trans. Acoust., Speech,
Signal Processing , Vol. 36, No. 8, pp. 1313-1325, 1988.
[24] A. Hamza and H. Krim, "Image denoising: A nonlinear robust statistical
approach", IEEE Trans. Signal Process., vol. 49, no. 12, pp. 3045-3054,
Dec. 2001.
[25] Sardy S., Tseng P., and Brace A., ÔÇÿRobust Wavelet Denoising-, IEEE
Trans. Signal Processing., Vol. 49, No. 6, pp. 1146-1152, 2001.
[26] Ponomaryov V.I, Funes F. J. G, Pogrebnyak O.B, and De Rivera L. N.,
ÔÇÿDenoising robust image filter with retention of small-size details in
presence of complex noise mixture,- in Proc. SPIE Conf. Visual
Communications and Image Processing, Vol. 4671 II, San Jose, CA, pp.
877-887, 2002.
[27] Black M.J. and Rangarajan A. (1994), ÔÇÿThe outlier process: Unifying
line Processes and robust statistics-, IEEE Conf. Computer Vision and
Pattern Recognition. (Online). Available: citeseer.nj.nec.com/
black94outlier.html
[28] Black M.J., Guillermo Sapiro, David Marimont, and David Heeger
(1998), ÔÇÿRobust Anisotropic Diffusion-, IEEE Trans. on Image
Processing, Vol. 7, No.3, pp. 421- 432, 1998.
[29] Huber P.S., ÔÇÿRobust Statistics-, John Wiley,1981.
[30] Hampel F.R., Ronchetti E.M., Rousseeuw P.J. and Stahel W.A., ÔÇÿRobust
Statistics: The Approach Based on Influence Functions-, New York:
Wiley, 1986.
[31] Black M.J., ÔÇÿRobust Incremental Optical Flow-, PhD thesis, Yale
University, New Haven, CT, Research Report YALEU/ DCS/RR-923,
1992.
[32] Black M.J and A. Rangarajan, "On the unification of line processes,
outlier rejection, and robust statistics with applications to early vision,"
International Journal of Computer Vision, Vol.19 , pp. 57-91, 1996.
@article{"International Journal of Information, Control and Computer Sciences:50957", author = "V.R.Vijaykumar and P.T.Vanathi and P.Kanagasabapathy and D.Ebenezer", title = "Robust Statistics Based Algorithm to Remove Salt and Pepper Noise in Images", abstract = "In this paper, a robust statistics based filter to remove salt and pepper noise in digital images is presented. The function of the algorithm is to detect the corrupted pixels first since the impulse noise only affect certain pixels in the image and the remaining pixels are uncorrupted. The corrupted pixels are replaced by an estimated value using the proposed robust statistics based filter. The proposed method perform well in removing low to medium density impulse noise with detail preservation upto a noise density of 70% compared to standard median filter, weighted median filter, recursive weighted median filter, progressive switching median filter, signal dependent rank ordered mean filter, adaptive median filter and recently proposed decision based algorithm. The visual and quantitative results show the proposed algorithm outperforms in restoring the original image with superior preservation of edges and better suppression of impulse noise
", keywords = "Image denoising, Nonlinear filter, Robust Statistics,and Salt and Pepper Noise.", volume = "3", number = "11", pages = "2516-10", }
