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Removing random-valued impulse noise with reliable weight
1. | School of mathematical science, Inner Mongolia University, No.235 Daxuexilu Road, 010021 Hohhot, Inner Mongolia, China |
2. | School of Computer Science, University of Nottingham, Nottingham NG8 1BB, UK |
3. | UMR 6205, Laboratoire de Mathématiques de Bretagne Atlantique, Université de Bretagne-Sud, Campus de Tohannic, BP 573, 56017 Vannes, France |
4. | School of Computer and Software, Nanjing University of Information Science and Technology, Nanjing 210044, China |
5. | Institute of Image Processing and Pattern Recognition, Shanghai Jiao Tong University, No. 800 Dongchuan Road, Minhang District, Shanghai 200240, China |
In this paper, we present a patch based weighted means filter for removing an impulse noise by adapting the fundamental idea of the non-local means filter to the random-valued impulse noise. Our approach is to give a weight to a pixel in order to evaluate the probability that the pixel is contaminated by the impulse noise, which we call Reliable Weight of the pixel. With the help of the Reliable Weights we introduce the similarity function to measure the similarity among patches of the image contaminated by a random impulse noise. It turns out that the similarity function has significant anti impulse noise interference ability. We then incorporate the Reliable Weights and the similarity function into a filter designed to remove the random impulse noise. Under suitable conditions, we establish two convergence theorems to demonstrate that our method is feasible. Simulation results confirm that our filter is competitive compared to recently proposed methods.
References:
[1] |
E. Abreu, M. Lightstone, S. K Mitra and K. Arakawa,
A new efficient approach for the removal of impulse noise from highly corrupted images, IEEE Transactions on Image Processing, 5 (1996), 1012-1025.
doi: 10.1109/83.503916. |
[2] |
I. Aizenberg, C. Butakoff and D. Paliy,
Impulsive noise removal using threshold boolean filtering based on the impulse detecting functions, IEEE Signal Processing Letters, 12 (2005), 63-66.
doi: 10.1109/LSP.2004.838198. |
[3] |
T. Y. Al-Naffouri, A. A. Quadeer and G. Caire,
Impulse noise estimation and removal for ofdm systems, IEEE Transactions on communications, 62 (2014), 976-989.
doi: 10.1109/TCOMM.2014.012414.130244. |
[4] |
N. Alajlan, M. Kamel and E. Jernigan,
Detail preserving impulsive noise removal, Signal Processing: Image Communication, 19 (2004), 993-1003.
doi: 10.1016/j.image.2004.08.003. |
[5] |
A. S. Awad,
Standard deviation for obtaining the optimal direction in the removal of impulse noise, IEEE Signal Processing Letters, 18 (2011), 407-410.
doi: 10.1109/LSP.2011.2154330. |
[6] |
E. Beşdok and M. Emin Yüksel,
Impulsive noise suppression from images with jarque-bera test based median filter, AEU-International Journal of Electronics and Communications, 59 (2005), 105-110.
|
[7] |
A. C. Bovik, Handbook of Image and Video Processing, Access Online via Elsevier, 2010. |
[8] |
D. R. K. Brownrigg,
The weighted median filter, Communications of the ACM, 27 (1984), 807-818.
doi: 10.1145/358198.358222. |
[9] |
R. H. Chan, C.-W. Ho and M. Nikolova,
Salt-and-pepper noise removal by median-type noise detectors and detail-preserving regularization, IEEE Transactions on Image Processing, 14 (2005), 1479-1485.
doi: 10.1109/TIP.2005.852196. |
[10] |
R. H. Chan, C. Hu and M. Nikolova,
An iterative procedure for removing random-valued impulse noise, IEEE Signal Processing Letters, 11 (2004), 921-924.
doi: 10.1109/LSP.2004.838190. |
[11] |
T. Chen, K.-K. Ma and L.-H. Chen,
Tri-state median filter for image denoising, IEEE Transactions on Image Processing, 8 (1999), 1834-1838.
|
[12] |
T. Chen and H. R. Wu,
Adaptive impulse detection using center-weighted median filters, IEEE Signal Processing Letters, 8 (2001), 1-3.
doi: 10.1109/97.889633. |
[13] |
___, Space variant median filters for the restoration of impulse noise corrupted images, IEEE Transactions on Circuits and Systems Ⅱ: Analog and Digital Signal Processing 48 (2001), 784–789. |
[14] |
V. Crnojevic, V. Senk and Z. Trpovski,
Advanced impulse detection based on pixel-wise mad, IEEE Signal Processing Letters, 11 (2004), 589-592.
doi: 10.1109/LSP.2004.830117. |
[15] |
J. Delon and A. Desolneux,
A patch-based approach for removing impulse or mixed gaussian-impulse noise, SIAM Journal on Imaging Sciences, 6 (2013), 1140-1174.
doi: 10.1137/120885000. |
[16] |
J. Delon, A. Desolneux and T. Guillemot,
Parigi: A patch-based approach to remove impulse-gaussian noise from images, Image Processing On Line, 6 (2016), 130-154.
doi: 10.5201/ipol.2016.161. |
[17] |
Y. Dong, R. H. Chan and S. Xu,
A detection statistic for random-valued impulse noise, IEEE Transactions on Image Processing, 16 (2007), 1112-1120.
doi: 10.1109/TIP.2006.891348. |
[18] |
R. Garnett, T. Huegerich, C. Chui and W. He,
A universal noise removal algorithm with an impulse detector, IEEE Transactions on Image Processing, 14 (2005), 1747-1754.
doi: 10.1109/TIP.2005.857261. |
[19] |
R. C. Gonzalez and R. E. Woods, Digital Image Processing, Englewood Cliffs, NJ: Prentice-Hall, 2002. |
[20] |
M.-H. Hsieh, F.-C. Cheng, M.-C. Shie and S.-J. Ruan,
Fast and efficient median filter for removing 1–99% levels of salt-and-pepper noise in images, Engineering Applications of Artificial Intelligence, 26 (2013), 1333-1338.
doi: 10.1016/j.engappai.2012.10.012. |
[21] |
H. Hu, B. Li and Q. Liu,
Removing mixture of gaussian and impulse noise by patch-based weighted means, Journal of Scientific Computing, 67 (2016), 103-129.
doi: 10.1007/s10915-015-0073-9. |
[22] |
S. Huang and J. Zhu,
Removal of salt-and-pepper noise based on compressed sensing, Electronics Letters, 46 (2010), 1198-1199.
doi: 10.1049/el.2010.0833. |
[23] |
I. F. Jafar, J. Amman, R. A. AlNa'mneh and K. A. Darabkh,
Efficient improvements on the BDND filtering algorithm for the removal of high-density impulse noise, IEEE Transactions on Image Processing, 22 (2013), 1223-1232.
doi: 10.1109/TIP.2012.2228496. |
[24] |
Q. Jin, L. Bai, J. Yang, I. Grama and Q. Liu, A new method for removing random-valued impulse noise, International Conference on Neural Information Processing, Springer, 2014, 9–16.
doi: 10.1007/978-3-319-12643-2_2. |
[25] |
Q. Jin, I. Grama, C. Kervrann and Q. Liu,
Nonlocal means and optimal weights for noise removal, Siam Journal on Imaging Sciences, 10 (2017), 1878-1920.
doi: 10.1137/16M1080781. |
[26] |
Q. Jin, I. Grama and Q. Liu,
A new poisson noise filter based on weights optimization, Journal of Scientific Computing, 58 (2014), 548-573.
doi: 10.1007/s10915-013-9743-7. |
[27] |
S.-J. Ko and Y. H. Lee,
Center weighted median filters and their applications to image enhancement, IEEE Transactions on Circuits and Systems, 38 (1991), 984-993.
doi: 10.1109/31.83870. |
[28] |
B. Li, Q. Liu, J. Xu and X. Luo,
A new method for removing mixed noises, Science China Information Sciences, 54 (2011), 51-59.
doi: 10.1007/s11432-010-4128-0. |
[29] |
C.-Y. Lien, P.-Y. Chen, L.-Y. Chang, Y.-M. Lin and P.-K. Chang, An efficient denoising chip for the removal of impulse noise, IEEE International Symposium on Circuits and Systems, 2010, 1169–1172.
doi: 10.1109/ISCAS.2010.5537308. |
[30] |
C.-Y. Lien, C.-C. Huang, P.-Y. Chen and Y.-F. Lin,
An efficient denoising architecture for removal of impulse noise in images, IEEE Transactions on Computers, 62 (2013), 631-643.
doi: 10.1109/TC.2011.256. |
[31] |
H.-M. Lin and A. N. Willson Jr,
Median filters with adaptive length, IEEE Transactions on Circuits and Systems, 35 (1988), 675-690.
doi: 10.1109/31.1805. |
[32] |
T. Melange, M. Nachtegael and E. E. Kerre,
Fuzzy Random Impulse Noise Removal From Color Image Sequences, IEEE Transactions on Image Processing, 20 (2011), 959-970.
doi: 10.1109/TIP.2010.2077305. |
[33] |
M. S. Nair and P. M. Ameera Mol, Noise adaptive weighted switching median filter for removing high density impulse noise, Advances in Computing and Communications, Springer, 2011, 193–204.
doi: 10.1007/978-3-642-22720-2_19. |
[34] |
M. Nikolova,
A variational approach to remove outliers and impulse noise, Journal of Mathematical Imaging and Vision, 20 (2004), 99-120.
|
[35] |
G. Pok, J.-C. Liu and A. S. Nair,
Selective removal of impulse noise based on homogeneity level information, IEEE Transactions on Image Processing, 12 (2003), 85-92.
|
[36] |
K. Prathiba, R. Rathi and C. S. Christopher, Random valued impulse denoising using robust direction based detector, Information & Communication Technologies (ICT), 2013 IEEE Conference on, IEEE, 2013, 1237–1242.
doi: 10.1109/CICT.2013.6558290. |
[37] |
W. K. Pratt, Median Filtering, Image Process. Inst., Univ. Southern California, Los Angeles, 1975. |
[38] |
W. Pruitt,
Summability of independent random variables, J. Math. Mech., 15 (1966), 769-776.
|
[39] |
F. Russo,
Impulse noise cancellation in image data using a two-output nonlinear filter, Measurement, 36 (2004), 205-213.
doi: 10.1016/j.measurement.2004.09.002. |
[40] |
K. S. Srinivasan and D. Ebenezer,
A new fast and efficient decision-based algorithm for removal of high-density impulse noises, IEEE Signal Processing Letters, 14 (2007), 189-192.
doi: 10.1109/LSP.2006.884018. |
[41] |
T. Sun and Y. Neuvo,
Detail-preserving median based filters in image processing, Pattern Recognition Letters, 15 (1994), 341-347.
doi: 10.1016/0167-8655(94)90082-5. |
[42] |
C. Wang, T. Chen and Z. Qu, A novel improved median filter for salt-and-pepper noise from highly corrupted images, Systems and Control in Aeronautics and Astronautics (ISSCAA), 2010 3rd International Symposium on, IEEE, 2010, 718–722. |
[43] |
S.-S. Wang and C.-H. Wu,
A new impulse detection and filtering method for removal of wide range impulse noises, Pattern Recognition, 42 (2009), 2194-2202.
doi: 10.1016/j.patcog.2009.01.022. |
[44] |
Z. Wang and D. Zhang,
Progressive switching median filter for the removal of impulse noise from highly corrupted images, Circuits and Systems II: Analog and Digital Signal Processing, IEEE Transactions on, 46 (1999), 78-80.
|
[45] |
M. Waqas, S. G. Javed and A. Khan, Random-valued impulse noise removal from images: K-means and luo-statistics based detector and nonlocal means based estimator, Applied Sciences and Technology (IBCAST), 2014 11th International Bhurban Conference on, IEEE, 2014, 130–135.
doi: 10.1109/IBCAST.2014.6778135. |
[46] |
L. Wenbin,
A new efficient impulse detection algorithm for the removal of impulse noise, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 88 (2005), 2579-2586.
|
[47] |
P. S. Windyga,
Fast impulsive noise removal, IEEE Transactions on Image Processing, 10 (2001), 173-179.
doi: 10.1109/83.892455. |
[48] |
J. Wu and C. Tang,
Pde-based random-valued impulse noise removal based on new class of controlling functions, IEEE Transactions on Image Processing, 20 (2011), 2428-2438.
doi: 10.1109/TIP.2011.2131664. |
[49] |
___, Random-valued impulse noise removal using fuzzy weighted non-local means, Signal,
Image and Video Processing, 8 (2014), 349–355. |
[50] |
B. Xiong and Z. Yin,
A universal denoising framework with a new impulse detector and nonlocal means, IEEE Transactions on Image Processing, 21 (2012), 1663-1675.
doi: 10.1109/TIP.2011.2172804. |
[51] |
Y. Y. Zhou, Z. F. Ye and J. J. Huang,
Improved decision-based detail-preserving variational method for removal of random-valued impulse noise, IET Image Processing, 6 (2012), 976-985.
doi: 10.1049/iet-ipr.2011.0312. |
[52] |
Z. Zhou,
Cognition and removal of impulse noise with uncertainty, IEEE Transactions on Image Processing, 21 (2012), 3157-3167.
doi: 10.1109/TIP.2012.2189577. |
[53] |
Z. Zhu, X. Zhang, X. Wan and Q. Wang,
A random-valued impulse noise removal algorithm with local deviation index and edge-preserving regularization, Signal, Image and Video Processing, 9 (2015), 221-228.
doi: 10.1007/s11760-013-0426-5. |
[54] |
Z. Zhu, X. Zhang, Q. Wang, X. Wan and Y. Xiao,
Edge-preserving regularized filter with spatial local outlier measure and q-estimate, Circuits, Systems, and Signal Processing, 33 (2014), 629-642.
doi: 10.1007/s00034-013-9644-x. |
show all references
References:
[1] |
E. Abreu, M. Lightstone, S. K Mitra and K. Arakawa,
A new efficient approach for the removal of impulse noise from highly corrupted images, IEEE Transactions on Image Processing, 5 (1996), 1012-1025.
doi: 10.1109/83.503916. |
[2] |
I. Aizenberg, C. Butakoff and D. Paliy,
Impulsive noise removal using threshold boolean filtering based on the impulse detecting functions, IEEE Signal Processing Letters, 12 (2005), 63-66.
doi: 10.1109/LSP.2004.838198. |
[3] |
T. Y. Al-Naffouri, A. A. Quadeer and G. Caire,
Impulse noise estimation and removal for ofdm systems, IEEE Transactions on communications, 62 (2014), 976-989.
doi: 10.1109/TCOMM.2014.012414.130244. |
[4] |
N. Alajlan, M. Kamel and E. Jernigan,
Detail preserving impulsive noise removal, Signal Processing: Image Communication, 19 (2004), 993-1003.
doi: 10.1016/j.image.2004.08.003. |
[5] |
A. S. Awad,
Standard deviation for obtaining the optimal direction in the removal of impulse noise, IEEE Signal Processing Letters, 18 (2011), 407-410.
doi: 10.1109/LSP.2011.2154330. |
[6] |
E. Beşdok and M. Emin Yüksel,
Impulsive noise suppression from images with jarque-bera test based median filter, AEU-International Journal of Electronics and Communications, 59 (2005), 105-110.
|
[7] |
A. C. Bovik, Handbook of Image and Video Processing, Access Online via Elsevier, 2010. |
[8] |
D. R. K. Brownrigg,
The weighted median filter, Communications of the ACM, 27 (1984), 807-818.
doi: 10.1145/358198.358222. |
[9] |
R. H. Chan, C.-W. Ho and M. Nikolova,
Salt-and-pepper noise removal by median-type noise detectors and detail-preserving regularization, IEEE Transactions on Image Processing, 14 (2005), 1479-1485.
doi: 10.1109/TIP.2005.852196. |
[10] |
R. H. Chan, C. Hu and M. Nikolova,
An iterative procedure for removing random-valued impulse noise, IEEE Signal Processing Letters, 11 (2004), 921-924.
doi: 10.1109/LSP.2004.838190. |
[11] |
T. Chen, K.-K. Ma and L.-H. Chen,
Tri-state median filter for image denoising, IEEE Transactions on Image Processing, 8 (1999), 1834-1838.
|
[12] |
T. Chen and H. R. Wu,
Adaptive impulse detection using center-weighted median filters, IEEE Signal Processing Letters, 8 (2001), 1-3.
doi: 10.1109/97.889633. |
[13] |
___, Space variant median filters for the restoration of impulse noise corrupted images, IEEE Transactions on Circuits and Systems Ⅱ: Analog and Digital Signal Processing 48 (2001), 784–789. |
[14] |
V. Crnojevic, V. Senk and Z. Trpovski,
Advanced impulse detection based on pixel-wise mad, IEEE Signal Processing Letters, 11 (2004), 589-592.
doi: 10.1109/LSP.2004.830117. |
[15] |
J. Delon and A. Desolneux,
A patch-based approach for removing impulse or mixed gaussian-impulse noise, SIAM Journal on Imaging Sciences, 6 (2013), 1140-1174.
doi: 10.1137/120885000. |
[16] |
J. Delon, A. Desolneux and T. Guillemot,
Parigi: A patch-based approach to remove impulse-gaussian noise from images, Image Processing On Line, 6 (2016), 130-154.
doi: 10.5201/ipol.2016.161. |
[17] |
Y. Dong, R. H. Chan and S. Xu,
A detection statistic for random-valued impulse noise, IEEE Transactions on Image Processing, 16 (2007), 1112-1120.
doi: 10.1109/TIP.2006.891348. |
[18] |
R. Garnett, T. Huegerich, C. Chui and W. He,
A universal noise removal algorithm with an impulse detector, IEEE Transactions on Image Processing, 14 (2005), 1747-1754.
doi: 10.1109/TIP.2005.857261. |
[19] |
R. C. Gonzalez and R. E. Woods, Digital Image Processing, Englewood Cliffs, NJ: Prentice-Hall, 2002. |
[20] |
M.-H. Hsieh, F.-C. Cheng, M.-C. Shie and S.-J. Ruan,
Fast and efficient median filter for removing 1–99% levels of salt-and-pepper noise in images, Engineering Applications of Artificial Intelligence, 26 (2013), 1333-1338.
doi: 10.1016/j.engappai.2012.10.012. |
[21] |
H. Hu, B. Li and Q. Liu,
Removing mixture of gaussian and impulse noise by patch-based weighted means, Journal of Scientific Computing, 67 (2016), 103-129.
doi: 10.1007/s10915-015-0073-9. |
[22] |
S. Huang and J. Zhu,
Removal of salt-and-pepper noise based on compressed sensing, Electronics Letters, 46 (2010), 1198-1199.
doi: 10.1049/el.2010.0833. |
[23] |
I. F. Jafar, J. Amman, R. A. AlNa'mneh and K. A. Darabkh,
Efficient improvements on the BDND filtering algorithm for the removal of high-density impulse noise, IEEE Transactions on Image Processing, 22 (2013), 1223-1232.
doi: 10.1109/TIP.2012.2228496. |
[24] |
Q. Jin, L. Bai, J. Yang, I. Grama and Q. Liu, A new method for removing random-valued impulse noise, International Conference on Neural Information Processing, Springer, 2014, 9–16.
doi: 10.1007/978-3-319-12643-2_2. |
[25] |
Q. Jin, I. Grama, C. Kervrann and Q. Liu,
Nonlocal means and optimal weights for noise removal, Siam Journal on Imaging Sciences, 10 (2017), 1878-1920.
doi: 10.1137/16M1080781. |
[26] |
Q. Jin, I. Grama and Q. Liu,
A new poisson noise filter based on weights optimization, Journal of Scientific Computing, 58 (2014), 548-573.
doi: 10.1007/s10915-013-9743-7. |
[27] |
S.-J. Ko and Y. H. Lee,
Center weighted median filters and their applications to image enhancement, IEEE Transactions on Circuits and Systems, 38 (1991), 984-993.
doi: 10.1109/31.83870. |
[28] |
B. Li, Q. Liu, J. Xu and X. Luo,
A new method for removing mixed noises, Science China Information Sciences, 54 (2011), 51-59.
doi: 10.1007/s11432-010-4128-0. |
[29] |
C.-Y. Lien, P.-Y. Chen, L.-Y. Chang, Y.-M. Lin and P.-K. Chang, An efficient denoising chip for the removal of impulse noise, IEEE International Symposium on Circuits and Systems, 2010, 1169–1172.
doi: 10.1109/ISCAS.2010.5537308. |
[30] |
C.-Y. Lien, C.-C. Huang, P.-Y. Chen and Y.-F. Lin,
An efficient denoising architecture for removal of impulse noise in images, IEEE Transactions on Computers, 62 (2013), 631-643.
doi: 10.1109/TC.2011.256. |
[31] |
H.-M. Lin and A. N. Willson Jr,
Median filters with adaptive length, IEEE Transactions on Circuits and Systems, 35 (1988), 675-690.
doi: 10.1109/31.1805. |
[32] |
T. Melange, M. Nachtegael and E. E. Kerre,
Fuzzy Random Impulse Noise Removal From Color Image Sequences, IEEE Transactions on Image Processing, 20 (2011), 959-970.
doi: 10.1109/TIP.2010.2077305. |
[33] |
M. S. Nair and P. M. Ameera Mol, Noise adaptive weighted switching median filter for removing high density impulse noise, Advances in Computing and Communications, Springer, 2011, 193–204.
doi: 10.1007/978-3-642-22720-2_19. |
[34] |
M. Nikolova,
A variational approach to remove outliers and impulse noise, Journal of Mathematical Imaging and Vision, 20 (2004), 99-120.
|
[35] |
G. Pok, J.-C. Liu and A. S. Nair,
Selective removal of impulse noise based on homogeneity level information, IEEE Transactions on Image Processing, 12 (2003), 85-92.
|
[36] |
K. Prathiba, R. Rathi and C. S. Christopher, Random valued impulse denoising using robust direction based detector, Information & Communication Technologies (ICT), 2013 IEEE Conference on, IEEE, 2013, 1237–1242.
doi: 10.1109/CICT.2013.6558290. |
[37] |
W. K. Pratt, Median Filtering, Image Process. Inst., Univ. Southern California, Los Angeles, 1975. |
[38] |
W. Pruitt,
Summability of independent random variables, J. Math. Mech., 15 (1966), 769-776.
|
[39] |
F. Russo,
Impulse noise cancellation in image data using a two-output nonlinear filter, Measurement, 36 (2004), 205-213.
doi: 10.1016/j.measurement.2004.09.002. |
[40] |
K. S. Srinivasan and D. Ebenezer,
A new fast and efficient decision-based algorithm for removal of high-density impulse noises, IEEE Signal Processing Letters, 14 (2007), 189-192.
doi: 10.1109/LSP.2006.884018. |
[41] |
T. Sun and Y. Neuvo,
Detail-preserving median based filters in image processing, Pattern Recognition Letters, 15 (1994), 341-347.
doi: 10.1016/0167-8655(94)90082-5. |
[42] |
C. Wang, T. Chen and Z. Qu, A novel improved median filter for salt-and-pepper noise from highly corrupted images, Systems and Control in Aeronautics and Astronautics (ISSCAA), 2010 3rd International Symposium on, IEEE, 2010, 718–722. |
[43] |
S.-S. Wang and C.-H. Wu,
A new impulse detection and filtering method for removal of wide range impulse noises, Pattern Recognition, 42 (2009), 2194-2202.
doi: 10.1016/j.patcog.2009.01.022. |
[44] |
Z. Wang and D. Zhang,
Progressive switching median filter for the removal of impulse noise from highly corrupted images, Circuits and Systems II: Analog and Digital Signal Processing, IEEE Transactions on, 46 (1999), 78-80.
|
[45] |
M. Waqas, S. G. Javed and A. Khan, Random-valued impulse noise removal from images: K-means and luo-statistics based detector and nonlocal means based estimator, Applied Sciences and Technology (IBCAST), 2014 11th International Bhurban Conference on, IEEE, 2014, 130–135.
doi: 10.1109/IBCAST.2014.6778135. |
[46] |
L. Wenbin,
A new efficient impulse detection algorithm for the removal of impulse noise, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 88 (2005), 2579-2586.
|
[47] |
P. S. Windyga,
Fast impulsive noise removal, IEEE Transactions on Image Processing, 10 (2001), 173-179.
doi: 10.1109/83.892455. |
[48] |
J. Wu and C. Tang,
Pde-based random-valued impulse noise removal based on new class of controlling functions, IEEE Transactions on Image Processing, 20 (2011), 2428-2438.
doi: 10.1109/TIP.2011.2131664. |
[49] |
___, Random-valued impulse noise removal using fuzzy weighted non-local means, Signal,
Image and Video Processing, 8 (2014), 349–355. |
[50] |
B. Xiong and Z. Yin,
A universal denoising framework with a new impulse detector and nonlocal means, IEEE Transactions on Image Processing, 21 (2012), 1663-1675.
doi: 10.1109/TIP.2011.2172804. |
[51] |
Y. Y. Zhou, Z. F. Ye and J. J. Huang,
Improved decision-based detail-preserving variational method for removal of random-valued impulse noise, IET Image Processing, 6 (2012), 976-985.
doi: 10.1049/iet-ipr.2011.0312. |
[52] |
Z. Zhou,
Cognition and removal of impulse noise with uncertainty, IEEE Transactions on Image Processing, 21 (2012), 3157-3167.
doi: 10.1109/TIP.2012.2189577. |
[53] |
Z. Zhu, X. Zhang, X. Wan and Q. Wang,
A random-valued impulse noise removal algorithm with local deviation index and edge-preserving regularization, Signal, Image and Video Processing, 9 (2015), 221-228.
doi: 10.1007/s11760-013-0426-5. |
[54] |
Z. Zhu, X. Zhang, Q. Wang, X. Wan and Y. Xiao,
Edge-preserving regularized filter with spatial local outlier measure and q-estimate, Circuits, Systems, and Signal Processing, 33 (2014), 629-642.
doi: 10.1007/s00034-013-9644-x. |














Images | Baboon | Bridge | Lena | Pentagon | Average | ||||||||||
p | |||||||||||||||
Method | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR |
MF |
22.52db | 20.65db | 19.36db | 25.04db | 22.17db | 19.36db | 32.37db | 27.64db | 21.58db | 28.29db | 25.16db | 23.41db | 27.06db | 23.91db | 20.93db |
SS-II |
23.67db | 20.85db | 19.27db | 26.26db | 22.66db | 19.13db | 32.93db | 27.90db | 20.61db | 29.34db | 26.26db | 23.90db | 28.05db | 24.42db | 20.73db |
SS-I |
22.46db | 21.35db | 19.42db | 25.90db | 22.85db | 19.04db | 33.43db | 27.75db | 20.61db | 28.28db | 26.43db | 23.85db | 27.52db | 24.60db | 20.73db |
SD-ROM |
23.81db | 21.49db | 19.45db | 26.56db | 23.80db | 20.66db | 35.71db | 29.85db | 23.41db | 30.38db | 27.27db | 24.33db | 29.12db | 25.60db | 21.96db |
PSM |
23.43db | 21.07db | 19.56db | 26.33db | 22.75db | 19.73db | 35.09db | 28.92db | 22.06db | 29.18db | 26.19db | 23.87db | 28.51db | 24.73db | 21.31db |
TSM |
23.73db | 21.38db | 19.44db | 26.52db | 22.89db | 19.60db | 34.21db | 28.30db | 21.67db | 29.29db | 26.29db | 23.59db | 28.44db | 24.71db | 21.08db |
MSM |
24.02db | 21.52db | 19.63db | 27.27db | 23.55db | 20.07db | 35.44db | 29.26db | 22.14db | 30.34db | 27.04db | 24.22db | 29.27db | 25.34db | 21.52db |
ACWM |
24.17db | 21.58db | 19.56db | 27.08db | 23.23db | 19.27db | 36.07db | 28.79db | 21.19db | 30.23db | 26.84db | 23.50db | 29.39db | 25.11db | 20.88db |
PWMAD |
23.78db | 21.56db | 19.68db | 26.90db | 23.83db | 20.83db | 36.50db | 31.41db | 24.30db | 30.11db | 27.33db | 24.46db | 29.32db | 26.03db | 22.32db |
Luo-IMF |
24.18db | 21.41db | 19.08db | 27.05db | 23.88db | 19.74db | 36.90db | 30.25db | 22.96db | 30.42db | 26.93db | 23.72db | 29.64db | 25.62db | 21.38db |
TriF |
24.18db | 21.60db | 19.52db | 27.60db | 24.01db | 20.84db | 36.70db | 31.12db | 26.08db | 30.33db | 27.14db | 24.60db | 29.70db | 25.97db | 22.76db |
ACWM-EPR |
23.97db | 21.62db | 19.87db | 27.31db | 24.60db | 20.89db | 36.57db | 32.21db | 24.62db | 30.03db | 27.35db | 24.59db | 29.47db | 26.45db | 22.49db |
ROAD-EPR |
24.24db | 21.53db | 19.96db | 27.42db | 24.52db | 22.04db | 36.79db | 32.32db | 28.37db | 30.35db | 27.06db | 25.00db | 29.70db | 26.36db | 23.84db |
ROLD-EPR |
24.49db | 21.92db | 20.38db | 27.86db | 24.79db | 37.45db | 32.76db | 29.03db | 30.73db | 27.73db | 25.70db | 30.13db | 26.80db | 24.43db | |
FWNLM [49] | 23.45db | 21.71db | 20.45db | 26.82db | 24.23db | 22.23db | 34.95db | 32.12db | 28.03db | 30.26db | 27.48db | 25.48db | 28.87db | 26.39db | 24.05db |
PWMF [21] | 24.84db | 22.00db | 14.72db | 24.71db | 11.58db | 10.41db | 27.83db | 11.39db | 27.01db | 12.03db | |||||
PARIGI [15,16] | 24.46db | 21.85db | 19.79db | 26.53db | 24.06db | 21.40db | 36.62db | 31.94db | 27.61db | 30.63db | 25.44db | 29.56db | 26.57db | 23.56db | |
RRWF | 27.86db | 22.49db | 37.56db | 28.19db | 30.40db |
Images | Baboon | Bridge | Lena | Pentagon | Average | ||||||||||
p | |||||||||||||||
Method | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR |
MF |
22.52db | 20.65db | 19.36db | 25.04db | 22.17db | 19.36db | 32.37db | 27.64db | 21.58db | 28.29db | 25.16db | 23.41db | 27.06db | 23.91db | 20.93db |
SS-II |
23.67db | 20.85db | 19.27db | 26.26db | 22.66db | 19.13db | 32.93db | 27.90db | 20.61db | 29.34db | 26.26db | 23.90db | 28.05db | 24.42db | 20.73db |
SS-I |
22.46db | 21.35db | 19.42db | 25.90db | 22.85db | 19.04db | 33.43db | 27.75db | 20.61db | 28.28db | 26.43db | 23.85db | 27.52db | 24.60db | 20.73db |
SD-ROM |
23.81db | 21.49db | 19.45db | 26.56db | 23.80db | 20.66db | 35.71db | 29.85db | 23.41db | 30.38db | 27.27db | 24.33db | 29.12db | 25.60db | 21.96db |
PSM |
23.43db | 21.07db | 19.56db | 26.33db | 22.75db | 19.73db | 35.09db | 28.92db | 22.06db | 29.18db | 26.19db | 23.87db | 28.51db | 24.73db | 21.31db |
TSM |
23.73db | 21.38db | 19.44db | 26.52db | 22.89db | 19.60db | 34.21db | 28.30db | 21.67db | 29.29db | 26.29db | 23.59db | 28.44db | 24.71db | 21.08db |
MSM |
24.02db | 21.52db | 19.63db | 27.27db | 23.55db | 20.07db | 35.44db | 29.26db | 22.14db | 30.34db | 27.04db | 24.22db | 29.27db | 25.34db | 21.52db |
ACWM |
24.17db | 21.58db | 19.56db | 27.08db | 23.23db | 19.27db | 36.07db | 28.79db | 21.19db | 30.23db | 26.84db | 23.50db | 29.39db | 25.11db | 20.88db |
PWMAD |
23.78db | 21.56db | 19.68db | 26.90db | 23.83db | 20.83db | 36.50db | 31.41db | 24.30db | 30.11db | 27.33db | 24.46db | 29.32db | 26.03db | 22.32db |
Luo-IMF |
24.18db | 21.41db | 19.08db | 27.05db | 23.88db | 19.74db | 36.90db | 30.25db | 22.96db | 30.42db | 26.93db | 23.72db | 29.64db | 25.62db | 21.38db |
TriF |
24.18db | 21.60db | 19.52db | 27.60db | 24.01db | 20.84db | 36.70db | 31.12db | 26.08db | 30.33db | 27.14db | 24.60db | 29.70db | 25.97db | 22.76db |
ACWM-EPR |
23.97db | 21.62db | 19.87db | 27.31db | 24.60db | 20.89db | 36.57db | 32.21db | 24.62db | 30.03db | 27.35db | 24.59db | 29.47db | 26.45db | 22.49db |
ROAD-EPR |
24.24db | 21.53db | 19.96db | 27.42db | 24.52db | 22.04db | 36.79db | 32.32db | 28.37db | 30.35db | 27.06db | 25.00db | 29.70db | 26.36db | 23.84db |
ROLD-EPR |
24.49db | 21.92db | 20.38db | 27.86db | 24.79db | 37.45db | 32.76db | 29.03db | 30.73db | 27.73db | 25.70db | 30.13db | 26.80db | 24.43db | |
FWNLM [49] | 23.45db | 21.71db | 20.45db | 26.82db | 24.23db | 22.23db | 34.95db | 32.12db | 28.03db | 30.26db | 27.48db | 25.48db | 28.87db | 26.39db | 24.05db |
PWMF [21] | 24.84db | 22.00db | 14.72db | 24.71db | 11.58db | 10.41db | 27.83db | 11.39db | 27.01db | 12.03db | |||||
PARIGI [15,16] | 24.46db | 21.85db | 19.79db | 26.53db | 24.06db | 21.40db | 36.62db | 31.94db | 27.61db | 30.63db | 25.44db | 29.56db | 26.57db | 23.56db | |
RRWF | 27.86db | 22.49db | 37.56db | 28.19db | 30.40db |
Images | Aerial | Airplane | B.wall | Cam | Clock | Male512 | Male1024 | M.surface | P.bubbles | R.chart | Barbara | boat | couple | F.print | hill | house | Average |
Method | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR |
FWNLM [49] | 36.50db | 40.78db | 36.47db | 40.02db | 37.08db | 37.56db | 37.51db | 38.51db | 38.09db | 38.85db | 40.51db | 38.37db | |||||
PWMF[21] | 36.04db | 39.77db | 36.15db | 38.52db | 39.52db | 38.38db | 38.76db | 36.03db | 36.62db | 37.51db | 37.88db | 37.55db | 36.32db | 38.54db | 39.85db | 37.83db | |
PARIGI [15,16] | 33.13db | 40.46db | 32.64db | 36.63db | 38.95db | 35.71db | 37.09db | 34.79db | 34.85db | 37.06db | 35.90db | 35.67db | 32.07db | 36.53db | 39.89db | 36.23db | |
RRWF | 38.36db | 38.46db | 39.56db | 37.57db | 37.80db | 37.88db | 36.24db |
Images | Aerial | Airplane | B.wall | Cam | Clock | Male512 | Male1024 | M.surface | P.bubbles | R.chart | Barbara | boat | couple | F.print | hill | house | Average |
Method | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR |
FWNLM [49] | 36.50db | 40.78db | 36.47db | 40.02db | 37.08db | 37.56db | 37.51db | 38.51db | 38.09db | 38.85db | 40.51db | 38.37db | |||||
PWMF[21] | 36.04db | 39.77db | 36.15db | 38.52db | 39.52db | 38.38db | 38.76db | 36.03db | 36.62db | 37.51db | 37.88db | 37.55db | 36.32db | 38.54db | 39.85db | 37.83db | |
PARIGI [15,16] | 33.13db | 40.46db | 32.64db | 36.63db | 38.95db | 35.71db | 37.09db | 34.79db | 34.85db | 37.06db | 35.90db | 35.67db | 32.07db | 36.53db | 39.89db | 36.23db | |
RRWF | 38.36db | 38.46db | 39.56db | 37.57db | 37.80db | 37.88db | 36.24db |
Images | Aerial | Airplane | B.wall | Cam | Clock | Male512 | Male1024 | M.surface | P.bubbles | R.chart | Barbara | boat | couple | F.print | hill | house | Average |
Method | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR |
FWNLM [49] | 33.17db | 37.95db | 33.32db | 35.56db | 36.91db | 35.06db | 36.28db | 35.00db | 34.47db | 35.80db | 34.96db | 34.40db | 32.33db | 35.56db | 37.55db | 35.20db | |
PWMF[21] | 38.14db | 33.47db | 36.33db | 34.77db | 34.88db | 34.64db | 35.28db | 34.95db | 35.96db | 37.93db | 35.51db | ||||||
PARIGI [15, 16] | 30.80db | 36.34db | 30.93db | 34.56db | 34.72db | 33.01db | 34.15db | 33.22db | 32.27db | 35.66db | 33.08db | 32.90db | 32.45db | 28.9594db | 33.69db | 36.29db | 33.31db |
RRWF | 33.43db | 35.79db | 36.94db | 35.41db | 35.74db | 34.78db | 32.55db |
Images | Aerial | Airplane | B.wall | Cam | Clock | Male512 | Male1024 | M.surface | P.bubbles | R.chart | Barbara | boat | couple | F.print | hill | house | Average |
Method | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR |
FWNLM [49] | 33.17db | 37.95db | 33.32db | 35.56db | 36.91db | 35.06db | 36.28db | 35.00db | 34.47db | 35.80db | 34.96db | 34.40db | 32.33db | 35.56db | 37.55db | 35.20db | |
PWMF[21] | 38.14db | 33.47db | 36.33db | 34.77db | 34.88db | 34.64db | 35.28db | 34.95db | 35.96db | 37.93db | 35.51db | ||||||
PARIGI [15, 16] | 30.80db | 36.34db | 30.93db | 34.56db | 34.72db | 33.01db | 34.15db | 33.22db | 32.27db | 35.66db | 33.08db | 32.90db | 32.45db | 28.9594db | 33.69db | 36.29db | 33.31db |
RRWF | 33.43db | 35.79db | 36.94db | 35.41db | 35.74db | 34.78db | 32.55db |
Images | Aerial | Airplane | B.wall | Cam | Clock | Male512 | Male1024 | M.surface | P.bubbles | R.chart | Barbara | boat | couple | F.print | hill | house | Average |
Method | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR |
FWNLM [49] | 31.84db | 37.39db | 32.28db | 33.54db | 33.63db | 33.64db | 32.79db | 32.55db | 33.18db | 32.67db | 30.12db | 33.55db | 35.60db | 33.47db | |||
PARIGI[15,16] | 30.13db | 35.83db | 30.19db | 33.44db | 33.71db | 31.50db | 32.27db | 32.14db | 30.55db | 34.56db | 31.18db | 31.62db | 31.00db | 28.21db | 31.75db | 34.54db | 32.04db |
RRWF | 35.35db | 32.61db | 34.10db |
Images | Aerial | Airplane | B.wall | Cam | Clock | Male512 | Male1024 | M.surface | P.bubbles | R.chart | Barbara | boat | couple | F.print | hill | house | Average |
Method | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR | PSNR |
FWNLM [49] | 31.84db | 37.39db | 32.28db | 33.54db | 33.63db | 33.64db | 32.79db | 32.55db | 33.18db | 32.67db | 30.12db | 33.55db | 35.60db | 33.47db | |||
PARIGI[15,16] | 30.13db | 35.83db | 30.19db | 33.44db | 33.71db | 31.50db | 32.27db | 32.14db | 30.55db | 34.56db | 31.18db | 31.62db | 31.00db | 28.21db | 31.75db | 34.54db | 32.04db |
RRWF | 35.35db | 32.61db | 34.10db |
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