Figure 1.
two kinds of edge contained in neighbor, (a) vertical edge, (b) slope edge
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D.C. programming approach for solving an applied ore-processing problem
April 2018, 14(2): 597-611.
doi: 10.3934/jimo.2017062
An optimized direction statistics for detecting and removing random-valued impulse noise
| 1. | School of Computer Science, Chengdu University of Information Technology, No.24 Block 1, Xuefu Road, 610225, Chengdu, China |
| 2. | School of Computer Science and Engineering, University of Electronic Science and Technology of China, No.2006, Xiyuan Ave, 611731, Chengdu, China |
In this paper, we propose a robust local image statistic based on optimized direction, by which we can distinguish image details and edges from impulse noise effectively. Therefore it can identify noisy pixels more accurately. Meanwhile, we combine it with the edge-preserving regularization to remove random-valued impulse noise in the cause of precise estimated value. Simulation results show that our method can preserve edges and details efficiently even at high noise levels.
Keywords:
Random-valued impulse noise,
weight rank-order differences,
detail-preserving regularization,
image denoising.
Mathematics Subject Classification:
Primary: 94A08; Secondary: 47A52.
Citation:
Hao Yang, Hang Qiu, Leiting Chen. An optimized direction statistics for detecting and removing random-valued impulse noise. Journal of Industrial & Management Optimization,
2018, 14
(2)
: 597-611.
doi: 10.3934/jimo.2017062
![]()
References:
| [1] |
E. Abreu, M. Lightstone and S. K. Mitra,
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] |
S. Akkoul, R. Lédée and R. Leconge,
A new adaptive switching median filter, IEEE Signal Processing Letters, 17 (2010), 587-590.
doi: 10.1109/LSP.2010.2048646. |
| [3] |
G. Arce and J. Paredes,
Recursive weighted median filters admitting negative weights and their optimization, IEEE Transactions on Image Processing, 48 (2000), 768-779.
doi: 10.1109/78.824671. |
| [4] |
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. |
| [5] |
M. J. Black and A. Rangarajan,
On the unification of line processes, outlier rejection, and robust statistics with applications in early vision, International Journal of Computer Vision, 19 (1996), 57-91.
doi: 10.1007/BF00131148. |
| [6] |
A. C. Bovik, Handbook of Image and Video Processing, 2nd edition, Academic press, 2010, New York, 2010. |
| [7] |
D. R. K. Brownrigg,
The weighted median filter, Communications of the ACM, 27 (1984), 807-818.
doi: 10.1145/358198.358222. |
| [8] |
J.-F. Cai, R. H. Chan and C. Fiore,
Minimization of a detail-preserving regularization functional for impulse noise removal, IEEE Transactions on Image Processing, 29 (2007), 79-91.
doi: 10.1007/s10851-007-0027-4. |
| [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.-W. Ho and C.-Y. Leung,
Minimization of detail-preserving regularization functional by Newton's method with continuation, Proceedings -International Conference on Image Processing, ICIP, 1 (2005), 125-128.
doi: 10.1109/ICIP.2005.1529703. |
| [11] |
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. |
| [12] |
P. Charbonnier, L. Blanc-Féraud and G. Aubert,
Deterministic edge-preserving regularization in computed imaging, IEEE Transactions on Image Processing, 6 (1997), 298-311.
doi: 10.1109/83.551699. |
| [13] |
T. Chen and H. R. Wu,
Adaptive impulse detection using center-weighted medial filters, IEEE Transactions on Image Processing Letters, 8 (2001), 1-3.
doi: 10.1109/97.889633. |
| [14] |
Y. Dong, H. R. Chan and S. Xu,
Edge-preserving regularization, Image denoising, Noise detector, Random-valued impulse noise, IEEE Transactions on Image Processing, 16 (2007), 1112-1120.
doi: 10.1109/TIP.2006.891348. |
| [15] |
Y. Dong and S. Xu,
A new directional weighted median filter for removal of random-valued impulse noise, IEEE Transactions on Image Processing, 14 (2007), 193-196.
doi: 10.1109/LSP.2006.884014. |
| [16] |
R. Garnett, T. Huegerich and C. Chui,
A universal noise removal algorithm with an impulse detector, IEEE Transactions on Image Processing, 14 (2005), 1747-1754.
doi: 10.1109/TIP.2005.857261. |
| [17] |
U. Ghaneka, A. K. Singh and and R. Pandey,
A contrast enhancement-based filter for removal of random valued impulse noise, IEEE Signal Processing Letters, 17 (2010), 47-50.
doi: 10.1109/LSP.2009.2032479. |
| [18] |
R. Gonzalez and R. Woods, Digital Image Processing, 2nd edition, Addision-Wesley Publishing Companyl, 2007. |
| [19] |
P. J. Green,
Bayesian reconstructions from emission tomography data using a modified EM algorithm, IEEE Transactions on Medical Imaging, 9 (1990), 84-93.
doi: 10.1109/42.52985. |
| [20] |
H. H. Dam, K. L. Teo and S. Nordebo,
The dual parameterization approach to optimal least square FIR filter design subject to maximum error constraints, IEEE Transactions on Signal Processing, 48 (2000), 2314-2320.
doi: 10.1109/78.852012. |
| [21] |
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. |
| [22] |
S. Z. Li,
On discontinuity-adaptive smoothness priors in computer vision, IEEE Transactions on Pattern Analysis and Machine Intelligence, 17 (1995), 576-586.
doi: 10.1109/34.387504. |
| [23] |
L. Liu, C. P. Chen and Y. Zhou,
A new weighted mean filter with a two-phase detector for removing impulse noise, Information Sciences, 315 (2015), 1-16.
doi: 10.1016/j.ins.2015.03.067. |
| [24] |
W. Luo,
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.
doi: 10.1093/ietfec/e88-a.10.2579. |
| [25] |
M. Nikolova,
A variational approach to remove outliers and impulse noise, Journal of Mathematical Imaging and Vision, 20 (2004), 99-120.
doi: 10.1023/B:JMIV.0000011920.58935.9c. |
| [26] |
W. K. Pratt, Median Filtering, Image Proc Institute, University of Southern California, Los Angeles, Tech. Rep., 1975. |
| [27] |
F. Russo,
Hybrid neuro-fuzzy filter for impulse noise removal, Pattern Recognition, 32 (1999), 1843-1855.
doi: 10.1016/S0031-3203(99)00009-6. |
| [28] |
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. |
| [29] |
K. Toh and N. Isa,
Cluster-based adaptive fuzzy switching median filter for universal impulse noise reduction, IEEE Transactions on Consumer Electronics, 56 (2010), 2560-2568.
doi: 10.1109/TCE.2010.5681141. |
| [30] |
D. Van De Ville, M. Nachtegael and D. Van der Weken,
Noise reduction by fuzzy image filtering, IEEE Transactions on Fuzzy Systems, 11 (2003), 429-436.
doi: 10.1109/TFUZZ.2003.814830. |
| [31] |
C. R. Vogel and M. E. Oman,
Fast, robust total variation-based reconstruction of noisy, blurred images, IEEE Transactions on Image Processing, 7 (1998), 813-824.
doi: 10.1109/83.679423. |
| [32] |
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. |
| [33] |
H. Xu, G. Zhu and H. Peng,
Adaptive fuzzy switching filter for images corrupted by impulse noise, Pattern Recognition Letters, 25 (2004), 1657-1663.
doi: 10.1016/j.patrec.2004.05.025. |
| [34] |
M. E. Yüksel and A. Baştürk,
A simple generalized neuro-fuzzy operator for efficient removal of impulse noise from highly corrupted digital images, AEU -International Journal of Electronics and Communications, 5 (1996), 1012-1025.
doi: 10.1016/j.aeue.2004.10.002. |
| [35] |
M. E. Yüksel,
A hybrid neuro-fuzzy filter for edge preserving restoration of images corrupted by impulse noise, IEEE Transactions on Image Processing, 15 (2006), 928-936.
doi: 10.1109/TIP.2005.863941. |
| [36] |
X.-Y. Zeng and L.-H. Yang,
Mixed impulse and gaussian noise removal using detail-preserving regularization, Optical Engineering, 49 (2010), 097002-097002.
doi: 10.1117/1.3485756. |
show all references
References:
| [1] |
E. Abreu, M. Lightstone and S. K. Mitra,
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] |
S. Akkoul, R. Lédée and R. Leconge,
A new adaptive switching median filter, IEEE Signal Processing Letters, 17 (2010), 587-590.
doi: 10.1109/LSP.2010.2048646. |
| [3] |
G. Arce and J. Paredes,
Recursive weighted median filters admitting negative weights and their optimization, IEEE Transactions on Image Processing, 48 (2000), 768-779.
doi: 10.1109/78.824671. |
| [4] |
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. |
| [5] |
M. J. Black and A. Rangarajan,
On the unification of line processes, outlier rejection, and robust statistics with applications in early vision, International Journal of Computer Vision, 19 (1996), 57-91.
doi: 10.1007/BF00131148. |
| [6] |
A. C. Bovik, Handbook of Image and Video Processing, 2nd edition, Academic press, 2010, New York, 2010. |
| [7] |
D. R. K. Brownrigg,
The weighted median filter, Communications of the ACM, 27 (1984), 807-818.
doi: 10.1145/358198.358222. |
| [8] |
J.-F. Cai, R. H. Chan and C. Fiore,
Minimization of a detail-preserving regularization functional for impulse noise removal, IEEE Transactions on Image Processing, 29 (2007), 79-91.
doi: 10.1007/s10851-007-0027-4. |
| [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.-W. Ho and C.-Y. Leung,
Minimization of detail-preserving regularization functional by Newton's method with continuation, Proceedings -International Conference on Image Processing, ICIP, 1 (2005), 125-128.
doi: 10.1109/ICIP.2005.1529703. |
| [11] |
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. |
| [12] |
P. Charbonnier, L. Blanc-Féraud and G. Aubert,
Deterministic edge-preserving regularization in computed imaging, IEEE Transactions on Image Processing, 6 (1997), 298-311.
doi: 10.1109/83.551699. |
| [13] |
T. Chen and H. R. Wu,
Adaptive impulse detection using center-weighted medial filters, IEEE Transactions on Image Processing Letters, 8 (2001), 1-3.
doi: 10.1109/97.889633. |
| [14] |
Y. Dong, H. R. Chan and S. Xu,
Edge-preserving regularization, Image denoising, Noise detector, Random-valued impulse noise, IEEE Transactions on Image Processing, 16 (2007), 1112-1120.
doi: 10.1109/TIP.2006.891348. |
| [15] |
Y. Dong and S. Xu,
A new directional weighted median filter for removal of random-valued impulse noise, IEEE Transactions on Image Processing, 14 (2007), 193-196.
doi: 10.1109/LSP.2006.884014. |
| [16] |
R. Garnett, T. Huegerich and C. Chui,
A universal noise removal algorithm with an impulse detector, IEEE Transactions on Image Processing, 14 (2005), 1747-1754.
doi: 10.1109/TIP.2005.857261. |
| [17] |
U. Ghaneka, A. K. Singh and and R. Pandey,
A contrast enhancement-based filter for removal of random valued impulse noise, IEEE Signal Processing Letters, 17 (2010), 47-50.
doi: 10.1109/LSP.2009.2032479. |
| [18] |
R. Gonzalez and R. Woods, Digital Image Processing, 2nd edition, Addision-Wesley Publishing Companyl, 2007. |
| [19] |
P. J. Green,
Bayesian reconstructions from emission tomography data using a modified EM algorithm, IEEE Transactions on Medical Imaging, 9 (1990), 84-93.
doi: 10.1109/42.52985. |
| [20] |
H. H. Dam, K. L. Teo and S. Nordebo,
The dual parameterization approach to optimal least square FIR filter design subject to maximum error constraints, IEEE Transactions on Signal Processing, 48 (2000), 2314-2320.
doi: 10.1109/78.852012. |
| [21] |
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. |
| [22] |
S. Z. Li,
On discontinuity-adaptive smoothness priors in computer vision, IEEE Transactions on Pattern Analysis and Machine Intelligence, 17 (1995), 576-586.
doi: 10.1109/34.387504. |
| [23] |
L. Liu, C. P. Chen and Y. Zhou,
A new weighted mean filter with a two-phase detector for removing impulse noise, Information Sciences, 315 (2015), 1-16.
doi: 10.1016/j.ins.2015.03.067. |
| [24] |
W. Luo,
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.
doi: 10.1093/ietfec/e88-a.10.2579. |
| [25] |
M. Nikolova,
A variational approach to remove outliers and impulse noise, Journal of Mathematical Imaging and Vision, 20 (2004), 99-120.
doi: 10.1023/B:JMIV.0000011920.58935.9c. |
| [26] |
W. K. Pratt, Median Filtering, Image Proc Institute, University of Southern California, Los Angeles, Tech. Rep., 1975. |
| [27] |
F. Russo,
Hybrid neuro-fuzzy filter for impulse noise removal, Pattern Recognition, 32 (1999), 1843-1855.
doi: 10.1016/S0031-3203(99)00009-6. |
| [28] |
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. |
| [29] |
K. Toh and N. Isa,
Cluster-based adaptive fuzzy switching median filter for universal impulse noise reduction, IEEE Transactions on Consumer Electronics, 56 (2010), 2560-2568.
doi: 10.1109/TCE.2010.5681141. |
| [30] |
D. Van De Ville, M. Nachtegael and D. Van der Weken,
Noise reduction by fuzzy image filtering, IEEE Transactions on Fuzzy Systems, 11 (2003), 429-436.
doi: 10.1109/TFUZZ.2003.814830. |
| [31] |
C. R. Vogel and M. E. Oman,
Fast, robust total variation-based reconstruction of noisy, blurred images, IEEE Transactions on Image Processing, 7 (1998), 813-824.
doi: 10.1109/83.679423. |
| [32] |
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. |
| [33] |
H. Xu, G. Zhu and H. Peng,
Adaptive fuzzy switching filter for images corrupted by impulse noise, Pattern Recognition Letters, 25 (2004), 1657-1663.
doi: 10.1016/j.patrec.2004.05.025. |
| [34] |
M. E. Yüksel and A. Baştürk,
A simple generalized neuro-fuzzy operator for efficient removal of impulse noise from highly corrupted digital images, AEU -International Journal of Electronics and Communications, 5 (1996), 1012-1025.
doi: 10.1016/j.aeue.2004.10.002. |
| [35] |
M. E. Yüksel,
A hybrid neuro-fuzzy filter for edge preserving restoration of images corrupted by impulse noise, IEEE Transactions on Image Processing, 15 (2006), 928-936.
doi: 10.1109/TIP.2005.863941. |
| [36] |
X.-Y. Zeng and L.-H. Yang,
Mixed impulse and gaussian noise removal using detail-preserving regularization, Optical Engineering, 49 (2010), 097002-097002.
doi: 10.1117/1.3485756. |
Figure 2.
Directions and hops
Figure 3.
The mean PSNR values associated with different $\alpha$ values
Figure 4.
Total error detection
Figure 5.
Results obtained by different algorithms for restoring the test lena image corrupted by random-valued impulse noise with 40 % noise density. (a) Noisy image, (b) ACWM, (c) Luo's method, (d) ASWM, (e) DWM, (f) ROAD-Trilateral, (g) ROR-NLM, (h) ROLD-EPR, (i) Proposed Method.
Figure 6.
Run time of detection vs. removal noises with different density
Figure 7.
Run time of detection vs. removal noises with different scale image
| | |
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| | |
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Table 2.
Comparison of noise detection results for image "Lena" with various ratios of random-valued impulse noise
| Method | 40% | 50% | 60% | ||||||
| Miss | False-hit | Total | Miss | False-hit | Total | Miss | False-hit | Total | |
| ACWM[13] | 14249 | 1928 | 16177 | 20596 | 3602 | 24198 | 31165 | 6668 | 37833 |
| Luo[24] | 14365 | 1713 | 16078 | 20596 | 2135 | 22371 | 33374 | 2886 | 36260 |
| CEF[17] | 14727 | 6141 | 20868 | 17490 | 7745 | 25235 | 21314 | 8657 | 29971 |
| ASWM[2] | 7381 | 11042 | 18423 | 10614 | 12050 | 22664 | 19577 | 16845 | 36422 |
| DWM[15] | 11600 | 7937 | 19537 | 15035 | 8652 | 23687 | 15373 | 14215 | 29588 |
| ROR-NLM[32] | 12443 | 3056 | 15499 | 15778 | 3655 | 19433 | 21601 | 5917 | 27518 |
| ROAD[16] | 13476 | 8079 | 21555 | 13771 | 10055 | 23826 | 17212 | 9330 | 26542 |
| ROLD[14] | 13987 | 7471 | 21458 | 16331 | 7875 | 24206 | 17245 | 9223 | 26468 |
| Proposed | 10158 | 5234 | 15392 | 11302 | 6583 | 17885 | 15234 | 7623 | 22857 |
| Method | 40% | 50% | 60% | ||||||
| Miss | False-hit | Total | Miss | False-hit | Total | Miss | False-hit | Total | |
| ACWM[13] | 14249 | 1928 | 16177 | 20596 | 3602 | 24198 | 31165 | 6668 | 37833 |
| Luo[24] | 14365 | 1713 | 16078 | 20596 | 2135 | 22371 | 33374 | 2886 | 36260 |
| CEF[17] | 14727 | 6141 | 20868 | 17490 | 7745 | 25235 | 21314 | 8657 | 29971 |
| ASWM[2] | 7381 | 11042 | 18423 | 10614 | 12050 | 22664 | 19577 | 16845 | 36422 |
| DWM[15] | 11600 | 7937 | 19537 | 15035 | 8652 | 23687 | 15373 | 14215 | 29588 |
| ROR-NLM[32] | 12443 | 3056 | 15499 | 15778 | 3655 | 19433 | 21601 | 5917 | 27518 |
| ROAD[16] | 13476 | 8079 | 21555 | 13771 | 10055 | 23826 | 17212 | 9330 | 26542 |
| ROLD[14] | 13987 | 7471 | 21458 | 16331 | 7875 | 24206 | 17245 | 9223 | 26468 |
| Proposed | 10158 | 5234 | 15392 | 11302 | 6583 | 17885 | 15234 | 7623 | 22857 |
Table 3.
Comparison of restoration results in PSNR for images corrupted with random-valued impulse noise
| Method | "Lena" image | "Bridge" image | "Pentagon" image | ||||||
| 40 % | 50 % | 60 % | 40 % | 50 % | 60 % | 40 % | 50 % | 60 % | |
| ACWM[13] | 29.58 | 24.63 | 20.40 | 23.52 | 21.41 | 19.12 | 27.09 | 25.47 | 23.41 |
| Luo[24] | 30.77 | 27.16 | 22.62 | 23.59 | 21.62 | 19.17 | 27.00 | 25.33 | 22.78 |
| CEF[17] | 32.11 | 29.76 | 25.90 | 23.85 | 22.79 | 21.41 | 27.16 | 26.24 | 25.12 |
| ASWM[2] | 32.29 | 29.23 | 25.04 | 23.97 | 22.58 | 21.11 | 27.29 | 26.20 | 24.98 |
| DWM[15] | 32.34 | 29.32 | 25.49 | 24.07 | 22.58 | 21.13 | 27.23 | 26.07 | 25.03 |
| ROR-NLM[32] | 32.97 | 30.02 | 25.60 | 24.18 | 22.84 | 21.19 | 27.68 | 26.56 | 25.36 |
| ROAD[16] | 32.07 | 30.24 | 27.42 | 23.73 | 23.09 | 21.88 | 26.61 | 25.92 | 24.82 |
| ROLD[14] | 32.75 | 31.12 | 28.98 | 24.51 | 23.51 | 22.52 | 27.58 | 26.65 | 25.61 |
| Proposed | 33.62 | 31.73 | 29.56 | 24.98 | 23.82 | 22.79 | 27.92 | 26.98 | 25.93 |
| Method | "Lena" image | "Bridge" image | "Pentagon" image | ||||||
| 40 % | 50 % | 60 % | 40 % | 50 % | 60 % | 40 % | 50 % | 60 % | |
| ACWM[13] | 29.58 | 24.63 | 20.40 | 23.52 | 21.41 | 19.12 | 27.09 | 25.47 | 23.41 |
| Luo[24] | 30.77 | 27.16 | 22.62 | 23.59 | 21.62 | 19.17 | 27.00 | 25.33 | 22.78 |
| CEF[17] | 32.11 | 29.76 | 25.90 | 23.85 | 22.79 | 21.41 | 27.16 | 26.24 | 25.12 |
| ASWM[2] | 32.29 | 29.23 | 25.04 | 23.97 | 22.58 | 21.11 | 27.29 | 26.20 | 24.98 |
| DWM[15] | 32.34 | 29.32 | 25.49 | 24.07 | 22.58 | 21.13 | 27.23 | 26.07 | 25.03 |
| ROR-NLM[32] | 32.97 | 30.02 | 25.60 | 24.18 | 22.84 | 21.19 | 27.68 | 26.56 | 25.36 |
| ROAD[16] | 32.07 | 30.24 | 27.42 | 23.73 | 23.09 | 21.88 | 26.61 | 25.92 | 24.82 |
| ROLD[14] | 32.75 | 31.12 | 28.98 | 24.51 | 23.51 | 22.52 | 27.58 | 26.65 | 25.61 |
| Proposed | 33.62 | 31.73 | 29.56 | 24.98 | 23.82 | 22.79 | 27.92 | 26.98 | 25.93 |
Table 4.
Run time of detection vs. removal noises with different density
| Noise Density | Run Time(s) | ||
| Detection | Removal | Total | |
| 30 % | 4.72 | 34.69 | 39.41 |
| 40 % | 4.83 | 73.30 | 78.13 |
| 50 % | 4.67 | 163.53 | 168.20 |
| 60 % | 4.65 | 239.58 | 244.23 |
| 70 % | 4.87 | 271.64 | 276.51 |
| Noise Density | Run Time(s) | ||
| Detection | Removal | Total | |
| 30 % | 4.72 | 34.69 | 39.41 |
| 40 % | 4.83 | 73.30 | 78.13 |
| 50 % | 4.67 | 163.53 | 168.20 |
| 60 % | 4.65 | 239.58 | 244.23 |
| 70 % | 4.87 | 271.64 | 276.51 |
Table 5.
Run time of detection vs. removal noises with different scale image
| Image Scale | Run Time(s) | |
| Detection | Removal | |
| 64×64 | 0.38 | 5.5 |
| 128× 128 | 1.13 | 14.28 |
| 256×256 | 4.27 | 34.69 |
| 512×512 | 17.19 | 111.64 |
| Image Scale | Run Time(s) | |
| Detection | Removal | |
| 64×64 | 0.38 | 5.5 |
| 128× 128 | 1.13 | 14.28 |
| 256×256 | 4.27 | 34.69 |
| 512×512 | 17.19 | 111.64 |
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