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A new variational approach based on level-set function for convex hull problem with outliers
Bilinear constraint based ADMM for mixed Poisson-Gaussian noise removal
1. | School of Mathematical Sciences, Tianjin Normal University, Tianjin, 300387, China |
2. | Department of Mathematics, The University of Hong Kong, Pokfulam, Hong Kong |
3. | Center for Applied Mathematics, Tianjin University, Tianjin, 300072, China |
In this paper, we propose new operator-splitting algorithms for the total variation regularized infimal convolution (TV-IC) model [
References:
[1] |
B. Begovic, V. Stankovic and L. Stankovic, Contrast enhancement and denoising of Poisson and Gaussian mixture noise for solar images, 18th IEEE International Conference on Image Processing (ICIP), Brussels, Belgium, 2011, 185-188.
doi: 10.1109/ICIP.2011.6115829. |
[2] |
F. Benvenuto, A. L. Camera, C. Theys, A. Ferrari, H. Lantéri and M. Bertero, The study of an iterative method for the reconstruction of images corrupted by Poisson and Gaussian noise, Inverse Problems, 24 (2008), 035016, 20pp.
doi: 10.1088/0266-5611/24/3/035016. |
[3] |
S. Boyd, N. Parikh, E. Chu, B. Peleato and J. Eckstein,
Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers, Found. Trends Mach. Learn., 3 (2011), 1-122.
doi: 10.1561/9781601984616. |
[4] |
L. Calatroni, C. Cao, J. D. L. Reyes, C. Schönlieb and T. Valkonen, Bilevel approaches for learning of variational imaging models, Variational Methods, 252-290, Radon Ser. Comput. Appl. Math., 18, De Gruyter, Berlin, 2017. |
[5] |
L. Calatroni and K. Papafitsoros, Analysis and automatic parameter selection of a variational model for mixed Gaussian and salt-and-pepper noise removal, Inverse Problems, 35 (2019), 114001, 37pp.
doi: 10.1088/1361-6420/ab291a. |
[6] |
L. Calatroni, J. D. L. Reyes and C. Schönlieb,
Infimal convolution of data discrepancies for mixed noise removal, SIAM Journal on Imaging Sciences, 10 (2017), 1196-1233.
doi: 10.1137/16M1101684. |
[7] |
A. Chakrabarti and T. E. Zickler, Image restoration with signal-dependent Camera noise, preprint, arXiv: 1204.2994. |
[8] |
A. Chambolle,
An algorithm for total variation minimization and applications, J. Math. Imaging Vis., 20 (2004), 89-97.
|
[9] |
H. Chang, P. Enfedaque and S. Marchesini,
Blind ptychographic phase retrieval via convergent alternating direction method of multipliers, SIAM Journal on Imaging Sciences, 12 (2019), 153-185.
doi: 10.1137/18M1188446. |
[10] |
C. Chen, B. He, Y. Ye and X. Yuan,
The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent, Mathematical Programming, 155 (2016), 57-79.
doi: 10.1007/s10107-014-0826-5. |
[11] |
E. Chouzenoux, A. Jezierska, J. Pesquet and H. Talbot,
A convex approach for image restoration with exact poisson-gaussian likelihood, SIAM J. Imaging Sciences, 8 (2015), 2662-2682.
doi: 10.1137/15M1014395. |
[12] |
W. Deng, M. Lai, Z. Peng and W. Yin,
Parallel multi-block ADMM with O (1/k) convergence, Journal of Scientific Computing, 71 (2017), 712-736.
doi: 10.1007/s10915-016-0318-2. |
[13] |
Q. Ding and Y. Long and X. Zhang and J. A. Fessler, Statistical image reconstruction using mixed poisson-gaussian noise model for X-ray CT, preprint, arXiv: 1801.09533. |
[14] |
J. Eckstein and D. P. Bertsekas,
On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators, Mathematical Programming, 55 (1992), 293-318.
doi: 10.1007/BF01581204. |
[15] |
A. Foi, M. Trimeche, V. Katkovnik and K. Egiazarian,
Practical poissonian-gaussian noise modeling and fitting for single-image raw-data, IEEE Transactions on Image Processing, 17 (2008), 1737-1754.
doi: 10.1109/TIP.2008.2001399. |
[16] |
D. Gabay and B. Mercier,
A dual algorithm for the solution of nonlinear variational problems via finite element approximation, Computers & Mathematics with Applications, 2 (1976), 17-40.
doi: 10.1016/0898-1221(76)90003-1. |
[17] |
R. Glowinski and A. Marroco, Sur l'approximation, par éléments finis d'ordre un, et la résolution, par pénalisation-dualité d'une classe de problèmes de Dirichlet non linéaires, Revue Française D'automatique, Informatique, Recherche Opérationnelle. Analyse Numérique, 9 (1975), 41-76.
doi: 10.1051/m2an/197509R200411. |
[18] |
D. Hajinezhad and Q. Shi,
Alternating direction method of multipliers for a class of nonconvex bilinear optimization: convergence analysis and applications, Journal of Global Optimization, 70 (2018), 261-288.
doi: 10.1007/s10898-017-0594-x. |
[19] |
M. Hong, Z. Luo and M. Razaviyayn,
Convergence analysis of alternating direction method of multipliers for a family of nonconvex problems, SIAM Journal on Optimization, 26 (2016), 337-364.
doi: 10.1137/140990309. |
[20] |
P. J. Huber,
Robust Estimation of a Location Parameter, The Annals of Mathematical Statistics, 35 (1964), 73-101.
doi: 10.1214/aoms/1177703732. |
[21] |
A. Jezierska, C. Chaux, J. Pesquet and H. Talbot, An EM approach for Poisson-Gaussian noise modeling, 19th European Signal Processing Conference (EUSIPCO), Barcelona, Spain, 2011, 2244-2248. |
[22] |
A. Lanza, S. Morigi, F. Sgallari and Y. Wen,
Image restoration with Poisson-Gaussian mixed noise, Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization, 2 (2014), 12-24.
doi: 10.1080/21681163.2013.811039. |
[23] |
T. Le, R. Chartrand and T. Asaki,
A variational approach to reconstructing images corrupted by poisson noise, Journal of Mathematical Imaging and Vision, 27 (2007), 257-263.
doi: 10.1007/s10851-007-0652-y. |
[24] |
J. Li, Z. Shen, R. Yin and X. Zhang,
A reweighted $L^2$ method for image restoration with Poisson and mixed Poisson-Gaussian noise, Inverse Problems & Imaging, 9 (2015), 875-894.
doi: 10.3934/ipi.2015.9.875. |
[25] |
T. Lin, S. Ma and S. Zhang,
On the global linear convergence of the admm with multiblock variables, SIAM Journal on Optimization, 25 (2015), 1478-1497.
doi: 10.1137/140971178. |
[26] |
Y. Lou and M. Yan,
Fast L1-L2 minimization via a proximal operator, Journal of Scientific Computing, 74 (2018), 767-785.
doi: 10.1007/s10915-017-0463-2. |
[27] |
M. Mäkitalo and A. Foi,
Optimal inversion of the generalized Anscombe transformation for Poisson-Gaussian noise, IEEE Transactions on Image Processing, 22 (2013), 91-103.
doi: 10.1109/TIP.2012.2202675. |
[28] |
Y. Marnissi, Y. Zheng and J. Pesquet, Fast variational Bayesian signal recovery in the presence of Poisson-Gaussian noise, IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Shanghai, China, 2016, 3964-3968.
doi: 10.1109/ICASSP.2016.7472421. |
[29] |
J. Mei, Y. Dong, T. Huang and W. Yin,
Cauchy noise removal by nonconvex ADMM with convergence guarantees, Journal of Scientific Computing, 74 (2018), 743-766.
doi: 10.1007/s10915-017-0460-5. |
[30] |
F. Murtagh, J.-L Starck and A. Bijaoui,
Image restoration with noise suppression using a multiresolution support, Astronomy & Astrophysics, Suppl. Ser, 112 (1995), 179-189.
|
[31] |
B. O' Donoghue, G. Stathopoulos and S. Boyd,
A splitting method for optimal control, IEEE Transactions on Control Systems Technology, 21 (2013), 2432-2442.
|
[32] |
C. T. Pham, G. Gamard, A. Kopylov and T. Tran,
An algorithm for image restoration with mixed noise using total variation regularization, Turkish Journal of Electrical Engineering & Computer Sciences, 26 (2018), 2832-2846.
doi: 10.3906/elk-1803-100. |
[33] |
J. D. L. Reyes and C. Schönlieb,
Image denoising: Learning the noise model via nonsmooth PDE-constrained optimization, Inverse Problems & Imaging, 7 (2013), 1183-1214.
doi: 10.3934/ipi.2013.7.1183. |
[34] |
L. Rudin, S. Osher and E. Fatemi,
Nonlinear total variation based noise removal algorithms, Physica. D, 60 (1992), 259-268.
doi: 10.1016/0167-2789(92)90242-F. |
[35] |
J.-L. Starck, F. Murtagh and A. Bijaoui, Image Processing and Data Analysis: The Multiscale Approach, Cambridge University Press, New York, USA, 1998.
doi: 10.1017/CBO9780511564352.![]() ![]() ![]() |
[36] |
D. N. H. Thanh and S. D. Dvoenko,
A method of total variation to remove the mixed Poisson-Gaussian noise, Pattern Recognition and Image Analysis, 26 (2016), 285-293.
doi: 10.1134/S1054661816020231. |
[37] |
Y. Wang, W. Yin and J. Zeng,
Global convergence of ADMM in nonconvex nonsmooth optimization, Journal of Scientific Computing, 78 (2019), 29-63.
doi: 10.1007/s10915-018-0757-z. |
[38] |
Z. Wang, A. C. Bovik, H. R. Sheikh and E. P. Simoncelli,
Image quality assessment: From error visibility to structural similarity, IEEE Transactions on Image Processing, 13 (2004), 600-612.
doi: 10.1109/TIP.2003.819861. |
[39] |
C. Wu and X. Tai,
Augmented Lagrangian method, dual methods, and split Bregman iteration for ROF, vectorial TV, and high order models, SIAM Journal on Imaging Sciences, 3 (2010), 300-339.
doi: 10.1137/090767558. |
[40] |
C. Wu, J. Zhang and X. Tai,
Augmented Lagrangian method for total variation restoration with non-quadratic fidelity, Inverse Problems & Imaging, 5 (2011), 237-261.
doi: 10.3934/ipi.2011.5.237. |
show all references
References:
[1] |
B. Begovic, V. Stankovic and L. Stankovic, Contrast enhancement and denoising of Poisson and Gaussian mixture noise for solar images, 18th IEEE International Conference on Image Processing (ICIP), Brussels, Belgium, 2011, 185-188.
doi: 10.1109/ICIP.2011.6115829. |
[2] |
F. Benvenuto, A. L. Camera, C. Theys, A. Ferrari, H. Lantéri and M. Bertero, The study of an iterative method for the reconstruction of images corrupted by Poisson and Gaussian noise, Inverse Problems, 24 (2008), 035016, 20pp.
doi: 10.1088/0266-5611/24/3/035016. |
[3] |
S. Boyd, N. Parikh, E. Chu, B. Peleato and J. Eckstein,
Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers, Found. Trends Mach. Learn., 3 (2011), 1-122.
doi: 10.1561/9781601984616. |
[4] |
L. Calatroni, C. Cao, J. D. L. Reyes, C. Schönlieb and T. Valkonen, Bilevel approaches for learning of variational imaging models, Variational Methods, 252-290, Radon Ser. Comput. Appl. Math., 18, De Gruyter, Berlin, 2017. |
[5] |
L. Calatroni and K. Papafitsoros, Analysis and automatic parameter selection of a variational model for mixed Gaussian and salt-and-pepper noise removal, Inverse Problems, 35 (2019), 114001, 37pp.
doi: 10.1088/1361-6420/ab291a. |
[6] |
L. Calatroni, J. D. L. Reyes and C. Schönlieb,
Infimal convolution of data discrepancies for mixed noise removal, SIAM Journal on Imaging Sciences, 10 (2017), 1196-1233.
doi: 10.1137/16M1101684. |
[7] |
A. Chakrabarti and T. E. Zickler, Image restoration with signal-dependent Camera noise, preprint, arXiv: 1204.2994. |
[8] |
A. Chambolle,
An algorithm for total variation minimization and applications, J. Math. Imaging Vis., 20 (2004), 89-97.
|
[9] |
H. Chang, P. Enfedaque and S. Marchesini,
Blind ptychographic phase retrieval via convergent alternating direction method of multipliers, SIAM Journal on Imaging Sciences, 12 (2019), 153-185.
doi: 10.1137/18M1188446. |
[10] |
C. Chen, B. He, Y. Ye and X. Yuan,
The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent, Mathematical Programming, 155 (2016), 57-79.
doi: 10.1007/s10107-014-0826-5. |
[11] |
E. Chouzenoux, A. Jezierska, J. Pesquet and H. Talbot,
A convex approach for image restoration with exact poisson-gaussian likelihood, SIAM J. Imaging Sciences, 8 (2015), 2662-2682.
doi: 10.1137/15M1014395. |
[12] |
W. Deng, M. Lai, Z. Peng and W. Yin,
Parallel multi-block ADMM with O (1/k) convergence, Journal of Scientific Computing, 71 (2017), 712-736.
doi: 10.1007/s10915-016-0318-2. |
[13] |
Q. Ding and Y. Long and X. Zhang and J. A. Fessler, Statistical image reconstruction using mixed poisson-gaussian noise model for X-ray CT, preprint, arXiv: 1801.09533. |
[14] |
J. Eckstein and D. P. Bertsekas,
On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators, Mathematical Programming, 55 (1992), 293-318.
doi: 10.1007/BF01581204. |
[15] |
A. Foi, M. Trimeche, V. Katkovnik and K. Egiazarian,
Practical poissonian-gaussian noise modeling and fitting for single-image raw-data, IEEE Transactions on Image Processing, 17 (2008), 1737-1754.
doi: 10.1109/TIP.2008.2001399. |
[16] |
D. Gabay and B. Mercier,
A dual algorithm for the solution of nonlinear variational problems via finite element approximation, Computers & Mathematics with Applications, 2 (1976), 17-40.
doi: 10.1016/0898-1221(76)90003-1. |
[17] |
R. Glowinski and A. Marroco, Sur l'approximation, par éléments finis d'ordre un, et la résolution, par pénalisation-dualité d'une classe de problèmes de Dirichlet non linéaires, Revue Française D'automatique, Informatique, Recherche Opérationnelle. Analyse Numérique, 9 (1975), 41-76.
doi: 10.1051/m2an/197509R200411. |
[18] |
D. Hajinezhad and Q. Shi,
Alternating direction method of multipliers for a class of nonconvex bilinear optimization: convergence analysis and applications, Journal of Global Optimization, 70 (2018), 261-288.
doi: 10.1007/s10898-017-0594-x. |
[19] |
M. Hong, Z. Luo and M. Razaviyayn,
Convergence analysis of alternating direction method of multipliers for a family of nonconvex problems, SIAM Journal on Optimization, 26 (2016), 337-364.
doi: 10.1137/140990309. |
[20] |
P. J. Huber,
Robust Estimation of a Location Parameter, The Annals of Mathematical Statistics, 35 (1964), 73-101.
doi: 10.1214/aoms/1177703732. |
[21] |
A. Jezierska, C. Chaux, J. Pesquet and H. Talbot, An EM approach for Poisson-Gaussian noise modeling, 19th European Signal Processing Conference (EUSIPCO), Barcelona, Spain, 2011, 2244-2248. |
[22] |
A. Lanza, S. Morigi, F. Sgallari and Y. Wen,
Image restoration with Poisson-Gaussian mixed noise, Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization, 2 (2014), 12-24.
doi: 10.1080/21681163.2013.811039. |
[23] |
T. Le, R. Chartrand and T. Asaki,
A variational approach to reconstructing images corrupted by poisson noise, Journal of Mathematical Imaging and Vision, 27 (2007), 257-263.
doi: 10.1007/s10851-007-0652-y. |
[24] |
J. Li, Z. Shen, R. Yin and X. Zhang,
A reweighted $L^2$ method for image restoration with Poisson and mixed Poisson-Gaussian noise, Inverse Problems & Imaging, 9 (2015), 875-894.
doi: 10.3934/ipi.2015.9.875. |
[25] |
T. Lin, S. Ma and S. Zhang,
On the global linear convergence of the admm with multiblock variables, SIAM Journal on Optimization, 25 (2015), 1478-1497.
doi: 10.1137/140971178. |
[26] |
Y. Lou and M. Yan,
Fast L1-L2 minimization via a proximal operator, Journal of Scientific Computing, 74 (2018), 767-785.
doi: 10.1007/s10915-017-0463-2. |
[27] |
M. Mäkitalo and A. Foi,
Optimal inversion of the generalized Anscombe transformation for Poisson-Gaussian noise, IEEE Transactions on Image Processing, 22 (2013), 91-103.
doi: 10.1109/TIP.2012.2202675. |
[28] |
Y. Marnissi, Y. Zheng and J. Pesquet, Fast variational Bayesian signal recovery in the presence of Poisson-Gaussian noise, IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Shanghai, China, 2016, 3964-3968.
doi: 10.1109/ICASSP.2016.7472421. |
[29] |
J. Mei, Y. Dong, T. Huang and W. Yin,
Cauchy noise removal by nonconvex ADMM with convergence guarantees, Journal of Scientific Computing, 74 (2018), 743-766.
doi: 10.1007/s10915-017-0460-5. |
[30] |
F. Murtagh, J.-L Starck and A. Bijaoui,
Image restoration with noise suppression using a multiresolution support, Astronomy & Astrophysics, Suppl. Ser, 112 (1995), 179-189.
|
[31] |
B. O' Donoghue, G. Stathopoulos and S. Boyd,
A splitting method for optimal control, IEEE Transactions on Control Systems Technology, 21 (2013), 2432-2442.
|
[32] |
C. T. Pham, G. Gamard, A. Kopylov and T. Tran,
An algorithm for image restoration with mixed noise using total variation regularization, Turkish Journal of Electrical Engineering & Computer Sciences, 26 (2018), 2832-2846.
doi: 10.3906/elk-1803-100. |
[33] |
J. D. L. Reyes and C. Schönlieb,
Image denoising: Learning the noise model via nonsmooth PDE-constrained optimization, Inverse Problems & Imaging, 7 (2013), 1183-1214.
doi: 10.3934/ipi.2013.7.1183. |
[34] |
L. Rudin, S. Osher and E. Fatemi,
Nonlinear total variation based noise removal algorithms, Physica. D, 60 (1992), 259-268.
doi: 10.1016/0167-2789(92)90242-F. |
[35] |
J.-L. Starck, F. Murtagh and A. Bijaoui, Image Processing and Data Analysis: The Multiscale Approach, Cambridge University Press, New York, USA, 1998.
doi: 10.1017/CBO9780511564352.![]() ![]() ![]() |
[36] |
D. N. H. Thanh and S. D. Dvoenko,
A method of total variation to remove the mixed Poisson-Gaussian noise, Pattern Recognition and Image Analysis, 26 (2016), 285-293.
doi: 10.1134/S1054661816020231. |
[37] |
Y. Wang, W. Yin and J. Zeng,
Global convergence of ADMM in nonconvex nonsmooth optimization, Journal of Scientific Computing, 78 (2019), 29-63.
doi: 10.1007/s10915-018-0757-z. |
[38] |
Z. Wang, A. C. Bovik, H. R. Sheikh and E. P. Simoncelli,
Image quality assessment: From error visibility to structural similarity, IEEE Transactions on Image Processing, 13 (2004), 600-612.
doi: 10.1109/TIP.2003.819861. |
[39] |
C. Wu and X. Tai,
Augmented Lagrangian method, dual methods, and split Bregman iteration for ROF, vectorial TV, and high order models, SIAM Journal on Imaging Sciences, 3 (2010), 300-339.
doi: 10.1137/090767558. |
[40] |
C. Wu, J. Zhang and X. Tai,
Augmented Lagrangian method for total variation restoration with non-quadratic fidelity, Inverse Problems & Imaging, 5 (2011), 237-261.
doi: 10.3934/ipi.2011.5.237. |













1 | 2 | 5 | 10 | 20 | 100 | ||
1 | 15.20 | 18.08 | 17.57 | 18.16 | 18.17 | 18.17 | |
1 | 16.20 | 18.39 | 16.35 | 18.40 | 18.40 | 18.40 | |
4 | 19.92 | 21.92 | 21.90 | 21.98 | 21.97 | 21.98 | |
4 | 20.05 | 22.37 | 22.36 | 22.47 | 22.48 | 22.49 | |
16 | 22.50 | 25.17 | 25.27 | 25.28 | 25.26 | 25.28 | |
16 | 23.59 | 26.17 | 26.40 | 26.37 | 26.38 | 26.40 |
1 | 2 | 5 | 10 | 20 | 100 | ||
1 | 15.20 | 18.08 | 17.57 | 18.16 | 18.17 | 18.17 | |
1 | 16.20 | 18.39 | 16.35 | 18.40 | 18.40 | 18.40 | |
4 | 19.92 | 21.92 | 21.90 | 21.98 | 21.97 | 21.98 | |
4 | 20.05 | 22.37 | 22.36 | 22.47 | 22.48 | 22.49 | |
16 | 22.50 | 25.17 | 25.27 | 25.28 | 25.26 | 25.28 | |
16 | 23.59 | 26.17 | 26.40 | 26.37 | 26.38 | 26.40 |
Image | Noisy | TV+ |
TV+KL | TV+EPG | TV+SP | TV+KL+ |
TV+PD | BCA | BCA |
||
Circle | 1 | 2.50 | 17.21 | 16.68 | 17.07 | 16.76 | 17.28 | 17.44 | 17.84 | 17.97 | |
0.0452 | 0.6147 | 0.4044 | 0.6580 | 0.4059 | 0.3975 | 0.7544 | 0.7125 | 0.9007 | |||
1 | 2.57 | 17.34 | 17.16 | 17.11 | 17.24 | 17.76 | 17.00 | 18.02 | 18.10 | ||
0.5494 | 0.6087 | 0.7997 | 0.7740 | 0.8678 | 0.8251 | 0.8711 | 0.8913 | 0.9029 | |||
4 | 5.92 | 21.48 | 20.44 | 20.74 | 20.77 | 21.29 | 21.64 | 22.01 | 21.78 | ||
0.0687 | 0.7149 | 0.4763 | 0.6260 | 0.5305 | 0.5259 | 0.9216 | 0.7153 | 0.9357 | |||
4 | 6.32 | 21.64 | 21.83 | 21.14 | 21.83 | 22.00 | 22.16 | 22.18 | 22.35 | ||
0.5793 | 0.7397 | 0.9385 | 0.9395 | 0.9385 | 0.9299 | 0.9466 | 0.9472 | 0.9180 | |||
16 | 9.88 | 24.64 | 22.33 | 22.54 | 22.62 | 23.89 | 23.54 | 25.28 | 25.04 | ||
0.0971 | 0.8411 | 0.5088 | 0.5315 | 0.5436 | 0.5438 | 0.8141 | 0.9697 | 0.8079 | |||
16 | 11.55 | 25.46 | 26.41 | 25.14 | 26.41 | 26.46 | 26.47 | 26.37 | 27.12 | ||
0.6149 | 0.8816 | 0.9500 | 0.9447 | 0.9500 | 0.9594 | 0.9651 | 0.9676 | 0.9168 | |||
Average | 6.46 | 21.30 | 20.81 | 20.62 | 20.94 | 21.45 | 21.38 | 21.95 | 22.06 | ||
0.3258 | 0.7335 | 0.6796 | 0.745 | 0.7061 | 0.6969 | 0.8788 | 0.8673 | 0.8970 | |||
Fluorescent Cells | 1 | 1.16 | 9.88 | 9.72 | 9.29 | 9.72 | 9.96 | 9.48 | 10.37 | 10.33 | |
0.0402 | 0.4861 | 0.4508 | 0.3149 | 0.4532 | 0.4512 | 0.4572 | 0.5026 | 0.4971 | |||
1 | 1.22 | 9.97 | 9.83 | 9.46 | 9.83 | 9.98 | 9.79 | 10.43 | 10.41 | ||
0.0598 | 0.5058 | 0.4954 | 0.3289 | 0.4954 | 0.5003 | 0.4471 | 0.5108 | 0.5014 | |||
4 | 3.14 | 11.10 | 11.58 | 11.12 | 11.54 | 11.75 | 11.62 | 11.66 | 12.06 | ||
0.1181 | 0.5554 | 0.5369 | 0.5093 | 0.5239 | 0.5588 | 0.5674 | 0.5753 | 0.5801 | |||
4 | 3.59 | 11.25 | 11.88 | 11.32 | 11.88 | 12.17 | 11.88 | 11.96 | 12.38 | ||
0.1680 | 0.5765 | 0.6078 | 0.4593 | 0.6078 | 0.6133 | 0.5531 | 0.6160 | 0.6139 | |||
16 | 5.77 | 13.43 | 12.66 | 12.52 | 12.64 | 13.27 | 13.45 | 13.37 | 13.50 | ||
0.2282 | 0.6424 | 0.5998 | 0.5271 | 0.5989 | 0.6383 | 0.6669 | 0.6557 | 0.6685 | |||
16 | 7.87 | 14.17 | 14.16 | 14.30 | 14.16 | 14.59 | 14.47 | 14.42 | 14.62 | ||
0.4003 | 0.7360 | 0.7228 | 0.6895 | 0.7228 | 0.7388 | 0.7309 | 0.7379 | 0.7368 | |||
Average | 3.79 | 11.63 | 11.64 | 11.34 | 11.63 | 11.95 | 11.78 | 12.04 | 12.22 | ||
0.1691 | 0.5837 | 0.5689 | 0.4710 | 0.5670 | 0.5835 | 0.5704 | 0.5997 | 0.5996 | |||
Cameraman | 1 | 1.97 | 13.06 | 14.25 | 13.13 | 14.19 | 14.30 | 14.30 | 14.59 | 14.56 | |
0.0496 | 0.4167 | 0.5498 | 0.3452 | 0.5322 | 0.5432 | 0.5524 | 0.5633 | 0.5644 | |||
1 | 2.00 | 13.09 | 14.36 | 13.04 | 14.36 | 14.40 | 14.33 | 14.57 | 14.52 | ||
0.0628 | 0.4238 | 0.4602 | 0.3342 | 0.4602 | 0.4760 | 0.4362 | 0.5854 | 0.5659 | |||
4 | 5.02 | 15.66 | 16.46 | 15.5 | 16.43 | 16.56 | 16.17 | 16.79 | 16.83 | ||
0.1178 | 0.5729 | 0.6552 | 0.4863 | 0.6540 | 0.6720 | 0.6422 | 0.6417 | 0.6655 | |||
4 | 5.28 | 15.81 | 16.27 | 15.64 | 16.27 | 16.47 | 16.14 | 16.99 | 17.00 | ||
0.1514 | 0.5879 | 0.6301 | 0.5027 | 0.6301 | 0.6160 | 0.6047 | 0.6697 | 0.6770 | |||
16 | 9.06 | 18.25 | 18.60 | 18.24 | 18.60 | 18.81 | 18.18 | 18.99 | 19.02 | ||
0.1992 | 0.6393 | 0.7126 | 0.6355 | 0.7181 | 0.7163 | 0.6527 | 0.7112 | 0.7214 | |||
16 | 10.24 | 18.88 | 19.44 | 18.83 | 19.44 | 19.64 | 19.59 | 19.81 | 19.53 | ||
0.2920 | 0.6980 | 0.7321 | 0.6616 | 0.7321 | 0.7503 | 0.7317 | 0.7614 | 0.7764 | |||
Average | 5.60 | 15.79 | 16.56 | 15.73 | 16.55 | 16.70 | 16.45 | 16.96 | 16.91 | ||
0.1455 | 0.5564 | 0.6233 | 0.4940 | 0.6211 | 0.6290 | 0.6033 | 0.6555 | 0.6618 |
Image | Noisy | TV+ |
TV+KL | TV+EPG | TV+SP | TV+KL+ |
TV+PD | BCA | BCA |
||
Circle | 1 | 2.50 | 17.21 | 16.68 | 17.07 | 16.76 | 17.28 | 17.44 | 17.84 | 17.97 | |
0.0452 | 0.6147 | 0.4044 | 0.6580 | 0.4059 | 0.3975 | 0.7544 | 0.7125 | 0.9007 | |||
1 | 2.57 | 17.34 | 17.16 | 17.11 | 17.24 | 17.76 | 17.00 | 18.02 | 18.10 | ||
0.5494 | 0.6087 | 0.7997 | 0.7740 | 0.8678 | 0.8251 | 0.8711 | 0.8913 | 0.9029 | |||
4 | 5.92 | 21.48 | 20.44 | 20.74 | 20.77 | 21.29 | 21.64 | 22.01 | 21.78 | ||
0.0687 | 0.7149 | 0.4763 | 0.6260 | 0.5305 | 0.5259 | 0.9216 | 0.7153 | 0.9357 | |||
4 | 6.32 | 21.64 | 21.83 | 21.14 | 21.83 | 22.00 | 22.16 | 22.18 | 22.35 | ||
0.5793 | 0.7397 | 0.9385 | 0.9395 | 0.9385 | 0.9299 | 0.9466 | 0.9472 | 0.9180 | |||
16 | 9.88 | 24.64 | 22.33 | 22.54 | 22.62 | 23.89 | 23.54 | 25.28 | 25.04 | ||
0.0971 | 0.8411 | 0.5088 | 0.5315 | 0.5436 | 0.5438 | 0.8141 | 0.9697 | 0.8079 | |||
16 | 11.55 | 25.46 | 26.41 | 25.14 | 26.41 | 26.46 | 26.47 | 26.37 | 27.12 | ||
0.6149 | 0.8816 | 0.9500 | 0.9447 | 0.9500 | 0.9594 | 0.9651 | 0.9676 | 0.9168 | |||
Average | 6.46 | 21.30 | 20.81 | 20.62 | 20.94 | 21.45 | 21.38 | 21.95 | 22.06 | ||
0.3258 | 0.7335 | 0.6796 | 0.745 | 0.7061 | 0.6969 | 0.8788 | 0.8673 | 0.8970 | |||
Fluorescent Cells | 1 | 1.16 | 9.88 | 9.72 | 9.29 | 9.72 | 9.96 | 9.48 | 10.37 | 10.33 | |
0.0402 | 0.4861 | 0.4508 | 0.3149 | 0.4532 | 0.4512 | 0.4572 | 0.5026 | 0.4971 | |||
1 | 1.22 | 9.97 | 9.83 | 9.46 | 9.83 | 9.98 | 9.79 | 10.43 | 10.41 | ||
0.0598 | 0.5058 | 0.4954 | 0.3289 | 0.4954 | 0.5003 | 0.4471 | 0.5108 | 0.5014 | |||
4 | 3.14 | 11.10 | 11.58 | 11.12 | 11.54 | 11.75 | 11.62 | 11.66 | 12.06 | ||
0.1181 | 0.5554 | 0.5369 | 0.5093 | 0.5239 | 0.5588 | 0.5674 | 0.5753 | 0.5801 | |||
4 | 3.59 | 11.25 | 11.88 | 11.32 | 11.88 | 12.17 | 11.88 | 11.96 | 12.38 | ||
0.1680 | 0.5765 | 0.6078 | 0.4593 | 0.6078 | 0.6133 | 0.5531 | 0.6160 | 0.6139 | |||
16 | 5.77 | 13.43 | 12.66 | 12.52 | 12.64 | 13.27 | 13.45 | 13.37 | 13.50 | ||
0.2282 | 0.6424 | 0.5998 | 0.5271 | 0.5989 | 0.6383 | 0.6669 | 0.6557 | 0.6685 | |||
16 | 7.87 | 14.17 | 14.16 | 14.30 | 14.16 | 14.59 | 14.47 | 14.42 | 14.62 | ||
0.4003 | 0.7360 | 0.7228 | 0.6895 | 0.7228 | 0.7388 | 0.7309 | 0.7379 | 0.7368 | |||
Average | 3.79 | 11.63 | 11.64 | 11.34 | 11.63 | 11.95 | 11.78 | 12.04 | 12.22 | ||
0.1691 | 0.5837 | 0.5689 | 0.4710 | 0.5670 | 0.5835 | 0.5704 | 0.5997 | 0.5996 | |||
Cameraman | 1 | 1.97 | 13.06 | 14.25 | 13.13 | 14.19 | 14.30 | 14.30 | 14.59 | 14.56 | |
0.0496 | 0.4167 | 0.5498 | 0.3452 | 0.5322 | 0.5432 | 0.5524 | 0.5633 | 0.5644 | |||
1 | 2.00 | 13.09 | 14.36 | 13.04 | 14.36 | 14.40 | 14.33 | 14.57 | 14.52 | ||
0.0628 | 0.4238 | 0.4602 | 0.3342 | 0.4602 | 0.4760 | 0.4362 | 0.5854 | 0.5659 | |||
4 | 5.02 | 15.66 | 16.46 | 15.5 | 16.43 | 16.56 | 16.17 | 16.79 | 16.83 | ||
0.1178 | 0.5729 | 0.6552 | 0.4863 | 0.6540 | 0.6720 | 0.6422 | 0.6417 | 0.6655 | |||
4 | 5.28 | 15.81 | 16.27 | 15.64 | 16.27 | 16.47 | 16.14 | 16.99 | 17.00 | ||
0.1514 | 0.5879 | 0.6301 | 0.5027 | 0.6301 | 0.6160 | 0.6047 | 0.6697 | 0.6770 | |||
16 | 9.06 | 18.25 | 18.60 | 18.24 | 18.60 | 18.81 | 18.18 | 18.99 | 19.02 | ||
0.1992 | 0.6393 | 0.7126 | 0.6355 | 0.7181 | 0.7163 | 0.6527 | 0.7112 | 0.7214 | |||
16 | 10.24 | 18.88 | 19.44 | 18.83 | 19.44 | 19.64 | 19.59 | 19.81 | 19.53 | ||
0.2920 | 0.6980 | 0.7321 | 0.6616 | 0.7321 | 0.7503 | 0.7317 | 0.7614 | 0.7764 | |||
Average | 5.60 | 15.79 | 16.56 | 15.73 | 16.55 | 16.70 | 16.45 | 16.96 | 16.91 | ||
0.1455 | 0.5564 | 0.6233 | 0.4940 | 0.6211 | 0.6290 | 0.6033 | 0.6555 | 0.6618 |
Image | TV+PD | BCA | BCA |
||
Circle | 1 | 40.4971 | 4.6052 | 1.0314 | |
1 | 18.5340 | 4.6922 | 1.2650 | ||
4 | 7.3436 | 0.7641 | 0.7001 | ||
4 | 39.6196 | 1.1891 | 0.6030 | ||
16 | 36.3221 | 1.2652 | 0.4643 | ||
16 | 39.5773 | 0.6123 | 0.3070 | ||
Average | 30.3156 | 2.1880 | 0.7285 | ||
Fluorescent Cells | 1 | 21.7999 | 8.3016 | 2.1735 | |
1 | 41.6892 | 8.9243 | 2.5687 | ||
4 | 40.1406 | 4.1263 | 2.4025 | ||
4 | 38.6224 | 3.8464 | 2.0889 | ||
16 | 37.7174 | 7.3265 | 6.1742 | ||
16 | 7.7788 | 7.6185 | 1.1258 | ||
Average | 31.2914 | 6.6906 | 2.7556 | ||
Cameraman | 1 | 9.3735 | 1.3062 | 1.2272 | |
1 | 40.9848 | 3.2183 | 0.9053 | ||
4 | 36.8623 | 0.6872 | 1.5084 | ||
4 | 36.4358 | 0.6179 | 1.4209 | ||
16 | 3.3691 | 0.5151 | 0.9925 | ||
16 | 11.0407 | 0.3607 | 0.5260 | ||
Average | 23.0140 | 1.1176 | 1.0967 |
Image | TV+PD | BCA | BCA |
||
Circle | 1 | 40.4971 | 4.6052 | 1.0314 | |
1 | 18.5340 | 4.6922 | 1.2650 | ||
4 | 7.3436 | 0.7641 | 0.7001 | ||
4 | 39.6196 | 1.1891 | 0.6030 | ||
16 | 36.3221 | 1.2652 | 0.4643 | ||
16 | 39.5773 | 0.6123 | 0.3070 | ||
Average | 30.3156 | 2.1880 | 0.7285 | ||
Fluorescent Cells | 1 | 21.7999 | 8.3016 | 2.1735 | |
1 | 41.6892 | 8.9243 | 2.5687 | ||
4 | 40.1406 | 4.1263 | 2.4025 | ||
4 | 38.6224 | 3.8464 | 2.0889 | ||
16 | 37.7174 | 7.3265 | 6.1742 | ||
16 | 7.7788 | 7.6185 | 1.1258 | ||
Average | 31.2914 | 6.6906 | 2.7556 | ||
Cameraman | 1 | 9.3735 | 1.3062 | 1.2272 | |
1 | 40.9848 | 3.2183 | 0.9053 | ||
4 | 36.8623 | 0.6872 | 1.5084 | ||
4 | 36.4358 | 0.6179 | 1.4209 | ||
16 | 3.3691 | 0.5151 | 0.9925 | ||
16 | 11.0407 | 0.3607 | 0.5260 | ||
Average | 23.0140 | 1.1176 | 1.0967 |
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