-
Previous Article
The Gaussian beam method for the wigner equation with discontinuous potentials
- IPI Home
- This Issue
-
Next Article
General convergent expectation maximization (EM)-type algorithms for image reconstruction
Fast total variation wavelet inpainting via approximated primal-dual hybrid gradient algorithm
1. | School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30308, United States |
References:
[1] |
C. Ballester, M. Bertalmio, V. Caselles, G. Sapiro and J. Verdera, Filling-in by joint interpolation of vector fields and gray levels,, Image Processing, 10 (2001), 1200.
doi: 10.1109/83.935036. |
[2] |
J. Barzilai and J. M. Borwein, Two point step size gradient methods,, IMA J. Numer. Anal., 8 (1988), 141.
doi: 10.1093/imanum/8.1.141. |
[3] |
M. Bertalmio, G. Sapiro, V. Caselles and C. Ballester, Image inpainting,, In, (2000), 417.
doi: 10.1145/344779.344972. |
[4] |
M. Bertalmio, L. Vese, G. Sapiro and S. Osher, Simultaneous structure and texture image inpainting,, IEEE Trans. Image Process., 12 (2003), 882. Google Scholar |
[5] |
D. Bertsekas, "Parallel and Distributed Computation,", Prentice Hall, (1989). Google Scholar |
[6] |
M. Burger, L. He and C.-B. Schönlieb, Cahn-Hilliard inpainting and a generalization for grayvalue images,, SIAM J. Imag. Sci., 2 (2009), 1129.
doi: 10.1137/080728548. |
[7] |
J.-F. Cai, R. Chan and Z. Shen, A framelet-based image inpainting algorithm,, Appl. Comput. Harmon. Anal., 24 (2008), 131.
doi: 10.1016/j.acha.2007.10.002. |
[8] |
J.-F. Cai, H. Ji, F. Shang and Z. Shen, Inpainting for compressed images,, Appl. Comput. Harmon. Anal., 29 (2010), 368.
doi: 10.1016/j.acha.2010.01.005. |
[9] |
A. Chambolle, An algorithm for total variation minimization and applications,, Special issue on mathematics and image analysis. J. Math. Imaging Vis., 20 (2004), 89.
doi: 10.1023/B:JMIV.0000011321.19549.88. |
[10] |
A. Chambolle, V. Caselles, M. Novaga, D. Cremers and T. Pock, "An Introduction to Total Variation for Image Analysis,", Technical Report, (2009). Google Scholar |
[11] |
A. Chambolle and T. Pock, A first-order primal-dual algorithm for convex problems with applications to imaging,, J. Math. Imaging Vis., 40 (2011), 120.
doi: 10.1007/s10851-010-0251-1. |
[12] |
R. Chan, Y. Wen and A. Yip, A fast optimization transfer algorithm for image inpainting in wavelet domains,, IEEE Trans. Image Process., 18 (2009), 1467.
doi: 10.1109/TIP.2009.2019806. |
[13] |
R. Chan, Y. Wen and A. Yip, A primal-dual method for total variation-based wavelet domain inpainting,, IEEE Trans. Image Process, 21 (2012), 106.
doi: 10.1109/TIP.2011.2159983. |
[14] |
R. H. Chan, J. Yang and X. Yuan, Alternating direction method for image inpainting in wavelet domains,, SIAM J. Imag. Sci., 4 (2012), 807.
doi: 10.1137/100807247. |
[15] |
T. Chan, S. Kang and J. Shen, Euler's elastica and curvature-based inpainting,, SIAM J. Appl. Math., 63 (2002), 564.
doi: 10.1137/S0036139901390088. |
[16] |
T. Chan, S. Osher and J. Shen, The digital TV filter and nonlinear denoising,, IEEE Trans. Image Process., 10 (2001), 231.
doi: 10.1109/83.902288. |
[17] |
T. Chan and J. Shen, Mathematical models for local nontexture inpaintings,, SIAM J. Appl. Math., 62 (2002), 1019.
doi: 10.1137/S0036139900368844. |
[18] |
T. Chan, J. Shen and H. Zhou, Total variation wavelet inpainting,, J. Math. Imaging Vis., 25 (2006), 107.
doi: 10.1007/s10851-006-5257-3. |
[19] |
T. F. Chan, G. H. Golub and P. Mulet, A nonlinear primal-dual method for total variationbased image restoration,, SIAM J. Optim., 20 (1999), 1964.
doi: 10.1137/S1064827596299767. |
[20] |
Y. Chen, W. W. Hager, F. Huang, D. T. Phan, X. Ye and W. Yin, Fast algorithms for image reconstruction with application to partially parallel MR imaging,, SIAM J. Imag. Sci., 5 (2012), 90.
doi: 10.1137/100792688. |
[21] |
J. Eckstein and D. Bertsekas, On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators,, Mathematical Programming, 55 (1992), 293.
doi: 10.1007/BF01581204. |
[22] |
A. Efros and T. Leung, Texture synthesis by non-parametric sampling,, In, 2 (1999), 1033.
doi: 10.1109/ICCV.1999.790383. |
[23] |
S. Esedoglu and J. Shen, Digital inpainting based on the Mumford-Shah-Euler image model,, European J. Appl. Math., 13 (2002), 353.
doi: 10.1017/S0956792502004904. |
[24] |
E. Esser, X. Zhang and T. Chan, A general framework for a class of first order primal-dual algorithms for tv minimization,, SIAM J. Imag. Sci., 3 (2010), 1015.
doi: 10.1137/09076934X. |
[25] |
D. Gabay and B. Mercier, A dual algorithm for the solution of nonlinear variational problems via finite-element approximations,, Comput. Math. Appl., 2 (1976), 17.
doi: 10.1016/0898-1221(76)90003-1. |
[26] |
R. Glowinski and A. Marrocco, Sur l'approximation par éléments finis d'ordre un, et la résolution par pénalisation-dualité d'une classe de problèmes de dirichlet nonlinéaires,, RAIRO Analyse Numérique, 9 (1975), 41.
|
[27] |
T. Goldstein and S. Osher, The split Bregman method for L1 regularized problems,, SIAM J. Imag. Sci., 2 (2009), 323.
doi: 10.1137/080725891. |
[28] |
B. He and X. Yuan, Convergence analysis of primal-dual algorithms for a saddle-point problem: From contraction perspective,, SIAM J. Imag. Sci., 5 (2011), 119.
doi: 10.1137/100814494. |
[29] |
B. Martinet, Régularisation d'inéquations variationnelles par approximations successives,, Rev. Francaise Inform. Rech. Oper. Ser. R-3, 4 (1970), 154.
|
[30] |
S. Masnou and J.-M. Morel, Level lines based discocclusion,, In, (1998).
doi: 10.1109/ICIP.1998.999016. |
[31] |
S. Osher, M. Burger, D. Goldfarb, J. Xu and W. Yin, An iterative regularization method for total variation-based image restoration,, Multiscale Model. Simul., 4 (2005), 460.
doi: 10.1137/040605412. |
[32] |
R. T. Rockafellar, Monotone operators and the proximal point algorithm,, SIAM J. Control, 14 (1976), 877.
doi: 10.1137/0314056. |
[33] |
L. Rudin, S. Osher and E. Fatemi, Non-linear total variation noise removal algorithm,, Physics D., 60 (1992), 259. Google Scholar |
[34] |
C. R. Vogel and M. E. Oman, Iterative methods for total variation denoising,, SIAM J. Sci. Comput., 17 (1996), 227.
doi: 10.1137/0917016. |
[35] |
Y. Wang, J. Yang, W. Yin and Y. Zhang, A new alternating minimization algorithm for total variation image reconstruction,, SIAM J. Imag. Sci., 1 (2008), 248.
doi: 10.1137/080724265. |
[36] |
C. Wu and X.-C. Tai, Augmented Lagrangian method, dual methods, and split Bregman iteration for ROF, vectorial TV, and high order models,, SIAM J. Imag. Sci., 3 (2010), 300.
doi: 10.1137/090767558. |
[37] |
J. Yang, Y. Zhang and W. Yin, A fast TVL1-L2 minimization algorithm for signal reconstruction from partial Fourier data,, IEEE Journal of Selected Topics in Signal Processing, 4 (2010), 288. Google Scholar |
[38] |
X. Ye, Y. Chen and F. Huang, Computational acceleration for MR image reconstruction in partially parallel imaging,, IEEE Trans. Med. Imag., 30 (2011), 1055. Google Scholar |
[39] |
X. Ye, Y. Chen, W. Lin and F. Huang, Fast MR image reconstruction for partially parallel imaging with arbitrary k-space trajectories,, IEEE Trans. Med. Imag., 30 (2011), 575. Google Scholar |
[40] |
X. Zhang, M. Burger, X. Bresson and S. Osher, Bregmanized nonlocal regularization for deconvolution and sparse reconstruction,, SIAM J. Imag. Sci., 3 (2010), 253.
doi: 10.1137/090746379. |
[41] |
X. Zhang, M. Burger and S. Osher, A unified primal-dual algorithm framework based on bregman iteration,, J. Sci. Comput., 46 (2011), 20.
doi: 10.1007/s10915-010-9408-8. |
[42] |
X. Zhang and T. Chan, Wavelet inpainting by nonlocal total variation,, Inverse Probl. Imag., 4 (2010), 191.
doi: 10.3934/ipi.2010.4.191. |
[43] |
M. Zhu and T. Chan, "An Efficient Primal-Dual Hybrid Gradient Algorithm for Total Variation Image Restoration,", Technical Report 08-34, (2008), 08. Google Scholar |
show all references
References:
[1] |
C. Ballester, M. Bertalmio, V. Caselles, G. Sapiro and J. Verdera, Filling-in by joint interpolation of vector fields and gray levels,, Image Processing, 10 (2001), 1200.
doi: 10.1109/83.935036. |
[2] |
J. Barzilai and J. M. Borwein, Two point step size gradient methods,, IMA J. Numer. Anal., 8 (1988), 141.
doi: 10.1093/imanum/8.1.141. |
[3] |
M. Bertalmio, G. Sapiro, V. Caselles and C. Ballester, Image inpainting,, In, (2000), 417.
doi: 10.1145/344779.344972. |
[4] |
M. Bertalmio, L. Vese, G. Sapiro and S. Osher, Simultaneous structure and texture image inpainting,, IEEE Trans. Image Process., 12 (2003), 882. Google Scholar |
[5] |
D. Bertsekas, "Parallel and Distributed Computation,", Prentice Hall, (1989). Google Scholar |
[6] |
M. Burger, L. He and C.-B. Schönlieb, Cahn-Hilliard inpainting and a generalization for grayvalue images,, SIAM J. Imag. Sci., 2 (2009), 1129.
doi: 10.1137/080728548. |
[7] |
J.-F. Cai, R. Chan and Z. Shen, A framelet-based image inpainting algorithm,, Appl. Comput. Harmon. Anal., 24 (2008), 131.
doi: 10.1016/j.acha.2007.10.002. |
[8] |
J.-F. Cai, H. Ji, F. Shang and Z. Shen, Inpainting for compressed images,, Appl. Comput. Harmon. Anal., 29 (2010), 368.
doi: 10.1016/j.acha.2010.01.005. |
[9] |
A. Chambolle, An algorithm for total variation minimization and applications,, Special issue on mathematics and image analysis. J. Math. Imaging Vis., 20 (2004), 89.
doi: 10.1023/B:JMIV.0000011321.19549.88. |
[10] |
A. Chambolle, V. Caselles, M. Novaga, D. Cremers and T. Pock, "An Introduction to Total Variation for Image Analysis,", Technical Report, (2009). Google Scholar |
[11] |
A. Chambolle and T. Pock, A first-order primal-dual algorithm for convex problems with applications to imaging,, J. Math. Imaging Vis., 40 (2011), 120.
doi: 10.1007/s10851-010-0251-1. |
[12] |
R. Chan, Y. Wen and A. Yip, A fast optimization transfer algorithm for image inpainting in wavelet domains,, IEEE Trans. Image Process., 18 (2009), 1467.
doi: 10.1109/TIP.2009.2019806. |
[13] |
R. Chan, Y. Wen and A. Yip, A primal-dual method for total variation-based wavelet domain inpainting,, IEEE Trans. Image Process, 21 (2012), 106.
doi: 10.1109/TIP.2011.2159983. |
[14] |
R. H. Chan, J. Yang and X. Yuan, Alternating direction method for image inpainting in wavelet domains,, SIAM J. Imag. Sci., 4 (2012), 807.
doi: 10.1137/100807247. |
[15] |
T. Chan, S. Kang and J. Shen, Euler's elastica and curvature-based inpainting,, SIAM J. Appl. Math., 63 (2002), 564.
doi: 10.1137/S0036139901390088. |
[16] |
T. Chan, S. Osher and J. Shen, The digital TV filter and nonlinear denoising,, IEEE Trans. Image Process., 10 (2001), 231.
doi: 10.1109/83.902288. |
[17] |
T. Chan and J. Shen, Mathematical models for local nontexture inpaintings,, SIAM J. Appl. Math., 62 (2002), 1019.
doi: 10.1137/S0036139900368844. |
[18] |
T. Chan, J. Shen and H. Zhou, Total variation wavelet inpainting,, J. Math. Imaging Vis., 25 (2006), 107.
doi: 10.1007/s10851-006-5257-3. |
[19] |
T. F. Chan, G. H. Golub and P. Mulet, A nonlinear primal-dual method for total variationbased image restoration,, SIAM J. Optim., 20 (1999), 1964.
doi: 10.1137/S1064827596299767. |
[20] |
Y. Chen, W. W. Hager, F. Huang, D. T. Phan, X. Ye and W. Yin, Fast algorithms for image reconstruction with application to partially parallel MR imaging,, SIAM J. Imag. Sci., 5 (2012), 90.
doi: 10.1137/100792688. |
[21] |
J. Eckstein and D. Bertsekas, On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators,, Mathematical Programming, 55 (1992), 293.
doi: 10.1007/BF01581204. |
[22] |
A. Efros and T. Leung, Texture synthesis by non-parametric sampling,, In, 2 (1999), 1033.
doi: 10.1109/ICCV.1999.790383. |
[23] |
S. Esedoglu and J. Shen, Digital inpainting based on the Mumford-Shah-Euler image model,, European J. Appl. Math., 13 (2002), 353.
doi: 10.1017/S0956792502004904. |
[24] |
E. Esser, X. Zhang and T. Chan, A general framework for a class of first order primal-dual algorithms for tv minimization,, SIAM J. Imag. Sci., 3 (2010), 1015.
doi: 10.1137/09076934X. |
[25] |
D. Gabay and B. Mercier, A dual algorithm for the solution of nonlinear variational problems via finite-element approximations,, Comput. Math. Appl., 2 (1976), 17.
doi: 10.1016/0898-1221(76)90003-1. |
[26] |
R. Glowinski and A. Marrocco, Sur l'approximation par éléments finis d'ordre un, et la résolution par pénalisation-dualité d'une classe de problèmes de dirichlet nonlinéaires,, RAIRO Analyse Numérique, 9 (1975), 41.
|
[27] |
T. Goldstein and S. Osher, The split Bregman method for L1 regularized problems,, SIAM J. Imag. Sci., 2 (2009), 323.
doi: 10.1137/080725891. |
[28] |
B. He and X. Yuan, Convergence analysis of primal-dual algorithms for a saddle-point problem: From contraction perspective,, SIAM J. Imag. Sci., 5 (2011), 119.
doi: 10.1137/100814494. |
[29] |
B. Martinet, Régularisation d'inéquations variationnelles par approximations successives,, Rev. Francaise Inform. Rech. Oper. Ser. R-3, 4 (1970), 154.
|
[30] |
S. Masnou and J.-M. Morel, Level lines based discocclusion,, In, (1998).
doi: 10.1109/ICIP.1998.999016. |
[31] |
S. Osher, M. Burger, D. Goldfarb, J. Xu and W. Yin, An iterative regularization method for total variation-based image restoration,, Multiscale Model. Simul., 4 (2005), 460.
doi: 10.1137/040605412. |
[32] |
R. T. Rockafellar, Monotone operators and the proximal point algorithm,, SIAM J. Control, 14 (1976), 877.
doi: 10.1137/0314056. |
[33] |
L. Rudin, S. Osher and E. Fatemi, Non-linear total variation noise removal algorithm,, Physics D., 60 (1992), 259. Google Scholar |
[34] |
C. R. Vogel and M. E. Oman, Iterative methods for total variation denoising,, SIAM J. Sci. Comput., 17 (1996), 227.
doi: 10.1137/0917016. |
[35] |
Y. Wang, J. Yang, W. Yin and Y. Zhang, A new alternating minimization algorithm for total variation image reconstruction,, SIAM J. Imag. Sci., 1 (2008), 248.
doi: 10.1137/080724265. |
[36] |
C. Wu and X.-C. Tai, Augmented Lagrangian method, dual methods, and split Bregman iteration for ROF, vectorial TV, and high order models,, SIAM J. Imag. Sci., 3 (2010), 300.
doi: 10.1137/090767558. |
[37] |
J. Yang, Y. Zhang and W. Yin, A fast TVL1-L2 minimization algorithm for signal reconstruction from partial Fourier data,, IEEE Journal of Selected Topics in Signal Processing, 4 (2010), 288. Google Scholar |
[38] |
X. Ye, Y. Chen and F. Huang, Computational acceleration for MR image reconstruction in partially parallel imaging,, IEEE Trans. Med. Imag., 30 (2011), 1055. Google Scholar |
[39] |
X. Ye, Y. Chen, W. Lin and F. Huang, Fast MR image reconstruction for partially parallel imaging with arbitrary k-space trajectories,, IEEE Trans. Med. Imag., 30 (2011), 575. Google Scholar |
[40] |
X. Zhang, M. Burger, X. Bresson and S. Osher, Bregmanized nonlocal regularization for deconvolution and sparse reconstruction,, SIAM J. Imag. Sci., 3 (2010), 253.
doi: 10.1137/090746379. |
[41] |
X. Zhang, M. Burger and S. Osher, A unified primal-dual algorithm framework based on bregman iteration,, J. Sci. Comput., 46 (2011), 20.
doi: 10.1007/s10915-010-9408-8. |
[42] |
X. Zhang and T. Chan, Wavelet inpainting by nonlocal total variation,, Inverse Probl. Imag., 4 (2010), 191.
doi: 10.3934/ipi.2010.4.191. |
[43] |
M. Zhu and T. Chan, "An Efficient Primal-Dual Hybrid Gradient Algorithm for Total Variation Image Restoration,", Technical Report 08-34, (2008), 08. Google Scholar |
[1] |
Bao Wang, Alex Lin, Penghang Yin, Wei Zhu, Andrea L. Bertozzi, Stanley J. Osher. Adversarial defense via the data-dependent activation, total variation minimization, and adversarial training. Inverse Problems & Imaging, 2021, 15 (1) : 129-145. doi: 10.3934/ipi.2020046 |
[2] |
Xuemei Chen, Julia Dobrosotskaya. Inpainting via sparse recovery with directional constraints. Mathematical Foundations of Computing, 2020, 3 (4) : 229-247. doi: 10.3934/mfc.2020025 |
[3] |
Xi Zhao, Teng Niu. Impacts of horizontal mergers on dual-channel supply chain. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020173 |
[4] |
Ferenc Weisz. Dual spaces of mixed-norm martingale hardy spaces. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020285 |
[5] |
Bo Tan, Qinglong Zhou. Approximation properties of Lüroth expansions. Discrete & Continuous Dynamical Systems - A, 2020 doi: 10.3934/dcds.2020389 |
[6] |
Yifan Chen, Thomas Y. Hou. Function approximation via the subsampled Poincaré inequality. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 169-199. doi: 10.3934/dcds.2020296 |
[7] |
Mostafa Mbekhta. Representation and approximation of the polar factor of an operator on a Hilbert space. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020463 |
[8] |
Bilal Al Taki, Khawla Msheik, Jacques Sainte-Marie. On the rigid-lid approximation of shallow water Bingham. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 875-905. doi: 10.3934/dcdsb.2020146 |
[9] |
P. K. Jha, R. Lipton. Finite element approximation of nonlocal dynamic fracture models. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1675-1710. doi: 10.3934/dcdsb.2020178 |
[10] |
Simone Fagioli, Emanuela Radici. Opinion formation systems via deterministic particles approximation. Kinetic & Related Models, 2021, 14 (1) : 45-76. doi: 10.3934/krm.2020048 |
[11] |
Zonghong Cao, Jie Min. Selection and impact of decision mode of encroachment and retail service in a dual-channel supply chain. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020167 |
[12] |
Hongxia Sun, Yao Wan, Yu Li, Linlin Zhang, Zhen Zhou. Competition in a dual-channel supply chain considering duopolistic retailers with different behaviours. Journal of Industrial & Management Optimization, 2021, 17 (2) : 601-631. doi: 10.3934/jimo.2019125 |
[13] |
Manuel Friedrich, Martin Kružík, Jan Valdman. Numerical approximation of von Kármán viscoelastic plates. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 299-319. doi: 10.3934/dcdss.2020322 |
[14] |
Baoli Yin, Yang Liu, Hong Li, Zhimin Zhang. Approximation methods for the distributed order calculus using the convolution quadrature. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1447-1468. doi: 10.3934/dcdsb.2020168 |
[15] |
Pierluigi Colli, Gianni Gilardi, Jürgen Sprekels. Deep quench approximation and optimal control of general Cahn–Hilliard systems with fractional operators and double obstacle potentials. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 243-271. doi: 10.3934/dcdss.2020213 |
[16] |
Michiyuki Watanabe. Inverse $N$-body scattering with the time-dependent hartree-fock approximation. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2021002 |
[17] |
Peter Frolkovič, Karol Mikula, Jooyoung Hahn, Dirk Martin, Branislav Basara. Flux balanced approximation with least-squares gradient for diffusion equation on polyhedral mesh. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 865-879. doi: 10.3934/dcdss.2020350 |
[18] |
Xiaoli Lu, Pengzhan Huang, Yinnian He. Fully discrete finite element approximation of the 2D/3D unsteady incompressible magnetohydrodynamic-Voigt regularization flows. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 815-845. doi: 10.3934/dcdsb.2020143 |
2019 Impact Factor: 1.373
Tools
Metrics
Other articles
by authors
[Back to Top]