`a`
Inverse Problems and Imaging (IPI)
 

A numerical study of a mean curvature denoising model using a novel augmented Lagrangian method
Pages: 975 - 996, Issue 6, December 2017

doi:10.3934/ipi.2017045      Abstract        References        Full text (6720.5K)           Related Articles

Wei Zhu - Department of Mathematics, University of Alabama, Box 870350, Tuscaloosa, AL 35487, United States (email)

1 L. Ambrosio and S. Masnou, A direct variational approach to a problem arising in image reconstruction, Interfaces Free Bound., 5 (2003), 63-81.       
2 L. Ambrosio and S. Masnou, On a variational problem arising in image reconstruction, Free Boundary Problems (Trento, 2002), Internat. Ser. Numer. Math., Birkhäuser, Basel, 147 (2004), 17-26.       
3 E. Bae, J. Shi and X. C. Tai, Graph cuts for curvature based image denoising, IEEE Trans. on Image Process, 20 (2011), 1199-1210.       
4 G. Bellettini, V. Caselles and M. Novaga, The total variation flow in $\mathbbR^n$, J. Differ. Equations, 184 (2002), 475-525.       
5 C. Brito-Loeza and K. Chen, Multigrid algorithm for high order denoising, SIAM J. Imaging. Sciences, 3 (2010), 363-389.       
6 A. Chambolle, An algorithm for total variation minimization and applications, J. Math. Imaging Vis., 20 (2004), 89-97.       
7 T. Chan, G. H. Golub and P. Mulet, A nonlinear primal-dual method for total variation-based image restoration, SIAM J. Sci. Comput., 20 (1999), 1964-1977.       
8 T. Chan and S. Esedoglu, Aspects of total variation regularized $L^{1}$ function approximation, SIAM J. Appl. Math., 65 (2005), 1817-1837.       
9 T. Chan, S. Esedo$\barg$lu, F. Park and M. H. Yip, Recent Developments in Total Variation Image Restoration, In Handbook of Mathematical Models in Computer Vision. Springer Verlag, 2005. Edt by N. Paragios, Y. Chen, O. Faugeras.
10 T. Chan, S. H. Kang and J. H. Shen, Euler's elastica and curvature based inpaintings, SIAM J. Appl. Math., 63 (2002), 564-592.       
11 M. P. do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, Inc., 1976.       
12 Y. Duan, Y. Wang, X.-C. Tai and J. Hahn, A fast augmented Lagrangian method for Euler's elastica model, SSVM 2011, LSCS, 6667 (2012), 144-156.
13 J. Eckstein and W. Yao, Understanding the Convergence of the Alternating Direction Method of Multipliers: Theoretical and Computational Perspectives, Pac. J. Optim., 11 (2015), 619-644.       
14 N. El-Zehiry and L. Grady, Fast global optimization of curvature, Proc. of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, (2010), 3257-3264.
15 T. Goldstein and S. Osher, The split Bregman method for L1-regularized problems, SIAM J. Imaging Sci., 2 (2009), 323-343.       
16 M. Hintermüller, C. N. Rautenberg and J. Hahn, Functional-analytic and numerical issues in splitting methods for total variation-based image reconstruction, Inverse Problems, 30 (2014), 055014, 34pp.       
17 R. March and M. Dozio, A variational method for the recovery of smooth boundaries, Image and Vision Computing, 15 (1997), 705-712.
18 S. Masnou, Disocclusion: A variational approach using level lines, IEEE Trans. Image Process., 11 (2002), 68-76.       
19 S. Masnou and J. M. Morel, Level lines based disocclusion, Proc. IEEE Int. Conf. on Image Processing, Chicago, IL, (1998), 259-263.
20 Y. Meyer, Oscillating Patterns in Image Processing and Nonlinear Evolution Equations, University Lecture Series, Vol 22, American Mathematical Society, Providence, RI, 2001.       
21 M. Myllykoski, R. Glowinski, T. Kárkkáinen and T. Rossi, A new augmented Lagrangian approach for L1-mean curvature image denoising, SIAM J. Imaging Sci., 8 (2015), 95-125.       
22 M. Nitzberg, D. Mumford and T. Shiota, Filering, Segmentation, and Depth, Lecture Notes in Computer Science, Vol. 662, Springer Verlag, Berlin, 1993.       
23 S. Osher, M. Burger, D. Goldfarb, J. J. Xu and W. T. Yin, An iterative regularization method for total variation-based image restoration, Multiscale Model. Simul., 4 (2005), 460-489.       
24 R. T. Rockafellar, Augmented Lagrangians and applications of the proximal point algorithm in convex programming, Mathematics of Operations Research, 1 (1976), 97-116.       
25 L. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithm, Physica D, 60 (1992), 259-268.       
26 T. Schoenemann, F. Kahl and D. Cremers, Curvature regularity for region-based image segmentation and inpainting: A linear programming relaxation, IEEE International Conference on Computer Vision (ICCV), 2009.
27 T. Schoenemann, F. Kahl, S. Masnou and D. Cremers, A linear framework for region-based image segmentation and inpainting involving curvature penalization, Int. J. Comput. Vision, 99 (2012), 53-68.       
28 D. Strong and T. Chan, Edge-preserving and scale-dependent properties of total variation regularization, Inverse Problem, 19 (2003), 165-187.       
29 X. C. Tai, J. Hahn and G. J. Chung, A fast algorithm for Euler's Elastica model using augmented Lagrangian method, SIAM J. Imaging Sciences, 4 (2011), 313-344.       
30 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. Imaging Sciences, 3 (2010), 300-339.       
31 F. Yang, K. Chen and B. Yu, Homotopy method for a mean curvature-based denoising model, Appl. Numer. Math., 62 (2012), 185-200.       
32 W. Zhu and T. Chan, A variational model for capturing illusory contours using curvature, J. Math. Imaging Vision, 27 (2007), 29-40.       
33 W. Zhu and T. Chan, Image denoising using mean curvature of image surface, SIAM J. Imaging Sciences, 5 (2012), 1-32.       
34 W. Zhu, T. Chan and S. Esedo$\barg$lu, Segmentation with depth: A level set approach, SIAM J. Sci. Comput., 28 (2006), 1957-1973.       
35 W. Zhu, X. C. Tai and T. Chan, Augmented Lagrangian method for a mean curvature based image denoising model, Inverse Probl. Imag., 7 (2013), 1409-1432.       
36 W. Zhu, X. C. Tai and T. Chan, Image segmentation using Euler's elastica as the regularization, J. Sci. Comput., 57 (2013), 414-438.       

Go to top