Geometry of total variation regularized L p-model

Journal of Computational and Applied Mathematics

Volumn 236, Issue 8, 2012, Pages 2223-2234

  Shi, Yuying ^a   Wang, Li Lian ^b   Tai, Xue Cheng ^b,c  

^a NORTH CHINA ELECTRIC POWER UNIVERSITY   (China)

^b NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

^c UNIVERSITY OF BERGEN   (Norway)

Author keywords

Augmented Lagrangian methods; Feature selection; Feature separation; G norm; TV Lp model

Indexed keywords

AUGMENTED LAGRANGIAN METHODS; FEATURE SEPARATION; G-NORM; INTRINSIC FEATURES; NUMERICAL ALGORITHMS; NUMERICAL RESULTS; SCALE SELECTION; THEORETICAL RESULT; TOTAL VARIATION;

ALGORITHMS; LAGRANGE MULTIPLIERS; NUMERICAL METHODS;

FEATURE EXTRACTION;

EID: 84855522875     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2011.09.043     Document Type: Conference Paper

References (39)

1. L. Rudin, S. Osher, and E. Fatemi Nonlinear total variation based noise removal algorithms Physica D 60 1992 259 268
2. L. Evans, and R. Gariepy Measure theory and fine properties of functions Studies in Advanced Mathematics 1992 CRC Press Roca Baton, FL
3. E. Giusti Minimal Surfaces and Functions of Bounded Variation Monographs in Mathematics vol. 80 1984 Birkhauser Verlag Basel
4. S. Alliney Digital filters as absolute norm regularizers IEEE Trans. Signal Process. 40 1992 1548 1562
5. M. Nikolova Minimizers of cost-functions involving nonsmooth data-fidelity terms SIAM J. Numer. Anal. 40 2002 965 994
6. L 1 function approximation SIAM J. Appl. Math. 65 2005 1817 1837 (Pubitemid 41639797)
7. J. Darbon, Total variation minimization with L1 data fidelity as a contrast invariant filter, in: Image and Signal Processing and Analysis, 2005. ISPA 2005. Proceedings of the 4th International Symposium on, 1517, 2005, pp. 221226.
8. Y. Meyer Oscillating Patterns in Image Processing and Nonlinear Evolution Equations 2001 AMS Providence
9. 1 norm Multiscale Model. Simul. 1 2003 349 370
10. T. Le, and L. Vese Image decomposition using total variation and div (BMO) Multiscale Model. Simul. 4 2005 390 423 (Pubitemid 43885245)
11. J. Garnett, P. Jones, T. Le, and L. Vese Image decompositions using bounded variation and generalized homogeneous Besov spaces Appl. Comput. Harmon. Anal. 23 2007 25 56 (Pubitemid 46856882)
12. S. Lee, and J. Seo Noise removal with Gauss curvature-driven diffusion IEEE Trans. Image Process. 14 2005 904 909 (Pubitemid 40889985)
13. S. Lee, and M. Kang Total variation-based image noise reduction with generalized fidelity function IEEE Signal Process. Lett. 14 2007 832 835 (Pubitemid 350130773)
14. M. Lysaker, A. Lundervold, and X.C. Tai Noise removal using fourth-order partial differential equations with applications to medical magnetic resonance images in space and time IEEE Trans. Image Process. 12 2003 1579 1590
15. J. Darbon, and M. Sigelle Image restoration with discrete constrained total variation part II: levelable functions, convex priors and non-convex cases J. Math. Imaging Vision 26 2006 277 291 (Pubitemid 44916362)
16. S. Osher, and O. Scherzer G-norm properties of bounded variation regularization Comm. Math. Sci. 2 2004 237 254
17. O. Scherzer, W. Yin, and S. Osher Slope and G-set characterization of set-valued functions and applications to non-differentiable optimization problems Comm. Math. Sci. 3 2005 479 492
18. L 2) decompositions Multiscale Model. Simul. 2 2004 554 579
19. L 1 model for multiscale decomposition Multiscale Model. Simul. 6 2006 190 211
20. H. Federer Geometric Measure Theory 1969 Springer New York
21. L. Ambrosio, N. Fusco, and D. Pallara Functions of Bounder Variation and Free Discountinuity Problems 2000 Oxford University Press New York
22. M. Nikolova A variational approach to remove outliers and impulse noise J. Math. Imaging Vision 20 2004 99 120
23. S. Keeling Total variation based convex filters for medical imaging Appl. Math. Comput. 139 2003 101 119
24. A. Haddad, and Y. Meyer An improvement of RudinOsherFatemi model Appl. Comput. Harmon. Anal. 22 2007 319 334
25. S. Kindermann, S. Osher, and J. Xu Denoising by BV-duality J. Sci. Comput. 28 2006 414 444
26. C. Vogel, and M. Oman Iterative methods for total variation denoising SIAM J. Sci. Comput. 17 1998 813 824
27. T. Chan, G. Golub, and P. Mulet A nonlinear primaldual method for total variation-based image restoration SIAM J. Sci. Comput. 20 1999 1964 1977
28. E. Bae, X. Tai, Graph cut optimization for the piecewise constant level set method applied to multiphase image segmentation, in: Sapce and Variational Methods in Computer Vision, SSVM 2009, 2009, pp. 113.
29. 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 460 489 (Pubitemid 43885248)
30. Y. Wang, J. Yang, W. Yin, and Y. Zhang A new alternating minimization algorithm for total variation image reconstruction SIAM J. Imaging Sci. 1 2008 248 272
31. Q. Chang, and I. Chen Acceleration methods for total variation-based image denoising SIAM J. Sci. Comput. 25 2003 982 994
32. X. Tai, and C. Wu Augmented Lagrangian method, dual methods and split Bregman iteration for ROF model, scale space and variational methods in computer vision Second International Conference, SSVM 2009, Voss, Norway, June 15, 2009. Proceedings Lecture Notes in Comput. Sci. vol. 5567 2009 Springer 502 513
33. C. Wu, and X. Tai Augmented Lagrangian method, dual methods, and split Bregman iteration for ROF, vectorial TV, and high order models SIAM J. Imaging Sci. 3 2010 300 339
34. C. Wu, J. Zhang, and X. Tai Augmented Lagrangian method for total variation restoration with non-quadratic fidelity Inverse Probl. Imaging 5 2011 237 261
35. X. Bresson, S. Esedoglu, P. Vandergheynst, J.P. Thiran, and S. Osher Fast global minimization of the active contour/snake model J. Math. Imaging Vision 28 2007 151 167 (Pubitemid 47312505)
36. L 1 functional Variational, Geometric, and Level Set Methods in Computer Vision vol. 3752 2005 73 84
37. W. Yin, D. Goldfarb, and S. Osher A comparision of three total variation based texture extraction models J. Vis. Commun. Image Represent. 18 2007 240 252 (Pubitemid 46678858)
38. F. Alizadeh, and D. Goldfarb Second-order cone programming Math. Program. 95 2003 3 51 (Pubitemid 44757862)
39. D. Goldfarb, and W. Yin Second-order cone programming methods for total variation based image restoration SIAM J. Sci. Comput. 27 2005 622 645