Split bregman algorithm, douglas-rachford splitting and frame shrinkage

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5567 LNCS, Issue , 2009, Pages 464-476

  Setzer, Simon ^a  

^a UNIVERSITY OF MANNHEIM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

A-FRAMES; CONVEX ANALYSIS; DOUGLAS; GRADIENT DESCENT; IMAGE DE-NOISING; OPERATOR SPLITTING METHOD; PARSEVAL FRAMES; RE-PROJECTION; SPLITTING ALGORITHMS; VARIATIONAL METHODS;

ALGORITHMS; COMPUTER VISION; MATHEMATICAL OPERATORS; SHRINKAGE;

CONVERGENCE OF NUMERICAL METHODS;

EID: 69049120535     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-02256-2_39     Document Type: Conference Paper

References (29)

1. DeVore, R.A., Lucier, B.J.: Fast wavelet techniques for near-optimal image processing. In: IEEE MILCOM 1992 Conf. Rec., vol. 3, pp. 1129-1135. IEEE Press, San Diego (1992)
2. Chambolle, A.: Total variation minimization and a class of binary MRF models. In: Rangarajan, A., Vemuri, B.C., Yuille, A.L. (eds.) EMMCVPR 2005. LNCS, vol. 3757, pp. 136-152. Springer, Heidelberg (2005)
3. Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60, 259-268 (1992)
4. Mrázek, P.,Weickert, J.: Rotationally invariant wavelet shrinkage. In: Michaelis, B., Krell, G. (eds.) DAGM 2003. LNCS, vol. 2781, pp. 156-163. Springer, Heidelberg (2003)
5. Welk, M., Steidl, G., Weickert, J.: Locally analytic schemes: A link between diffusion filtering and wavelet shrinkage. Applied and Computational Harmonic Analysis 24, 195-224 (2008)
6. Lions, P.L., Mercier, B.: Splitting algorithms for the sum of two nonlinear operators. SIAM Journal on Numerical Analysis 16(6), 964-979 (1979)
7. Tseng, P.: Applications of a splitting algorithm to decomposition in convex programming and variational inequalities. SIAM Journal on Control and Optimization 29, 119-138 (1991)
8. Combettes, P.L.: Solving monotone inclusions via compositions of nonexpansive averaged operators. Optimization 53(5-6), 475-504 (2004)
9. Combettes, P.L., Wajs, V.R.: Signal recovery by proximal forward-backward splitting. Multiscale Modeling and Simulation 4, 1168-1200 (2005)
10. Douglas, J., Rachford, H.H.: On the numerical solution of heat conduction problems in two and three space variables. Transactions of the American Mathematical Society 82(2), 421-439 (1956)
11. Bregman, L.M.: The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming. USSR Computational Mathematics and Mathematical Physics 7(3), 200-217 (1967)
12. Eckstein, J.: Nonlinear proximal point algorithms using Bregman functions, with applications to convex programming. Mathematics of Operations Research 18(1), 202-226 (1993)
13. Kiwiel, K.C.: Proximal minimization methods with generalized Bregman functions. SIAM Journal on Control and Optimization 35(4), 1142-1168 (1997)
14. Frick, K.: The Augmented Lagrangian Method and Associated Evolution Equations, Dissertation, University of Innsbruck (2008)
15. Rockafellar, R.T.: Augmented Lagrangians and applications of the proximal point algorithm in convex programming. Mathematics of Operations Research 1(2), 97- 116 (1976)
16. Browder, F.E., Petryshyn, W.V.: The solution by iteration of nonlinear functional equations in Banach spaces. Bulletin of the American Mathematical Society 72, 571-575 (1966)
17. Iusem, A.N.: Augmented Lagrangian methods and proximal point methods for convex optimization. Investigación Operativa 8, 11-49 (1999)
18. Goldstein, D., Osher, S.: The Split Bregman method for l1 regularized problems. UCLA CAM Report (2008)
19. Yin, W., Osher, S., Goldfarb, D., Darbon, J.: Bregman iterative algorithms for -1- minimization with applications to compressed sensing. SIAM Journal on Imaging Sciences 1(1), 143-168 (2008)
20. Eckstein, J., Bertsekas, D.P.: On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators. Mathematical Programming 55, 293-318 (1992)
21. Gabay, D.: Applications of the method of multipliers to variational inequalities. In: Fortin, M., Glowinski, R. (eds.) Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary-Value Problems. Studies in Mathematics and its Applications, vol. 15, pp. 299-331. North-Holland, Amsterdam (1983)
22. Chambolle, A.: An algorithm for total variation minimization and applications. Journal of Mathematical Imaging and Vision 20, 89-97 (2004)
23. Aujol, J.F.: Some first-order algorithms for total variation based image restoration. Preprint ENS Cachan (2008)
24. Zhu, M., Chan, T.: An efficient primal-dual hybrid gradient algorithm for total variation image restauration. UCLA CAM Report (2008)
25. Daubechies, I., Han, B., Ron, A., Shen, Z.: Framelets: MRA-based construction of wavelet frames. Applied and Computational Harmonic Analysis 14, 1-46 (2003)
26. Dong, B., Shen, Z.: Pseudo-splines, wavelets and framelets. Applied and Computational Harmonic Analysis 22, 78-104 (2007)
27. Setzer, S., Steidl, G.: Split Bregman method, gradient descent reprojection method and Parseval frames. Preprint Univ. Mannheim (2008)
28. Chan, R.H., Setzer, S., Steidl, G.: Inpainting by flexible Haar-wavelet shrinkage. SIAM Journal on Imaging Science 1, 273-293 (2008)
29. Wang, Y., Yang, J., Yin, W., Zhang, Y.: A new alternating minimization algorithm for total variation image reconstruction. SIAM Journal on Imaging Sciences 1(3), 248-272 (2008)