Diagonal preconditioning for first order primal-dual algorithms in convex optimization

Proceedings of the IEEE International Conference on Computer Vision

Volumn , Issue , 2011, Pages 1762-1769

  Pock, Thomas ^a   Chambolle, Antonin ^b  

^a GRAZ UNIVERSITY OF TECHNOLOGY   (Austria)

^b CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER VISION PROBLEMS; FIRST-ORDER; LINEAR PROGRAMMING PROBLEM; NUMERICAL RESULTS; PRECONDITIONED ALGORITHMS; PRECONDITIONERS; PRECONDITIONING TECHNIQUES; PRIMAL DUAL ALGORITHMS; STEP METHOD; STEP SIZE;

CONVEX OPTIMIZATION; IMAGE PROCESSING;

ALGORITHMS;

EID: 84856673847     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ICCV.2011.6126441     Document Type: Conference Paper

References (16)

1. A. Bhusnurmath and C. Taylor. Graph cuts via l1 norm minimization. IEEE Transactions on Pattern Analysis and Machine Intelligence, 30:1866-1871, 2008.
2. S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge University Press, 2004.
3. Y. Boykov and V. Kolmogorov. An experimental comparison of min-cut/max-flow algorithms for energy minimization in computer vision. In A. J. M. Figueiredo, J. Zerubia, editor, Energy Minimization Methods in Computer Vision and Pattern Recognition, volume 2134 of LNCS, pages 359-374. Springer, 2001.
4. A. Chambolle. Total variation minimization and a class of binary MRF models. In Energy Minimization Methods in Computer Vision and Pattern Recognition, pages 136-152, 2005.
5. A. Chambolle and T. Pock. A first-order primal-dual algorithm for convex problems with applications to imaging. Journal of Mathematical Imaging and Vision, 2010. online first.
6. T. Chan and S. Esedoglu. Aspects of total variation regularized L1 function approximation. SIAM J. Appl. Math., 65(5):1817-1837, 2004.
7. J. Eckstein. Splitting Methods for Monotone Operators with Application to Parallel Optimization. PhD thesis, MIT, 1989.
8. E. Esser, X. Zhang, and T. Chan. A general framework for a class of first order primal-dual algorithms for convex optimization in imaging science. SIAM J. Imaging Sci., 3:1015-1046, 2010.
9. L. Ford and D. Fulkerson. Flows in Networks. Princeton University Press, Princeton, New Jersey, 1962.
10. B. He and X. Yuan. Convergence analysis of primal-dual algorithms for total variation image restoration. Technical report, Nanjing University, China, 2010.
11. J. Lellmann, D. Breitenreicher, and C. Schnörr. Fast and exact primal-dual iterations for variational problems in computer vision. In K. Daniilidis, P. Maragos, and N. Paragios, editors, European Conference on Computer Vision (ECCV), volume 6312 of LNCS, pages 494-505. Springer Berlin /Heidelberg, 2010.
12. M. Nikolova. A variational approach to remove outliers and impulse noise. Journal of Mathematical Imaging and Vision, 20(1-2):99-120, 2004.
13. T. Pock, D. Cremers, H. Bischof, and A. Chambolle. An algorithm for minimizing the Mumford-Shah functional. In International Conference on Computer Vision (ICCV), 2009.
14. R. T. Rockafellar. Monotone operators and the proximal point algorithm. SIAM Journal on Control and Optimization, 14(5):877-898, 1976.
15. T. Schoenemann, F. Kahl, and D. Cremers. Curvature regularity for region-based image segmentation and inpainting: A linear programming relaxation. In IEEE International Conference on Computer Vision (ICCV), Kyoto, Japan, 2009.
16. X. Zhang, M. Burger, and S. Osher. A unified primal-dual algorithm framework based onbregman iteration. Journal of Scientific Computing, 46:20-46, 2011.