Fast Newton-type methods for total variation regularization

Proceedings of the 28th International Conference on Machine Learning, ICML 2011

Volumn , Issue , 2011, Pages 313-320

  Barbero, Álvaro ^a   Sra, Suvrit ^b  

^a UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

^b MAX PLANCK INSTITUTE FOR INTELLIGENT SYSTEMS   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BUILDING BLOCKES; HIGHER-DIMENSIONAL; IMAGE DE-NOISING; IMAGE DECONVOLUTION; NEWTON-TYPE METHODS; OPTIMIZATION PROBLEMS; PROXIMITY OPERATOR; STATE-OF-THE-ART ALGORITHMS; TOTAL VARIATION; TOTAL VARIATION REGULARIZATION;

ALGORITHMS; SIGNAL PROCESSING;

LEARNING SYSTEMS;

EID: 80053439604     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (35)

1. Afonso, Manya V., Bioucas-Dias, José M., and Figueiredo, Mário A. T. Fast image recovery using variable splitting and constrained optimization. IEEE Transactions on Image Processing, 19(9), September 2010.
2. Anderson, E. et al. LAPACK Users' Guide. Society for Industrial and Applied Mathematics, Philadelphia, PA, third edition, 1999. ISBN 0-89871-447-8 (paperback).
3. Barbero, A. and Sra, S. http://people.kyb.tuebingen.mpg.de/suvrit/work/ icml11.pdf, 2011.
4. Beck, A. and Teboulle, M. A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems. SIAM J. Imgaging Sciences, 2(1):183-202, 2009.
5. Bertsekas, Dimitri P. Projected newton methods for optimization problems with simple constraints. SIAM J. Control and Optimization, 20(2), March 1982.
6. Biggs, David S. C. and Andrews, Mark. Acceleration of iterative image restoration algorithms. Applied Optics, 36(8), March 1997.
7. Bioucas-Dias, José M. and Figueiredo, Mário A. T. A new twist: Two-step iterative shrinkage/thresholding algorithms for image restoration. IEEE Transactions on Image Processing, 16(12): 2992-3004, December 2007.
8. Byrd, Richard H., Lu, Peihuang, Nocedal, Jorge, and Zhu, Ciyou. A limited memory algorithm for bound constrained optimization. Technical report, Northwestern University, 1994.
9. Choksi, Rustum, van Gennip, Yves, and Oberman, Adam. Anisotropic total variation regularized l1-approximation and denoising/deblurring of 2d bar codes. Technical report, Department of Mathematics and Statistics, McGill University, July 2010.
10. Combettes, Patrick L. and Pesquet, Jean-Christophe. Proximal splitting methods in signal processing. arXiv, 2009.
11. Conn, A. R., Gould, N. I. M., and Toint, P. L. Trust-Region Methods. SIAM, 2000.
12. Dahl, Joachim, Hansen, Per Christian, Jensen, Søren Holdt, and Jensen, Tobias Lindstrøm. Algorithms and software for total variation image reconstruction via first-order methods. Numer Algor, (53):67-92, 2010.
13. Duchi, J. and Singer, Y. Online and Batch Learning using Forward-Backward Splitting. JMLR, Sep. 2009.
14. Friedman, J., Hastie, T., Höfling, H., and Tibshirani, R. Pathwise coordinate optimization. Annals of Applied Statistics, 1(2):302-332, August 2007.
15. Golub, T. R. et al. Molecular classification of cancer. Science, 286(5439):531-537, October 1999.
16. Harchaoui, Z. and Lévy-Leduc, C. Multiple Change-Point Estimation With a Total Variation Penalty. Journal of the American Statistical Association, 105(492):1480-1493, 2010.
17. Hua, Jianping, Tembe, Waibhav D., and Dougherty, Edward R. Performance of feature-selection methods in the classification of high-dimension data. Pattern Recognition, 42:409-424, 2009.
18. Kim, Dongmin, Sra, Suvrit, and Dhillon, Inderjit. A scalable trust-region algorithm with application to mixed-norm regression. In ICML, 2010.
19. Kolar, M., Song, L., Ahmed, A., and Xing, E. Estimaging time-varying networks. The Annals of Applied Statistics, 4(1):94-123, 2010.
20. Lin, Chih-Jen and Moré, Jorge J. Newton's method for large bound-constrained optimization problems. SIAM J. Optim., 9(4):1100-1127, 1999.
21. Liu, J., Ji, S., and Ye, J. SLEP: Sparse Learning with Efficient Projections. Arizona State University, 2009. http://www.public.asu.edu/jye02/ Software/SLEP.
22. Liu, J., Yuan, L., and Ye, J. An efficient algorithm for a class of fused lasso problems. In SIGKDD, 2010.
23. Moré, Jorge J. and Sorensen, D. C. Computing a trust region step. SIAM J. Sci. Stat. Comput., 4(3), September 1983.
24. Nesterov, Y. Gradient methods for minimizing composite objective function. Technical Report 76, Catholic University of Louvain, CORE, 2007.
25. Nocedal, Jorge and Wright, Stephen J. Numerical Optimization. Springer Verlag, 2000.
26. Rapaport, F. and Vert, E. Barillot J.-P. Classification of array-CGH data using fused SVM. Bioinformatics, 24(13):i375-i382, 2008. (Pubitemid 351911693)
27. Rogers, Simon, Girolami, Mark, Campbell, Colin, and Breitling, Rainer. The latent process decomposition of cdna microarray data sets. IEEE/ACM Trans. Comp. Bio. and Bioinformatics, 2 (2), April-June 2005.
28. Rudin, Leonid I., Osher, Stanley, and Fatemi, Emad. Nonlinear total variation based noise removal algorithms. Physica D, 60: 259-268, 1992.
29. Stransky, Nicolas et al. Regional copy number-independent deregulation of transcription in cancer. Nature Genetics, 38(12):1386-1396, December 2006.
30. Tibshirani, R. and Wang, P. Spatial smoothing and hot spot detection for CGH data using the fused lasso. Biostatistics, 9(1):18-29,2008. (Pubitemid 350274579)
31. Tibshirani, R., Saunders, M., Rosset, S., Zhu, J., and Knight, K. Sparsity and smoothness via the fused lasso. J. Royal Stat. Soc: Series B, 67(1):91-108(18), 2005.
32. U. Alon et al. Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays. Proc. Natl. Acad. Sci. USA, 96:6745-6750, June 1999. (Pubitemid 29274954)
33. Vert, J.-P. and Bleakley, K. Fast detection of multiple change-points shared by many signals using group LARS. In Advances in Neural Information Processing Systems, 2010.
34. Vogel, C. R. and Oman, M. E. Iterative methods for total variation denoising. SIAM J. Sci. Comput., 17(1):227-238, 1996. (Pubitemid 126621162)
35. Zhu, Mingqiang and Chan, Tony. An efficient primal-dual hybrid gradient algorithm for total variation image restoration. Technical report, UCLA CAM, 2008.