- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 101974, 9 pages
-Goodness for Low-Rank Matrix Recovery
1Department of Applied Mathematics, Beijing Jiaotong University, Beijing 100044, China
2Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, ON, Canada N2L 3G1
Received 21 January 2013; Accepted 17 March 2013
Academic Editor: Jein-Shan Chen
Copyright © 2013 Lingchen Kong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- C. Beck and R. D’Andrea, “Computational study and comparisons of LFT reducibility methods,” in Proceedings of the American Control Conference, Philadelphia, Pa, USA, June 1998.
- M. Mesbahi and G. P. Papavassilopoulos, “On the rank minimization problem over a positive semidefinite linear matrix inequality,” IEEE Transactions on Automatic Control, vol. 42, no. 2, pp. 239–243, 1997.
- M. Fazel, H. Hindi, and S. P. Boyd, “A rank minimization heuristic with application to minimum order system approximation,” in Proceedings of American Control Conference, pp. 4734–4739, June 2001.
- B. Recht, M. Fazel, and P. A. Parrilo, “Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization,” SIAM Review, vol. 52, no. 3, pp. 471–501, 2010.
- B. P. W. Ames and S. A. Vavasis, “Nuclear norm minimization for the planted clique and biclique problems,” Mathematical Programming, vol. 129, no. 1, pp. 69–89, 2011.
- J.-F. Cai, E. J. Candès, and Z. Shen, “A singular value thresholding algorithm for matrix completion,” SIAM Journal on Optimization, vol. 20, no. 4, pp. 1956–1982, 2010.
- E. J. Candès and B. Recht, “Exact matrix completion via convex optimization,” Foundations of Computational Mathematics, vol. 9, no. 6, pp. 717–772, 2009.
- C. Ding, D. Sun, and K. C. Toh, “An introduction to a class of matrix cone programming,” Tech. Rep., 2010.
- Z. Lin, M. Chen, L. Wu, and Y. Ma, “The augmented Lagrange multiplier method for exact recovery of a corrupted low-rank matrices,” http://arxiv.org/abs/1009.5055.
- Y. Liu, D. Sun, and K. C. Toh, “An implementable proximal point algorithmic framework for nuclear norm minimization,” Mathematical Programming, vol. 133, no. 1-2, pp. 399–436, 2012.
- Z. Liu and L. Vandenberghe, “Interior-point method for nuclear norm approximation with application to system identification,” SIAM Journal on Matrix Analysis and Applications, vol. 31, no. 3, pp. 1235–1256, 2009.
- S. Ma, D. Goldfarb, and L. Chen, “Fixed point and Bregman iterative methods for matrix rank minimization,” Mathematical Programming, vol. 128, no. 1-2, pp. 321–353, 2011.
- Y. Peng, A. Ganesh, J. Wright, W. Xu, and Y. Ma, “RASL: robust alignment by sparse and low-rank decomposition for linearly correlated images,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 34, no. 1, pp. 2233–2246, 2010.
- B. Recht, W. Xu, and B. Hassibi, “Necessary and sufficient conditions for success of the nuclear norm heuristic for rank minimization,” in Proceedings of the 47th IEEE Conference on Decision and Control (CDC '08), pp. 3065–3070, Cancun, Mexico, December 2008.
- M. Tao and X. Yuan, “Recovering low-rank and sparse components of matrices from incomplete and noisy observations,” SIAM Journal on Optimization, vol. 21, no. 1, pp. 57–81, 2011.
- E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Transactions on Information Theory, vol. 52, no. 2, pp. 489–509, 2006.
- E. J. Candes and T. Tao, “Decoding by linear programming,” IEEE Transactions on Information Theory, vol. 51, no. 12, pp. 4203–4215, 2005.
- D. L. Donoho, “Compressed sensing,” IEEE Transactions on Information Theory, vol. 52, no. 4, pp. 1289–1306, 2006.
- B. Recht, W. Xu, and B. Hassibi, “Null space conditions and thresholds for rank minimization,” Mathematical Programming, vol. 127, no. 1, pp. 175–202, 2011.
- S. Oymak and B. Hassibi, “New null space results and recovery thresholds for matrix rank minimization,” http://arxiv.org/abs/1011.6326.
- S. Oymak, K. Mohan, M. Fazel, and B. Hassibi, “A simplified approach to recovery conditions for low-rank matrices,” in Proceedings of International Symposium on Information Theory (ISIT '11), pp. 2318–2322, August 2011.
- V. Chandrasekaran, B. Recht, P. A. Parrilo, and A. S. Willsky, “The convex geometry of linear inverse problems,” in Proceedings of the 48th Annual Allerton Conference on Communication, Control, and Computing, 2011.
- A. d'Aspremont and L. El Ghaoui, “Testing the nullspace property using semidefinite programming,” Mathematical Programming, vol. 127, no. 1, pp. 123–144, 2011.
- A. Juditsky and A. Nemirovski, “On verifiable sufficient conditions for sparse signal recovery via minimization,” Mathematical Programming, vol. 127, no. 1, pp. 57–88, 2011.
- A. Juditsky, F. Karzan, and A. Nemirovski, “Verifiable conditions of -recovery for sparse signals with sign restrictions,” Mathematical Programming, vol. 127, no. 1, pp. 89–122, 2011.
- A. Juditsky, F. Karzan, and A. S. Nemirovski, “Accuracy guarantees for -recovery,” IEEE Transactions on Information Theory, vol. 57, no. 12, pp. 7818–7839, 2011.
- G. A. Watson, “Characterization of the subdifferential of some matrix norms,” Linear Algebra and Its Applications, vol. 170, pp. 33–45, 1992.
- R. T. Rockafellar and R. J.-B. Wets, Variational Analysis, Springer, New York, NY, USA, 2nd edition, 2004.
- A. S. Lewis and H. S. Sendov, “Nonsmooth analysis of singular values. II. Applications,” Set-Valued Analysis, vol. 13, no. 3, pp. 243–264, 2005.
- Y. Zhang, “Theory of Compressive Sensing via -Minimization: A Non-RIP Analysis and Extensions,” 2008.
- E. J. Candès and Y. Plan, “Tight oracle inequalities for low-rank matrix recovery from a minimal number of noisy random measurements,” IEEE Transactions on Information Theory, vol. 57, no. 4, pp. 2342–2359, 2011.
- K. Lee and Y. Bresler, “Guaranteed minimum rank approximation from linear observations by nuclear norm minimization with an ellipsoidal constraint,” http://arxiv.org/abs/0903.4742.
- R. Meka, P. Jain, and I. S. Dhillon, “Guaranteed rank minimization via singular value projection,” http://arxiv.org/abs/0909.5457.
- K. Mohan and M. Fazel, “New restricted isometry results for noisy low-rank matrix recovery,” in Proceedings of IEEE International Symposium on Information Theory (ISIT '10), Austin, Tex, USA, June 2010.
- D. L. Donoho, “Neighborly polytopes and sparse solution of underdetermined linear equations,” Tech. Rep., 2004.