Tight oracle bounds for low-rank matrix recovery from a minimal number of random measurements

作者: Yaniv Plan , Emmanuel J. Candès

DOI:

关键词: Matrix splittingInteger matrixRestricted isometry propertyMathematicsSquare matrixMatrix multiplicationNonnegative matrixDiscrete mathematicsMatrix (mathematics)Matrix analysis

摘要: … value of a certain ‘oracle’ error bound. In Section 2.4, we present an error bound handling the case when M has full rank but is well approximated by a low-rank matrix. Section 3 …

参考文章(25)
David Gross, Yi-Kai Liu, Steven T. Flammia, Stephen Becker, Jens Eisert, Quantum state tomography via compressed sensing. Physical Review Letters. ,vol. 105, pp. 150401- ,(2010) , 10.1103/PHYSREVLETT.105.150401
P. Massart, B. Laurent, Adaptive estimation of a quadratic functional by model selection Annals of Statistics. ,vol. 28, pp. 1302- 1338 ,(2000) , 10.1214/AOS/1015957395
Raghunandan H. Keshavan, Sewoong Oh, Andrea Montanari, Matrix completion from a few entries 2009 IEEE International Symposium on Information Theory. pp. 324- 328 ,(2009) , 10.1109/ISIT.2009.5205567
Shiqian Ma, Donald Goldfarb, Lifeng Chen, Fixed point and Bregman iterative methods for matrix rank minimization Mathematical Programming. ,vol. 128, pp. 321- 353 ,(2011) , 10.1007/S10107-009-0306-5
Emmanuel Candes, Terence Tao, None, The Dantzig selector: Statistical estimation when p is much larger than n Annals of Statistics. ,vol. 35, pp. 2313- 2351 ,(2007) , 10.1214/009053606000001523
P. Wojtaszczyk, Stability and Instance Optimality for Gaussian Measurements in Compressed Sensing Foundations of Computational Mathematics. ,vol. 10, pp. 1- 13 ,(2010) , 10.1007/S10208-009-9046-4
Dimitris Achlioptas, Database-friendly random projections: Johnson-Lindenstrauss with binary coins Journal of Computer and System Sciences. ,vol. 66, pp. 671- 687 ,(2003) , 10.1016/S0022-0000(03)00025-4
Emmanuel J Candes, Yaniv Plan, Matrix Completion With Noise Proceedings of the IEEE. ,vol. 98, pp. 925- 936 ,(2010) , 10.1109/JPROC.2009.2035722
M. Fazel, E. Candes, B. Recht, P. Parrilo, Compressed sensing and robust recovery of low rank matrices asilomar conference on signals, systems and computers. pp. 1043- 1047 ,(2008) , 10.1109/ACSSC.2008.5074571
Benjamin Recht, Maryam Fazel, Pablo A. Parrilo, Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization Siam Review. ,vol. 52, pp. 471- 501 ,(2010) , 10.1137/070697835