Robust principal component analysis?
- E. Candès, Xiaodong Li, Yi Ma, John Wright
- Computer ScienceJACM
- 18 December 2009
It is proved that under some suitable assumptions, it is possible to recover both the low-rank and the sparse components exactly by solving a very convenient convex program called Principal Component Pursuit; among all feasible decompositions, this suggests the possibility of a principled approach to robust principal component analysis.
Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
- E. Candès, J. Romberg, T. Tao
- Computer ScienceIEEE Transactions on Information Theory
- 10 September 2004
It is shown how one can reconstruct a piecewise constant object from incomplete frequency samples - provided that the number of jumps (discontinuities) obeys the condition above - by minimizing other convex functionals such as the total variation of f.
Decoding by linear programming
F can be recovered exactly by solving a simple convex optimization problem (which one can recast as a linear program) and numerical experiments suggest that this recovery procedure works unreasonably well; f is recovered exactly even in situations where a significant fraction of the output is corrupted.
An Introduction To Compressive Sampling
The theory of compressive sampling, also known as compressed sensing or CS, is surveyed, a novel sensing/sampling paradigm that goes against the common wisdom in data acquisition.
Exact Matrix Completion via Convex Optimization
It is proved that one can perfectly recover most low-rank matrices from what appears to be an incomplete set of entries, and that objects other than signals and images can be perfectly reconstructed from very limited information.
Enhancing Sparsity by Reweighted ℓ1 Minimization
- E. Candès, M. Wakin, Stephen P. Boyd
- Computer Science
- 10 November 2007
A novel method for sparse signal recovery that in many situations outperforms ℓ1 minimization in the sense that substantially fewer measurements are needed for exact recovery.
Stable signal recovery from incomplete and inaccurate measurements
- E. Candès, J. Romberg, T. Tao
- Computer Science
- 3 March 2005
It is shown that it is possible to recover x0 accurately based on the data y from incomplete and contaminated observations.
A Singular Value Thresholding Algorithm for Matrix Completion
- Jian-Feng Cai, E. Candès, Zuowei Shen
- Computer ScienceSIAM Journal on Optimization
- 18 October 2008
This paper develops a simple first-order and easy-to-implement algorithm that is extremely efficient at addressing problems in which the optimal solution has low rank, and develops a framework in which one can understand these algorithms in terms of well-known Lagrange multiplier algorithms.
The Dantzig selector: Statistical estimation when P is much larger than n
- E. Candès, Terence Tao
- Computer Science
- 5 June 2005
Is it possible to estimate β reliably based on the noisy data y?
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