Decoding by linear programming

@article{Cands2005DecodingBL,
  title={Decoding by linear programming},
  author={Emmanuel J. Cand{\`e}s and Terence Tao},
  journal={IEEE Transactions on Information Theory},
  year={2005},
  volume={51},
  pages={4203-4215}
}
  • E. Candès, T. Tao
  • Published 15 February 2005
  • Computer Science
  • IEEE Transactions on Information Theory
This paper considers a natural error correcting problem with real valued input/output. We wish to recover an input vector f/spl isin/R/sup n/ from corrupted measurements y=Af+e. Here, A is an m by n (coding) matrix and e is an arbitrary and unknown vector of errors. Is it possible to recover f exactly from the data y? We prove that under suitable conditions on the coding matrix A, the input f is the unique solution to the /spl lscr//sub 1/-minimization problem (/spl par/x/spl par//sub /spl lscr… 

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