Simple bounds for recovering low-complexity models

@article{Cands2013SimpleBF,
  title={Simple bounds for recovering low-complexity models},
  author={Emmanuel J. Cand{\`e}s and Benjamin Recht},
  journal={Math. Program.},
  year={2013},
  volume={141},
  pages={577-589}
}
This note presents a unified analysis of the recovery of simple objects from random linear measurements. When the linear functionals are Gaussian, we show that an s-sparse vector in R can be efficiently recovered from 2s log n measurements with high probability and a rank r, n×n matrix can be efficiently recovered from r(6n − 5r) measurements with high probability. For sparse vectors, this is within an additive factor of the best known nonasymptotic bounds. For low-rank matrices, this matches… CONTINUE READING
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