Stable signal recovery from incomplete and inaccurate measurements

@article{Cands2005StableSR,
  title={Stable signal recovery from incomplete and inaccurate measurements},
  author={Emmanuel J. Cand{\`e}s and Justin K. Romberg and Terence Tao},
  journal={Communications on Pure and Applied Mathematics},
  year={2005},
  volume={59}
}
Suppose we wish to recover a vector x0 ∈ ℝ𝓂 (e.g., a digital signal or image) from incomplete and contaminated observations y = A x0 + e; A is an 𝓃 Γ— 𝓂 matrix with far fewer rows than columns (𝓃 β‰ͺ 𝓂) and e is an error term. Is it possible to recover x0 accurately based on the data y?Β 
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