Stable signal recovery from incomplete and inaccurate measurements

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 × 𝓂 matrix with far fewer rows than columns (𝓃 ≪ 𝓂) and e is an error term. Is it possible to recover x0 accurately based on the data y?

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