Stable signal recovery from incomplete and inaccurate measurements

@inproceedings{Cands2006StableSR,
  title={Stable signal recovery from incomplete and inaccurate measurements},
  author={Emmanuel J. Cand{\`e}s and Justin Romberg and Terence Tao},
  year={2006}
}
Suppose we wish to recover an n-dimensional real-valued vector x_0 (e.g. a digital signal or image) from incomplete and contaminated observations y = A x_0 + e; A is a n by m matrix with far fewer rows than columns (n<<m) and e is an error term. Is it possible to recover x_0 accurately based on the data y? To recover x_0, we consider the solution x* to the l1-regularization problem min \|x\|_1 subject to \|Ax-y\|_2<= epsilon, where epsilon is the size of the error term e. We show that if A… CONTINUE READING
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