Stable signal recovery from incomplete and inaccurate measurements

@article{Cands2005StableSR,
  title={Stable signal recovery from incomplete and inaccurate measurements},
  author={E. Cand{\`e}s and J. Romberg and T. Tao},
  journal={Communications on Pure and Applied Mathematics},
  year={2005},
  volume={59},
  pages={1207-1223}
}
  • E. Candès, J. Romberg, T. Tao
  • Published 2005
  • Physics, Mathematics
  • Communications on Pure and Applied Mathematics
  • Suppose we wish to recover a vector x_0 Є R^m (e.g., a digital signal or image) from incomplete and contaminated observations y = Ax_0 + e; A is an 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 l_(1-)regularization problem min ‖x‖l_1 subject to ‖Ax - y‖l(2) ≤ Є, where Є is the size of the error term e. We show that if A obeys a uniform uncertainty… CONTINUE READING
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