= Robust null space property
{title2=$\|h_S\|_2\le\rho\|h_{S^c}\|_1/\sqrt s+\tau\|Ah\|_2$}
The displayed property holds for every $h$ and every $|S|\le s$, with $0\le\rho<1$ and $\tau>0$. It converts the cone inequality from <basis pursuit> minimality and the tube inequality from noisy feasibility into a two-constant bound $\|\hat x-x_0\|_2\le C_1\eta+C_2\sigma_s(x_0)/\sqrt s$. Both constants are needed in general; a fixed coefficient one on the approximation term does not follow.
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