In fact, this is like an aggressive continuation strategy in which we attempt to solve the nonconvex optimization problem in (\[formu:criterion3\]) at decreasing values of $\epsilon$. The convergence of the reweighted algorithm is retained if we fix $\epsilon$ when it is sufficiently small. In the ADMM implementation, we can further accelerate the algorithm by adopting loose convergence criteria in the first few iterations of RAM. Finally, note that we need to trade off the algorithm performance for computational time by keeping the number of iterations of RAM being small.

Numerical Simulations {#sec:simulation}
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Implementation Details of RAM
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In our implementation of RAM, we first scale the measurements and the noise such that $\frobn{\m{Y}_{\m{\Omega}}}^2=M$ (the noise energy becomes $\eta'^2=\frac{M\eta^2}{\frobn{\m{Y}}^2}$) and compensate the recovery afterwards. We start with $\m{u}_0=\m{0}$ and $\epsilon=1$ as default. We halve $\epsilon$ when beginning a new iteration until $\epsilon=\frac{1}{2^{10}}$ or $\epsilon<\frac{\eta'^2}{10}$. When $\eta=0$ we terminate RAM if the relative change (in the Frobenius norm) of the solution $\m{Y}^*$ at two consecutive iterations is less than $10^{-6}$ or the maximum number of iterations, set to 20, is reached. All simulations are carried out in Matlab v.8.1.0 on a PC with a Windows 7 system and a 3.4 GHz 