  Consider the compressed sensing setup where the support $s^*$ of an
$m$-sparse $d$-dimensional signal $x$ is to be recovered from $n$ linear
measurements with a given algorithm. Suppose that the measurements are such
that the algorithm does not guarantee perfect support recovery and that true
features may be missed. Can they efficiently be retrieved? This paper addresses
this question through a simple error-correction module referred to as LiRE.
LiRE takes as input an estimate $s_{in}$ of the true support $s^*$, and outputs
a refined support estimate $s_{out}$. In the noiseless measurement setup,
sufficient conditions are established under which LiRE is guaranteed to recover
the entire support, that is $s_{out}$ contains $s^*$. These conditions imply,
for instance, that in the high-dimensional regime LiRE can correct a sublinear
in $m$ number of errors made by Orthogonal Matching Pursuit (OMP). The
computational complexity of LiRE is $O(mnd)$. Experimental results with random
Gaussian design matrices show that LiRE substantially reduces the number of
measurements needed for perfect support recovery via Compressive Sampling
Matching Pursuit, Basis Pursuit (BP), and OMP. Interestingly, adding LiRE to
OMP yields a support recovery procedure that is more accurate and significantly
faster than BP. This observation carries over in the noisy measurement setup.
Finally, as a standalone support recovery algorithm with a random
initialization, experiments show that LiRE's reconstruction performance lies
between OMP and BP. These results suggest that LiRE may be used generically, on
top of any suboptimal baseline support recovery algorithm, to improve support
recovery or to operate with a smaller number of measurements, at the cost of a
relatively small computational overhead. Alternatively, LiRE may be used as a
standalone support recovery algorithm that is competitive with respect to OMP.
