  In many data acquisition systems it is common to observe signals whose
amplitudes have been clipped. We present two new algorithms for recovering a
clipped signal by leveraging the model assumption that the underlying signal is
sparse in the frequency domain. Both algorithms employ ideas commonly used in
the field of Compressive Sensing; the first is a modified version of Reweighted
$\ell_1$ minimization, and the second is a modification of a simple greedy
algorithm known as Trivial Pursuit. An empirical investigation shows that both
approaches can recover signals with significant levels of clipping
