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 ℓ1 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
@article{arxiv.1110.5063,
title = {Recovering a Clipped Signal in Sparseland},
author = {Alejandro J. Weinstein and Michael B. Wakin},
journal= {arXiv preprint arXiv:1110.5063},
year = {2011}
}