Recovering a Clipped Signal in Sparseland

TL;DR

This paper introduces two novel algorithms for reconstructing signals that have been clipped, assuming the original signals are sparse in the frequency domain, using techniques from Compressive Sensing.

Contribution

The paper proposes two new algorithms, a modified Reweighted $ ext{l}_1$ minimization and a modified Trivial Pursuit, for recovering clipped signals based on sparsity assumptions.

Findings

Both algorithms effectively recover signals with high clipping levels.

Empirical results demonstrate the algorithms' robustness and accuracy.

The methods outperform traditional approaches in clipped signal recovery.

Abstract

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