Recovery of sparse signals from amplitude-limited sample sets

Motivated by the compelling application of interference mitigation at wideband receivers in wireless communication and sensing systems, we consider the recovery of a frequency-sparse signal from samples of small magnitude. The standard ℓ₁-norm minimization results in an inadequate signal-dependent recovery performance, and hence we introduce three techniques to improve the quality of recovery. The performance of each of these three techniques is characterized through numerical simulations, from which we conclude that each of the proposed techniques show the promise of substantially improving recovery performance.