Robust compressive sensing of sparse signals: a review

@article{Carrillo2016RobustCS,
  title={Robust compressive sensing of sparse signals: a review},
  author={Rafael E. Carrillo and Ana B. Ramirez and Gonzalo R. Arce and Kenneth E. Barner and Brian M. Sadler},
  journal={EURASIP Journal on Advances in Signal Processing},
  year={2016},
  volume={2016},
  pages={1-17}
}
Compressive sensing generally relies on the ℓ2 norm for data fidelity, whereas in many applications, robust estimators are needed. Among the scenarios in which robust performance is required, applications where the sampling process is performed in the presence of impulsive noise, i.e., measurements are corrupted by outliers, are of particular importance. This article overviews robust nonlinear reconstruction strategies for sparse signals based on replacing the commonly used ℓ2 norm by M… 

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