Robust compressive sensing of sparse signals: a review

• Published in: EURASIP Journal on Advances in Signal Processing Vol. 2016; no. 1; pp. 1 - 17
• Main Authors: Carrillo, Rafael E., Ramirez, Ana B., Arce, Gonzalo R., Barner, Kenneth E., Sadler, Brian M.
• Format: Journal Article Book Review
• Language: English
• Published: Cham Springer International Publishing 19-10-2016; Springer; Springer Nature B.V
• Subjects: Detection; Engineering; Estimators; Noise; Nonlinear Signal and Image Processing - A Special Issue in Honour of Giovanni L. Sicuranza on his Seventy-Fifth Birthday; Nonlinearity; Norms; Quantum Information Technology; Review; Sampling; Signal processing; Signal,Image and Speech Processing; Spintronics; Strategy; Sampling methods; Impulsive noise; Signal reconstruction; Compressed sensing; Nonlinear estimation
• ISSN: 1687-6180; 1687-6172; 1687-6180
• DOI: 10.1186/s13634-016-0404-5

Compressive sensing generally relies on the
ℓ
2
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
ℓ
2
norm by M-estimators as data fidelity functions. The derived methods outperform existing compressed sensing techniques in impulsive environments, while achieving good performance in light-tailed environments, thus offering a robust framework for CS.