Compressive sensing as a new paradigm in wave scattering and propagation

The paradigm of Compressive Sensing (CS) has emerged in the last few years as a flexible and powerful methodological strategy to address synthesis and analysis problems arising in wave scattering and propagation engineering. The success of CS techniques is motivated by several factors, including (i) their capability to address sampling/recovery problems overcoming the classical Nyquist/Shannon limits, (ii) their flexibility and ease of adaptation to several different scenarios, including array design, direction-of-arrival estimation, microwave and radar imaging, (iii) the availability of powerful, effective, and numerically efficient implementations of CS sampling and retrieval algorithms. Accordingly, and despite their relatively recent introduction, the research on the development, application, generalization, and customization of CS techniques has already become one of the most active areas within wave scattering and propagation engineering. Within this framework, this invited paper is aimed at illustrating the fundamental features of Compressive Sensing as well as at discussing its potential applicability in wave scattering and propagation problems also through a review of the recent advances in the state-of-the-art concerning CS. Some current research trends and open challenges will be also discussed.