Compressive sensing as applied to inverse problems for imaging: theory, applications, current trends, and open challenges

Compressive sensing (CS) is currently one the most active research fields in information engineering and science. The flexibility, robustness, accuracy, effectiveness, and sound theory behind such a paradigm have motivated a great interest in developing and applying CS to many domains, including inverse scattering. Unfortunately, electromagnetic imaging problems have some unique theoretical features that prevent a straightforward exploitation of CS tools. Therefore, suitable CS-based strategies must be considered in such a framework.