Compressive sensing - basics, state-of-the-art, and advances in Electromagnetic engineering

Compressive Sensing (CS) represents a powerful and flexible paradigm that applies to the solution of both sampling problems (i.e. identifying the minimum [below Nyquist´s limit] number of non-adaptive samples that enable to acquire all the informative content of a given signal) and of recovery problems (i.e., perfectly retrieving a signal from far fewer measurements than those expected by Shannon´s law). Despite its recent introduction, the application of CS methodologies within Electromagnetics has already enabled several innovative design/synthesis methodologies and retrieval/diagnosis methods to be developed. The objective of this paper is to review fundamentals of Compressive Sensing, specifically focusing on their potential applicability to Electromagnetic engineering. Afterwards, the recent advances in the state-of-the-art concerning CS in Electromagnetics will be reviewed specifically highlighting applications in directions of arrival estimation, antenna array synthesis/diagnosis, and nondestructive testing/evaluation. Some open challenges and future trends will be finally discussed.