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Reconstruction of Noisy Electromagnetic Fields by Means of Compressive Sensing Theory

This paper deals with the emerging compressive sensing theory applied to reconstruction of the spatial distribution of a magnetic/electric field corrupted by additive noise. A typical application could be monitoring of the electromagnetic environment of a wide area where an electromagnetic source or susceptible electric/electronic apparatus are located. To this end, wireless field sensors can be assumed to be deployed over the monitored area and used to provide spatial samples of the field. The main advantages offered by compressive sensing include a number of sensors much smaller than the number foreseen by the traditional Shannon sampling theory, and the possibility to resort to nonuniform distribution of the sensors. A specific numerical analysis is devoted to investigate the effects of additive noise introduced by wireless technology, including quantization noise featuring low-cost sensors, environment and electronic noise.