Compressed Sensing for the Detection and Positioning of Dielectric Objects Inside Metal Enclosures by Means of Microwave Measurements

Based on compressed sensing and microwave measurements, we present a procedure for the detection and positioning of dielectric objects inside a metal enclosure, where the number of objects is unknown but assumed to be limited. The formulation features a convex quadratic optimization problem with 1-norm regularization, which allows for rapid detection and positioning given a precomputed dictionary. The dictionary consists of the scattering parameters computed from a single scattering object placed at the grid points of a structured grid that covers the entire measurement region. We test our method experimentally in a microwave measurement system that features a measurement region with a diameter of 11.6 cm. The measurement region is encircled by six aperture antennas, where each aperture is the end-opening of a rectangular waveguide operated from 2.7 to 4.2 GHz. We use acrylic-glass cylinders of radius 5.2 mm as scatterers and find that the compressed sensing method can correctly detect at least up to five scatterers with an average positioning accuracy of 3 mm. In addition, we investigate the performance of the method with respect to scarcity of data, where we omit scattering parameters or frequency points.