Performance of 2D Compressive Sensing on Wide-Beam Through-the-Wall Imaging

Compressive sensing has become an accepted and powerful alternative to conventional data sampling schemes. Hardware simplicity, data, and measurement time reduction and simplified imagery are some of its most attractive strengths. This work aims at exploring the possibilities of using sparse vector recovery theory for actual engineering and defense- and security-oriented applications. Conventional through-the-wall imaging using a synthetic aperture configuration can also take advantage of compressive sensing by reducing data acquisition rates and omitting certain azimuth scanning positions. An ultra-wideband stepped frequency system carrying wide beam antennas performs through-the-wall imaging of a real scene, including a hollow concrete block wall and a corner reflector behind it. Random downsampling rates lower than those announced by Nyquist’s theorem both in the fast-time and azimuth domains are studied, as well as downsampling limitations for accurate imaging. Separate dictionaries are considered and modeled depending on the objects to be reconstructed: walls or point targets. Results show that an easy interpretation of through-the-wall scenes using the -norm and orthogonal matching pursuit algorithms is possible thanks to the simplification of the reconstructed scene, for which only as low as 25% of the conventional SAR data are needed. 1. Introduction Previous research studies have explored numerous applications of through-the-wall imaging (TWI) in domains which can exploit the convenient penetration capabilities of the 1–5？GHz frequency band in most nonmetal building construction materials [1, 2]. Indeed, being able to perform nondestructive inspection of objects behind a solid wall is a noteworthy application. The literature on TWI widely copes with object or human detection—either moving [3–5] or static [6, 7]. Among others, military, law enforcement, and security operations have already taken profit of the satisfactory performance of TWI. Although most of the studies suggest using an active TWI approach wherever needed, some authors opt for adequately processing opportunistic signals in the surroundings of the scene such as widespread GSM [8] or wireless networks [9]. Despite presenting interesting wall penetration properties, the noncooperative—thus passive—nature of these approaches cannot assure complete reliability and availability, and consequently, an active approach is preferred. Synthetic Aperture Radar (SAR) allows competitive TWI using rather common antennas with wide beams and simple out-of-focus data acquisition. Thanks to