IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
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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 l1-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.