Inverse Scattering by Compressive Sensing and Signal Subspace Methods

This work, composed of the present conference paper plus the associated talk at the conference, explores new paradigms for both active and passive target localization, imaging and inverse scattering that are based on both signal subspace and compressive sensing methods (being of particular interest the basis pursuit problem). The signal subspace component provides signal-subspace-based imaging methods applicable to spatially extended targets. The compressive sensing approach is developed as a recent alternative to the solution of a broad class of target parameter estimation problems. Our research program emphasizes certain inverse source and scattering problems, for which one has a priori knowledge on sparsity of the sources, scatterers and their fields, in physically- derived representational dictionaries for those signals. The derived theory and algorithms are illustrated with computer simulations (the full account of which is left for the talk).