Compressive Sensing for Inverse Scattering

Compressive sensing is a new field in signal processing and applied mathematics. It allows one to simultaneously sample and compress signals which are known to have a sparse representation in a known basis or dictionary along with the subsequent recovery by linear programming (requiring polynomial (P) time) of the original signals with low or no error [1–3]. Compressive measurements or samples are non-adaptive, possibly random linear projections of the given signal. Most importantly, sparsity arises in many physical signals, hence this approach is of significant importance. The results in this area apply to biomedical imaging, astronomy, single-pixel photography, and many other disciplines.