Compressive sensing for multi-static scattering analysis

Compressive sensing (CS) is a framework in which one attempts to measure a signal in a compressive mode, implying that fewer total measurements are required vis-à-vis direct sampling methods. Compressive sensing exploits the fact that the signal of interest is compressible in some basis, and the CS measurements correspond to projections (typically random projections) performed on the basisfunction coefficients. In this paper we demonstrate that when a target is situated in the presence of a complicated background medium, the frequency-dependent multi-static fields scattered from the target may be measured in a CS manner; the CS measurements are performed by exploiting the natural wave propagation of the incident and scattered fields. This phenomenon is related to the field of time reversal, to which relationships are made. We also demonstrate that the CS framework may be employed to reduce the number of computations required in numerical linear scattering analyses. Example scattering results are presented for multi-static electromagnetic scattering, and application areas are also discussed.