Sparse Expansions Using Physical and Polynomial Basis Functions for Compressed Sensing of Frequency Domain EM Scattering

A scattering center model is proposed for providing a very efficient sparse expansion for radar scattering data based on physical and polynomial functions to represent the frequency dependence of the amplitude. Simple scattering centers are very inefficient in situations where a low residual error is needed in reconstructing the data from the sparse expansion. It is shown that the new approach overcomes errors associated with grid mismatch, overlapping scattering centers, and model discrepancies. Compressed sensing is applied to extract the sparse expansion with a greatly reduced set of samples. Convergence of the sparse expansion is demonstrated for selected targets.