Theoretical derivation of RIP-less compressive sensing for inverse scattering

Compressive sensing (CS) is a powerful sampling and reconstruction approach, if the unknown signal is sparse and the system matrix follows certain properties. It has been recently applied to inverse scattering problems numerous times without validating the properties of the system matrix. In this article, we seek to validate the applicability of CS to the inverse scattering problem. We formulate the problem such that the system matrix remains simple and universally applicable by using only a homogeneous background medium and then applying the CS constraints. Our analysis shows that the constraints can be satisfied under various scenarios. We then show the results of application of two such possible constraints.