Exploiting compressive sensing in microwave tomography and inverse scattering

Compressive sensing (CS) has impressive potentialities in inverse scattering problems, owing to the intrinsic nature of the targets to be retrieved in actual applications. However, inverse scattering problems are nonlinear, whereas the CS theory is well established only for linear recovery problems. Hence, efforts are required towards the actual exploitation of CS in inverse scattering based applications. As a step in this direction, we explore herein the performances of a solution procedure based on the joint exploitation of CS and a recently introduced inversion approach in which, by means of proper pre-processing techniques, the problem can be reduced to a linear problem. Notably, the underlying approximation holds true for a set of cases that largely exceeds the range of validity of the Born approximation.