Inverse scattering problems (ISP) in electromagnetics involves recovering the relative permittivity and geometry of the scattering object. The ISP has a wide range of applications such as breast cancer detection, subsurface imaging, non destructive testing of materials or exploring oil deposits in seabeds. The ISP generally involves estimating the integral or differential equation coefficients from scattered field data, making it highly non-linear and ill-posed. Most of the numerical techniques in ISP use the scattered field measurements implying the knowledge of the incident field and the location of the source to be known beforehand.



In this talk, we propose an inverse scattering algorithm to estimate the (1) incident and total field distribution over the entire scattering domain, (2) relative permittivity and geometrical shape of the scattering object using only a few total field measurements. Our method consists of two stages (I) field mapping (II) inverse imaging. To estimate the total and incident field over the entire scattering domain, we propose Total field - Compressive sensing based subspace optimization method (TCS-SOM). We also make use of a sampling scheme called 'Maximal Projection of Minimum Eigenspace' (MPME) to determine best locations for the total field measurements. In stage II we estimate the permittivity and geometry of the scattering object using the two-fold subspace optimization method (TSOM). We evaluate the performance of our algorithm on synthetically generated homogeneous and heterogeneous objects as well as the experimental Fresnel data set.