Imaging of unknown targets inside inhomogeneous backgrounds by means of qualitative inverse scattering

In this paper a new formulation of the Linear Sampling Method, called the no\u2013Sampling Linear Sampling Method, is applied to the imaging and detection of unknown scatterers located inside an inhomogeneous background. Namely, by following a previous work by Colton and Monk, a modified far\u2013 field equation is used, which allows one for using line current sources and near\u2013 field measurements. The Green\u2019s function of the inhomogeneous background is numerically computed and used as the right hand side of the modified far\u2013field equation. The proposed method is then applied to two different scenarios: the detection of breast tumors and the imaging of cracks inside a dielectric slab. A numerical analysis of the method capabilities is performed when the model parameters are not exactly known