Generally inverse scattering in electromagnetic is a problem including reconstruction of unknown objects in terms of shape and material. Some applications of this issue are imaging of unknown objects and locating by using scattered fields and Maxwell’s equations. There are two different methods for solving inverse scattering problems which one may group them under qualitative and quantitative titles. In the later one, there is a function that must be optimized and there is some iterative process.however, qualitative methods as the essential topic of this thesis, are investigated such inverse problems in applied mathematics. More speed of response while less needed priori information are the benefits of this method. Nevertheless, it has less precision toward quantitative methods. The linear sampling method (LSM) that is investigated in this project, is taking into consideration scientists that are working in Fields and Waves research area in the last years. The structure of this problem is based on one linear integral equation (IE) which is not required to weak approximation like Born one. In this thesis at first we will study and analyze the linear sampling method mathematically, then we use it as a solution for shaping reconstruction of unknown scatterer. In addition, we will investigate distinguished effective parameters in the shape reconstruction quality such as transmitter and receiver antennas number, frequency and external factors such as noise. In most important part of this project ,we will comprise the effect of incidence wave polarization in the quality of shape reconstruction in penetrable and impenetrable (Dielectric and Perfect Electric Conductor).Also we will present a new technique to optimize performance of reconstruction based on frequency and polarization as a key point. Further we discuss some other linear sampling method abilities the same as multi-scatterer reconstruction susceptibility in appropriate conditions. Keywords: Forward and Inverse Scattering, Linear Sampling Method, Ill-Posed Problems Singular Value Decomposition(SVD), Polarization Hybrid and Multi-Frequency Technique
