Linear Sampling Method

The linear sampling method (LSM) is most frequently used qualitative inversion methods, and has been numerically proven to be a fast and reliable method in many situations. This chapter discusses the LSM for the following reasons. The indicator function is easy to calculate and its physical meaning is straightforward. The chapter outlines the LSM, introducing the indicator function and the corresponding linear equation it satisfies. Although the LSM involves solving sets of linear equations when calculating the indicator function, it does not assume any linearizing approximation to the original nonlinear scattering operation, such as the Born approximation. The chapter provides physical interpretation to the mechanism of the LSM. It presents a modified LSM that is based on the multipole expansion of scattered field. The chapter explains the factorization method (FM) that is closely related to the LSM and more importantly provides the proof of the rigor of the LSM.