SubspaceMethods for Solving Electromagnetic Inverse Scattering Problems

Krishna Agarwal, Xudong Chen, Yu Zhong
2010 Methods and Applications of Analysis  
This paper presents a survey of the subspace methods and their applications to electromagnetic inverse scattering problems. Subspace methods can be applied to reconstruct both small scatterers and extended scatterers, with the advantages of fast speed, good stability, and higher resolution. For inverse scattering problems involving small scatterers, the multiple signal classification method is used to determine the locations of scatterers and then the least-squares method is used to calculate
more » ... e scattering strengths of scatterers. For inverse scattering problems involving extended scatterers, the subspace-based optimization method is used to reconstruct the refractive index of scatterers. pore, 117576. 407 2.2. Mathematical foundations. The key of the theoretical foundation lies in the injectivity of the so called current-to-field mapping operator, which is a map from the induced current (or secondary source) to the measured scattered field. Proposition. Define the operator Γ: C 3M to C 3N by (5) λ → [(Λλ)(r ′ 1 )] T , [(Λλ)(r ′ 2 )] T , . . . , [(Λλ)(r ′ N )] T T .
doi:10.4310/maa.2010.v17.n4.a6 fatcat:2vzu5sy4kjgtrhiv5rra6lbtea