Phaseless retrieval of point-like scatterers: Theoretical foundation of the subspace method

This paper investigates the theoretical foundation of subspace based method for solving electromagnetic inverse scattering problem of locating point-like scatterers and retrieving their polarization tensors, using phaseless scattering data. The key step is to prove the injectivity of a coefficient-to-intensity mapping operator. As corollaries, the multiple-signal-classification method can be used to locate point-like scatterers, and polarization tensors can be non-iteratively retrieved. This paper provides the theoretical foundation to recently published phaseless retrieval work. Finally, the advantage and disadvantage of the subspace method are discussed.