Complexity issues in inverse scattering problems

Summary form only given. The paper overviews the inverse scattering problem. It begins by discussing linear inverse scattering problems followed by nonlinear inverse scattering problems. Popular linear inverse scattering methods are diffraction tomography, holographic method, synthetic aperture radar method, and Born inversion method. These methods generally do not account for multiple scattering of the wave field inside a scatterer. Though simple, certain physics is missed in these methods. To account for multiple scattering, one has to resort to nonlinear inverse scattering methods. This can be achieved via the use of the Born iterative method, the distorted Born iterative method, or the Newton-type methods. The computational complexity of linear inverse scattering methods such as diffraction tomography is analyzed, and compared with the computational complexity of the nonlinear inverse scattering method, such as the Born iterative and distorted Born iterative methods. It is essential that fast forward solvers be used to solve the forward scattering problem for the nonlinear inverse scattering methods, since the bottleneck in these methods is the solution of the forward solver.