Subspace-Based Distorted-Born Iterative Method for Solving Inverse Scattering Problems

The electromagnetic inverse scattering problem can be effectively handled by means of the so-called distorted-Born iterative method (DBIM). A new method, denoted as the subspace-based DBIM (S-DBIM), is proposed. It updates the Green's function for the inhomogeneous background at each step of the iterative procedure, like DBIM. By linearly retrieving the deterministic subspace of the induced current, the S-DBIM estimates the total electric field more accurately than the DBIM does and thus exhibits a faster convergence speed. To avoid the computationally demanding and arguably hard choice of the optimal Tikhonov regularization term involved in the procedure, a second version of S-DBIM, which is more robust against noise and has faster convergence, is also proposed. Thorough numerical simulations show that both versions of S-DBIM achieve super-resolved retrievals of the benchmark "Austria" profile.