Efficient Jacobian Computation for High-Frequency Inverse Problem Solutions

Response Jacobians (gradients) can significantly improve the convergence of the reconstruction algorithms used in inverse problem solutions. However, the lack of efficient methods for computing response Jacobians has limited the applications of gradient-based algorithms to inverse problems when 3D numerical electromagnetic (EM) forward solvers are used. In this paper, we present the most recent developments in the self-adjoint sensitivity analysis (SASA) method for the computation of the response Jacobians with time-domain EM solvers. To our knowledge, our approach is the most computationally efficient method for EM sensitivity analysis with time-varying field solutions. It can deal with all types of optimizable (model) parameters, material parameters and shape parameters, of both dielectric and conducting objects in the structure of interest. Verification is carried out through the analysis of lossy dielectric structures.