Full-waveform Inversion for the Reconstruction of Electromagnetic Property Profiles Using Plane Microwaves

This study is concerned with microwave full-waveform inversion method for the reconstruction of electromagnetic properties in heterogeneous one-dimensional media. Perfectly-Matched-Layers (PMLs) are introduced as wave-absorbing boundary to reduce the originally infinite medium to a finite computational domain. The microwave full-waveform inversion method is based on an optimization approach constrained by PML-endowed Maxwell’s equations for plane electromagnetic waves. The approach attempts to minimize the objective functional consisting of the L 2 norm of a misfit between calculated and observed electric fields. Specifically, Lagrangian was constructed comprising the objective functional augmented by the PML-endowed Maxwell’s equations via Lagrange multipliers. Enforcing stationarity of the Lagrangian yields time-dependent state, adjoint, and time-independent control problems, which can be iteratively solved to update the electromagnetic properties of the medium such as permittivity and permeability. We used Fletcher-Reeves conjugate gradient method for updating the electromagnetic property profiles, and explored Tikhonov and Total Variation regularization methods to relieve the ill-posedness inherent in the fullwaveform inversion. Numerical results are reported showing the successful reconstruction of both smooth and sharply-varying electromagnetic property profiles with appropriate regularization methods.