The Finite-Element Method Contrast Source Inversion Algorithm for 2D Transverse Electric Vectorial Problems

The contrast source inversion algorithm is formulated using the finite-element method for two-dimensional transverse electric microwave imaging problems. Edge-based triangular elements with vector basis functions are utilized to solve the TE electromagnetic problem. A single finite-element method (FEM) mesh is used to model both the electric field as well as the contrast-source and contrast variables used in the inverse problem. The electromagnetic field is modeled by taking the unknown values to be the tangential components of the transverse electric field along the edges of each triangular element. The unknown contrast-source and contrast variables are located at the centroids of every triangular element of the same FEM mesh, but only inside the imaging domain. The adaptation of the FEM-contrast source inversion (FEM-CSI) algorithm to 2D-TE problems on such an arbitrary mesh requires the implementation of special transformation operators which are presented herein. The algorithm´s capabilities are demonstrated by inverting the Fresnel experimental TE datasets as well as synthetically generated data.