Microwave imaging using the finite-element method and a sensitivity analysis approach

A method for reconstructing the constitutive parameters of two-dimensional (2-D) penetrable scatterers from scattered field measurements is presented. This method is based on the differential formulation of the forward scatte ring problem, which is solved by applying the finite-element method (FEM). Given a set of scattered held measurements, the objective is to minimize a cost function which consists of two terms. The first is the standard error term, which is related to the measurements and their estimates, while the s econd term which is related to the Tikhonov regularization, is used to heal the ill posedness of the inverse problem. The iterative Polak-Ribiere nonl inear conjugate gradient algorithm is applied to the minimization of the co st function. During each iteration of the algorithm, the direction of corre ction is computed by using a sensitivity analysis approach, which is carrie d out by an elaborate finite-element scheme. The adoption of the finite-ele ment method results in sparse systems of equations, while the computational burden is further reduced by applying the adjoint state vector methodology . Finally, a microwave medical imaging application, which is related to the detection of proliferated bone marrow, is examined, while the robustness o f the proposed technique in the presence of noise and far different regular ization levels is investigated.