Inexact Newton backtracking method for solving microwave tomography inverse problem

An inexact Newton backtracking method (INBM) has been developed to obtain a stable solution of microwave tomography inverse problem. The problem is solved iteratively by linearization. Instead of finding direct regularized solution of linear ill-posed problem, iterative regulated approximation solver in term of INBM is proposed as a new alternative method. The iteration is guarded using a forcing term which is determined on the nonlinear and linearized steps of the microwave inverse problem. The method proposed is tested using numerical examples and experimental data. The quality of proposed method is evaluated by comparing it with the Levenberg Marquardt (LM) method.