Microwave Tomography Image Reconstruction Using Inexact Newton Backtracking Method

Abstract

This paper presents a method based on the inexact Newton backtracking method (INBM) for reconstructing microwave tomography (MWT) images. In the approach, the inexact Newton algorithm is applied to handle nonlinearity and regulate ill-posedness of MWT inverse problem in an iterative manner. The solution is gained by solving a Newton equation of the MWT inverse problem. However, instead of updating the solution with a direct regularized solution of the Newton equation, an implicit solution of the Newton equation where a forcing term is applied to control the accuracy is applied in each iteration, and backtracking method is used to ensure the convergence of the solution. Numerical simulation with several models and experimental test show that the INBM can effectively and accurately reconstruct the images of both real and imaginary parts of dielectric permittivity with a high convergence rate, as compared with the Levenberg Marquardt Method (LMM).