Fast microwave through wall imaging method with inhomogeneous background based on levenberg-marquardt algorithm

In this paper, a fast solution for microwave through wall imaging (TWI) with nonlinear inversion is proposed to reconstruct the unknown targets embedded in an inhomogeneous background medium. We treat inhomogeneous background, i.e., the wall around bounded in a finite domain as a known scatterer, which has the advantage of avoiding the time-consuming calculation of inhomogeneous background Green's function. Under this scheme, a new approach under the framework of difference integral equation model, i.e., difference Lippmann-Schwinger integral equation, with modified enhanced Levenberg-Marquardt algorithm is proposed. In particular, we used a hybrid regularized technique, i.e., generalized cross-validation and truncated singular value decomposition, to stabilize the inversion. It is shown that the proposed method runs fast and is stable in presence of noise. Also, it is able to alleviate the nonlinearity and reconstruct unknown scatterers of high contrast with respect to the background. Both the numerical and experimental TWI tests validate the efficiency of the proposed inversion method.