Fractional Regularized Distorted Born Iterative Method for Permittivity Reconstruction

Abstract

In this paper, we propose a fractional regularized distorted Born iterative method (DBIM) to solve non-linear ill-posed problems of microwave imaging. Fractional regularization is a modification to Tikhonov regularization, where singular values are weighed with fractional power. As a result, the well-known effect of oversmoothing present in Tikhonov regularization is reduced, thereby the output image quality is improved. The results of this method are compared with standard DBIM using Tikhonov regularization. Various numerical examples of simulated and experimental datasets containing homogeneous as well as heterogeneous scatterers are considered to validate the effectiveness of the proposed approach. It is found that the proposed method improves the accuracy of estimated images over conventional DBIM.

Keywords

• distorted born iterative method
• fractional regularization
• ill-posed problem
• microwave imaging
• tikhonov regularization