An Exponential Filtering Based Inversion Method for Microwave Imaging

Abstract

In this paper, a new methodology based on the exponential filtering of singular values is adopted to solve the linear ill-posed problem of microwave imaging. This technique filters out the insignificant singular values and works as an efficient low pass filter to eliminate high-frequency noise from the estimated solution. Standard Tikhonov regularization has also proven to be a special case of this method. To show the effectiveness of this approach, various numerical examples of synthetic data and experimental data of Fresnel's Institute are considered for the study. The reconstruction performance of this algorithm is quantified using the mean square error (MSE) and Pearson's correlation coefficient (PCC). Further, the effect of noise on these metrics is presented. The results are compared with the standard Tikhonov regularization method, and it is observed that the proposed reconstruction algorithm provides accurate results compared to the standard Tikhonov regularization method.

Keywords

• exponential filtering
• ill-posed problem
• microwave imaging
• singular values
• tikhonov regularization