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Alternating direction method of multiplier for solving electromagnetic inverse scattering problems

Published online by Cambridge University Press:  11 March 2020

Jian Liu Open the ORCID record for Jian Liu [Opens in a new window] ,
Huilin Zhou ,
Liangbing Chen  and
Tao Ouyang Open the ORCID record for Tao Ouyang [Opens in a new window]
Jian Liu
Affiliation:
School of Information Engineering, Nanchang University, 999 Xuefu Avenue, Honggutan New District, Nanchang, Jiangxi, China
Huilin Zhou*
Affiliation:
School of Information Engineering, Nanchang University, 999 Xuefu Avenue, Honggutan New District, Nanchang, Jiangxi, China
Liangbing Chen
Affiliation:
School of Information Engineering, Nanchang University, 999 Xuefu Avenue, Honggutan New District, Nanchang, Jiangxi, China
Tao Ouyang
Affiliation:
School of Information Engineering, Nanchang University, 999 Xuefu Avenue, Honggutan New District, Nanchang, Jiangxi, China
*
Author for correspondence: Huilin Zhou, E-mail: zhouhuilin@ncu.edu.cn
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Abstract

In this paper, a novel alternating direction method of multiplier (ADMM) is proposed to solve the inverse scattering problems. The proposed method is suitable for a wide range of applications with electromagnetic detection. In order to solve the internal ill-posed problem of the integral equation and make the reconstructed images more closer to the ground truth, first, the augmented Lagrangian method is introduced to transform the complex constrained optimization problem into the extremum problem of unconstrained cost function. Therefore, two artificial regularization factors of the cost function are optimized. Then, this proposed method decomposes the unconstrained global problem in the inversion process into three linear sub-problem forms of contrast source function, contrast function, and dual variables. And the form of the updated algebra for each sub-problem is not complicated. By cross-iterating and updating contrast source function, contrast function, and dual variables, the global minimization of the cost function can be accurately found. Finally, the proposed method is compared with the existing well-known iterative method for solving the inverse scattering problem. Both the numerical and experimental tests verify the validity and accuracy of the proposed ADMM.

Keywords

Alternating direction method of multiplier (ADMM)Inverse problemsIterative methods
Type
Radar
Information
International Journal of Microwave and Wireless Technologies , Volume 12 , Special Issue 8: Special Issue EuMW 2019. Part II , October 2020 , pp. 790 - 796
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Copyright
Copyright © Cambridge University Press and the European Microwave Association 2020

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