Alternating direction method of multiplier for solving electromagnetic inverse scattering problems

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.

An inverse scattering reconstruction method for perfect electric conductor‐dielectric hybrid target based on physics‐inspired network

“…Subsequently, Wang et al [22] built on this model-driven approach and proposed a physics-inspired deep unrolling network. Based on the alternating direction method of multipliers [27], the method decomposes the iterative process into four quasi-linear subproblems, alternately updating the intermediate variables with neural networks, in a way that achieves the simultaneous optimization of multiple variables and accurately reconstructs the target. However, such model-driven networks are mostly used for DIE targets only.…”

Determination of electromagnetic source localization with factorization method

“…These methods can be collected under two main titles as quantitative and qualitative MWI techniques. Quantitative MWI methods such as the truncated singular values decomposition [10,11], the contrast source inversion [12], and the alternating direction method of multiplier [13] propose a reconstruction of electrical and structural properties of targets. Such methods can recover the shape, location, and distribution of the electrical parameters of the considered area.…”