Proximal Alternating Direction Method of Multipliers for Solving 3-D Electromagnetic Inverse Scattering Problems

• Published in: IEEE transactions on microwave theory and techniques Vol. 72; no. 2; pp. 981 - 995
• Main Authors: Liu, Yufeng, Zhu, Zhibin, Wang, Shuo, Zhao, Ruwen, Zhang, Benxin
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.02.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: 3-D inverse scattering problems (ISPs); Algorithms; Contraction integral equation (CIE) model; Cost function; Fourier bases-expansion (FBE); ill-posedness; Integral equations; Inverse problems; Inverse scattering; L1/2 regularization; Mathematical models; Modelling; Multipliers; nonlinearity; proximal alternating direction method of multipliers (PADMM); Regularization; Solid modeling; Tensors; Three-dimensional displays
• ISSN: 0018-9480; 1557-9670
• DOI: 10.1109/TMTT.2023.3298203

In this article, based on the contraction integral equation (CIE) model which effectively reduces the nonlinearity of the 3-D inverse scattering problems (ISPs) and hybrid regularization technique [Fourier bases-expansion (FBE) regularization and <inline-formula> <tex-math notation="LaTeX">L_{1/2} </tex-math></inline-formula> regularization] which effectively alleviates the ill-posedness, a new cost function is established. FBE regularization is directly applied to modeling, and <inline-formula> <tex-math notation="LaTeX">L_{1/2} </tex-math></inline-formula> regularization is applied to unknowns to achieve more sparse solutions and better inversion efficiency. Furthermore, a weight adjustment nested scheme (WA-NS) is used in the inversion modeling process. Though the new cost function is nonconvex, nonsmooth, and non-Lipschitz, an efficient proximal alternating direction method of multipliers (PADMM) is proposed to solve the corresponding optimization problem. The accuracy of the inversion algorithm is verified by experiments on synthetic and experimental data.