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

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
$L_{1/2}$
regularization] which effectively alleviates the ill-posedness, a new cost function is established. FBE regularization is directly applied to modeling, and
$L_{1/2}$
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.