混合正则化方法用于二维逆散射问题

First, a new hybrid regularization method (nonconvex regularization and modified Fourier bases-expansion regularization) is proposed based on the two-dimensional inverse scattering problem to alleviate ill-posedness. Inspired by the successful applications of nonconvex regularization (NR) in many fields, we attempt to apply it to the modeling of inverse scattering problems. Specifically, we introduce prior information describing the sparsity of scatterers in the reconstruction task, aiming to improve the accuracy and effectiveness of the reconstruction results. By analyzing the discrete Fourier transform coefficients of the singular vectors of the matrix operator, we propose a modified Fourier bases-expansion (MFBE) regularization that introduces a new form of Fourier coefficient tensor. Then, we attempt to combine MFBE regularization with NR and propose a new hybrid regularization method. Based on the contraction integral equation (CIE) model that effectively reduces the nonlinearity of the inverse scattering problem, we demonstrate how to utilize the hybrid regularization method in modeling to obtain sparse solutions and how to solve the new loss function.