A Novel Hybrid Regularization Method for Solving Inverse Scattering Problems

The challenging task of solving inverse scattering problems (ISPs) is due to their inherent ill-posedness and nonlinearity. To alleviate ill-posedness, a novel hybrid regularization method [modified Fourier bases-expansion (MFBE) regularization and nonconvex regularization (NR)] is proposed. The MFBE regularization, directly applied to modeling, introduces a new Fourier coefficient tensor that takes into account information not only from the four corners but also from the four edges. NR, applied to the unknown, adds prior information describing the sparsity of scatterers to the reconstruction task. Then, in virtue of a new recently established contraction integral equation scattering model, which effectively reduces the nonlinearity of the ISPs, we propose a new cost function with the above hybrid regularization. The newly established cost function is solved by the alternating minimization scheme, where the contrast subproblem is simplified by the least squares method and the proximal operator. Numerical experiments are performed on synthetic and experimental data to verify the ability of the proposed method to recover high permittivity objects.