L2-Regularized Iterative Weighted Algorithm for Inverse Scattering

We propose a new inverse scattering technique based on sparsity for the application of microwave imaging. The underdetermined inverse problem appeared in the distorted born iterative method (DBIM) technique is solved using the suggested L₂-regularized iterative weighted algorithm (L₂-IWA). The L₂-regularizer has been introduced to stabilize the algorithm against nonlinear approximations, and the sparsity is enforced with the aid of another reweighted L₂-norm regularizer to address the ill-posedness of the inverse problem. The derived algorithm is a three-step iterative technique which solves the underdetermined set of equations at each DBIM iteration. Moreover, the convergence of the L₂-IWA technique is proved, analytically. The suggested method outperforms its other counterparts in various scenarios of homogeneous and heterogeneous breast models. Besides improving the resolution of the breast tumors, the L₂-IWA technique is shown to be robust against additive noise.