Sparsity-regularized Born iterations for electromagnetic inverse scattering

Electromagnetic inverse scattering [1] continues to be an active research area with applications ranging from environmental sensing to oil exploration and see-through-wall (STW) imaging. Among the many available techniques, the Born iterative method and its many descendants continue to be the most widely used [2]. The ill-posedness of Born iterations has often been alleviated via Tikhonov regularization [1], which promotes smoothness in the reconstruction. That said, in many applications including molecular and STW imaging [3], sparseness of the scatterers can be used to regularize the inverse scattering problem as well. Sparsity regularization was first proposed for linear inverse problems in [4] and then extended for image processing applications in [5–6]. In this paper, an inverse scattering technique that uses sparsity-regularized Born iterations is proposed. Application of the proposed technique to the reconstruction of a sparse two-dimensional (2D) dielectric profile shows that it produces images that are sharper than those obtained using Tikhonov-regularized Born iterations.