Joint L1-L2 regularization for inverse scattering

We propose a method for a solution of the inverse electromagnetic scattering problem using both L1 and L2 norms as regularization. The applicability of the method is demonstrated for a two-dimensional (2D) microwave imaging problem using the Born-iterative Method(BIM) with synthetically generated data. Though a single L2 regularization can estimate the dielectric constant profile, the reconstruction (if and when it converges) is over-smoothed. Similarly, a single L1 regularization fails when the problem is ill-conditioned. We propose an optimization strategy where both the regularization parameters are estimated simultaneously. Different object shapes have been considered to evaluate the performance. The results indicate that the method can produce an accurate object localization and estimation of the dielectric constant.