A Convolutional Sparsity Regularization for Solving Inverse Scattering Problems

In this letter, a convolutional sparsity regularization (CSR) is introduced into the framework of nonlinear iterative methods for solving inverse scattering problems (ISPs). The permittivity image of scatterers is sparsely represented in a convolutional form with prelearned dictionary filters. The CSR is then incorporated with the subspace-based optimization method (SOM), termed as (SOM-CSR), to reconstruct the target image as a sparse coding by dictionary filters. The whole optimization function of SOM-CSR is solved using an alternative iteration method. Both synthetic and experimental data are employed to validate the effectiveness of the proposed SOM-CSR method. The results demonstrate that the CSR, as a structural constraint, is beneficial to nonlinear iterative reconstruction methods for solving ISP in contrast to pixel-based inversion.