Multi-parameter Microwave Inverse Scattering with Group Sparsity Constraints

We present a multi-parameter inverse scattering method with group sparsity constraint, which improves the image reconstruction results in case the images of different parameters have similar shape or structure. In inverse scattering imaging, the system of equations to be solved is often under-determined where the number of measurements is less than the number of image pixels. This becomes even worse for objects described by a multi-parameter material model where the total number of unknowns grows by a factor of the number of material parameters. However, in many cases, images of different material parameters, such as permittivity and conductivity, share similar structure or shape, where group sparsity regularization can be used to effectively capture this prior information. We compare the inverse scattering of 3-parameter dispersive material objects using Tikhonov, sparsity, and group-sparsity regularization. After minimizing to the same measurement objective function error, compared with Tikhonov and sparsity regularization, the group sparsity regularized inversion produces a better shape and contrast reconstruction of all 3 parameters and achieves the lowest overall image pixel value error.