Sparse reconstruction algorithms for nonlinear microwave imaging

This paper presents a two-step inverse process which allows sparse recovery of the unknown (complex) dielectric profiles of scatterers for nonlinear microwave imaging. The proposed approach is applied to a nonlinear inverse scattering problem arising in microwave imaging and correlated with joint sparsity which gives multiple sparse solutions that share a common nonzero support. Numerical results demonstrate the potential of the proposed two step inversion approach when compared to existing sparse recovery algorithm for the case of small scatterers.