  One of the main computational drawbacks in the application of 3-D iterative
inversion techniques is the requirement of solving the field quantities for the
updated contrast in every iteration. In this paper, the 3-D electromagnetic
inverse scattering problem is put into a discretized finite-difference
frequency-domain scheme and linearized into a cascade of two linear
functionals. To deal with the nonuniqueness effectively, the joint structure of
the contrast sources is exploited using a sum-of-$\ell_1$-norm optimization
scheme. A cross-validation technique is used to check whether the optimization
process is accurate enough. The total fields are, then, calculated and used to
reconstruct the contrast by minimizing a cost functional defined as the sum of
the data error and state error. In this procedure, the total fields in the
inversion domain are computed only once, while the quality and accuracy of the
obtained reconstructions are maintained. The novel method is applied to
ground-penetrating radar imaging and through-the-wall imaging, in which the
validity and efficiency of the method is demonstrated.
