  In this paper, an unrolling algorithm of the iterative subspace-based
optimization method (SOM) is proposed for solving full-wave inverse scattering
problems (ISPs). The unrolling network, named SOM-Net, inherently embeds the
Lippmann- Schwinger physical model into the design of network structures. The
SOM-Net takes the deterministic induced current and the raw permittivity image
obtained from back-propagation (BP) as the input. It then updates the induced
current and the permittivity successively in sub-network blocks of the SOM- Net
by imitating iterations of the SOM. The final output of the SOM-Net is the full
predicted induced current, from which the scattered field and the permittivity
image can also be deduced analytically. The parameters of the SOM-Net are
optimized in a supervised manner with the total loss to simultaneously ensure
the consistency of the induced current, the scattered field, and the
permittivity in the governing equations. Numerical tests on both synthetic and
experimental data verify the superior performance of the proposed SOM-Net over
typical ones. The results on challenging examples like scatterers with tough
profiles or high permittivity demonstrate the good generalization ability of
the SOM-Net. With the use of deep unrolling technology, this work builds a
bridge between traditional iterative methods and deep learning methods for
solving ISPs.
