  An inverse scattering problem for SAR data in application to through-the-wall
imaging is addressed. In contrast with the conventional algorithms of SAR
imaging, that work with the linearized mathematical model based on the Born
approximation, the fully nonlinear case is considered here. To avoid the local
minima problem, the so-called "convexification" globally convergent inversion
scheme is applied to approximate the distribution of the slant range (SR)
dielectric constant in the 3-D domain. The benchmark scene of this paper
comprises a homogeneous dielectric wall and different dielectric targets hidden
behind it. The results comprise two dimensional images of the SR dielectric
constant of the scene of interest. Numerical results are obtained by the
proposed inversion method for both the computationally simulated and
experimental data. Our results show that the values, cross-range sizes and
locations of SR dielectric constants for targets hidden behind the wall are
close to those of real targets. Numerical comparison with the solution of the
linearized inverse scattering problem provided by the Born approximation,
commonly used in conventional SAR imaging, shows a significantly better
accuracy of our results.
