An inverse scattering problem (ISP) for synthetic aperture radar (SAR) data in application to through-the-wall imaging is addressed. In contrast with the conventional algorithms of SAR imaging, which 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 in the slant range (SR) plane of a function that is associated with the dielectric constant. It is demonstrated that this function estimates quite well both the value of the dielectric constant and the location of the target. The benchmark scene of this article comprises a homogeneous dielectric wall and different dielectric targets hidden behind it. The results comprise 2-D 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 ISP provided by the Born approximation, commonly used in conventional SAR imaging, shows a significantly better accuracy of our results.