This paper addresses the inverse scattering problem in the domain Omega. The input data, measured outside Omega, involve the waves generated by the interaction of plane waves with various directions and unknown scatterers fully occluded inside Omega. The output of this problem is the spatially dielectric constant of these scatterers. Our approach to solving this problem consists of two primary stages. Initially, we eliminate the unknown dielectric constant from the governing equation, resulting in a system of partial differential equations. Subsequently, we develop the Carleman contraction mapping method to effectively tackle this system. It is noteworthy to highlight this method's robustness. It does not request a precise initial guess of the true solution, and its computational cost is not expensive. Some numerical examples are presented.

翻译：本文研究了区域Omega内的逆散射问题。输入数据在Omega外部测量，涉及平面波与完全隐藏在Omega内部的未知散射体相互作用产生的波。该问题的输出是这些散射体的空间介电常数。我们的求解方法包含两个主要阶段。首先，我们从控制方程中消去未知介电常数，得到一个偏微分方程组。随后，我们开发了Carleman压缩映射方法以有效求解该方程组。值得强调的是该方法的稳健性：它不需要真实解的精确初始猜测，且计算成本较低。文中给出了一些数值算例。