We consider the inverse acoustic time domain scattering problem for absorbing scatterers modeled by impedance boundary conditions. We present and analyze a factorization method for reconstructing the obstacle boundary from far field measurements. The analysis is based on using the Laplace transform and proving the coercivity of the solution operator in suitable weighted spaces in time. This leads us to consider a modified far field operator parameterized by the imaginary part of Laplace variable which is different but can be arbitrarily close to the original far field operator. As a proof of concept we also provide some preliminary numerical examples to test and discuss the effectiveness of the resulting inversion method when applied to the original far field operator.

中文翻译：

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具有阻抗边界条件的障碍物的时域分解方法

我们考虑通过阻抗边界条件建模的吸收散射体的逆声时域散射问题。我们提出并分析一种从远场测量中重建障碍物边界的分解方法。该分析基于使用拉普拉斯变换并在适当的加权空间中证明了解算子的矫顽力。这使我们考虑由Laplace变量的虚部参数化的修改后的远场算子，该算子不同，但可以任意接近原始的远场算子。作为概念验证，我们还提供了一些初步的数值示例，以测试和讨论将所得反演方法应用于原始远场算子时的有效性。