The first term in the Born series, as we call the Born data, is linear with the scatterers. Here we present a scheme to map the total field data to the Born data in layered media using only the single-input single-output (SISO) setup. This nonlinear mapping is based on the reduced order model (ROM) approach, which constructs ROMs of the original wave operator. Normally, the construction of ROMs requires multi-input multi-output data. By introducing fictitious sensors, we estimate the Born data with SISO data in layered media. We give a simple way of using the time-domain Green’s function to estimate the received data for other fictitious sensors without calculating the complicated Sommerfeld integral. The resulting Born data contains only the single-scattering component, which can be helpful for many imaging applications. A numerical example is given incorporating the direct imaging back-propagation method. It validates the linearity of the Born data by providing an artifact-free image without the optimization process.

中文翻译：

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层状介质逆散射中 Born 数据的估计

玻恩级数中的第一项，我们称之为玻恩数据，与散射体呈线性关系。在这里，我们提出了一种方案，仅使用单输入单输出（SISO）设置将总字段数据映射到分层媒体中的 Born 数据。这种非线性映射基于降阶模型 (ROM) 方法，该方法构建了原始波算子的 ROM。通常，ROM的构建需要多输入多输出数据。通过引入虚拟传感器，我们利用分层介质中的 SISO 数据来估计 Born 数据。我们给出了一种使用时域格林函数来估计其他虚拟传感器接收到的数据的简单方法，而无需计算复杂的索末菲积分。生成的 Born 数据仅包含单散射分量，这对许多成像应用很有帮助。给出了结合直接成像反向传播方法的数值示例。它通过提供无伪影的图像（无需优化过程）来验证 Born 数据的线性度。