Data-driven reduced order models (ROMs) recently emerged as powerful tool for the solution of inverse scattering problems. The main drawback of this approach is that it was limited to the measurement arrays with reciprocally collocated transmitters and receivers, that is, square symmetric matrix (data) transfer functions. To relax this limitation, we use our previous work [14], where the ROMs were combined with the Lippmann-Schwinger integral equation to produce a direct nonlinear inversion method. In this work we extend this approach to more general transfer functions, including those that are non-symmetric, e.g., obtained by adding only receivers or sources. The ROM is constructed based on the symmetric subset of the data and is used to construct all internal solutions. Remaining receivers are then used directly in the Lippmann-Schwinger equation. We demonstrate the new approach on a number of 1D and 2D examples with non-reciprocal arrays, including a single input/multiple outputs (SIMO) inverse problem, where the data is given by just a single-row matrix transfer function.
翻译:数据驱动的减少顺序模型(ROMs)最近成为解决反散射问题的有力工具。这一方法的主要缺点是,它仅限于具有对等合用发射机和接收器的测量阵列,即平对称矩阵(数据)传输功能。为了放松这一限制,我们使用我们先前的工作[14],即将ROM与Lipmann-Schwinger综合方程式相结合,以产生一种直接的非线性非线性反转法。在这项工作中,我们将这一方法推广到更普遍的转移功能,包括非对称功能,例如,仅添加接收器或接收器获得的非对称函数。ROM是根据数据对称组构建的,用于构建所有内部解决方案。剩下的接收器随后直接用于Lippmann-Schwinger方程式。我们用非对称阵列的1D和2D实例展示新的方法,包括单一输入/多输出(SIMO)反向问题,数据仅由单行矩阵传输功能提供。