模型驱动的深度学习算法求解无相位逆散射问题
A Model-Informed Deep Learning Algorithm for Solving the Phaseless Inverse Scattering Problem
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中文总结 AI 辅助
提出一种无监督、两步式、模型驱动的深度学习框架，利用Lippmann-Schwinger积分方程和谱域方程耦合约束，通过神经网络参数化散射体和对比源，实现高效鲁棒的无相位逆散射重建。
中文摘要 AI 辅助
本文研究了一种无监督、两步式、模型驱动的深度学习框架，用于求解无相位逆散射问题。目标是利用多个入射波对应的总波模量的边界测量值，重建一个紧支撑函数，该函数表征散射体的特征。第一步，将无相位数据转换为与底层散射体直接相关的成像函数。受对比源方法的启发，我们利用Lippmann-Schwinger积分方程和涉及成像函数的基于谱的方程，推导出一个耦合的模型方程组。第二步，未知散射体和对比源函数分别被参数化为独立的馈入神经网络，并在每次迭代中使用推导出的模型方程组同时训练。Lippmann-Schwinger积分方程将底层物理规律作为模型约束强制执行，而包含成像函数的基于谱的方程则提供未知散射体形状和位置的几何信息。所提出的框架在保持对测量噪声鲁棒性的同时，实现了准确且高效的重建。此外，将问题的某些方面转换到谱域可以有效降低计算成本，使我们能够快速恢复未知散射体。在二维和三维设置中的数值实验证明了所提方法的有效性、稳定性和实际应用潜力。
英文摘要
We study in this paper an unsupervised, two-step, model-informed deep learning framework for solving the phaseless inverse scattering problem. The objective is to reconstruct a compactly supported function that characterizes a scatterer from boundary measurements of the modulus of the total wave corresponding to multiple incident waves. In the first step, the phaseless data are transformed into an imaging function that is directly related to the underlying scatterer. Motivated by the contrast source method, we derive a coupled system of model equations using the Lippmann-Schwinger integral equation and a spectral-based equation involving the imaging function. In the second step, the unknown scatterer and contrast source function are each parameterized as independent feedforward neural networks, which are trained simultaneously at each iteration using the derived system of model equations. The Lippmann-Schwinger integral equation enforces the underlying physics as a model constraint, while the spectral-based equation incorporating the imaging function supplies geometric information on the shape and location of the unknown scatterer. The resulting framework achieves accurate and efficient reconstructions while maintaining robustness to measurement noise. Furthermore, transforming some aspects of the problem to the spectral domain enables an effective reduction in the computational cost, allowing us to recover the unknown scatterer quickly. Numerical experiments in both two- and three-dimensional settings demonstrate the effectiveness, stability, and practical potential of the proposed approach.
发表机构
- Kansas State University（堪萨斯州立大学）
机构由 AI 辅助整理，请以论文原文为准。
