In this paper, we consider a deep learning approach to the limited aperture
inverse obstacle scattering problem. It is well known that traditional deep
learning relies solely on data, which may limit its performance for the inverse
problem when only indirect observation data and a physical model are available.
A fundamental question arises in light of these limitations: is it possible to
enable deep learning to work on inverse problems without labeled data and to be
aware of what it is learning? This work proposes a deep decomposition method
(DDM) for such purposes, which does not require ground truth labels. It
accomplishes this by providing physical operators associated with the
scattering model to the neural network architecture. Additionally, a deep
learning based data completion scheme is implemented in DDM to prevent
distorting the solution of the inverse problem for limited aperture data.
Furthermore, apart from addressing the ill-posedness imposed by the inverse
problem itself, DDM is a physics-aware machine learning technique that can have
interpretability property. The convergence result of DDM is theoretically
proven. Numerical experiments are presented to demonstrate the validity of the
proposed DDM even when the incident and observation apertures are extremely
limited.

本文探讨了一个针对有限孔径下逆障碍散射问题的深度学习方法，该方法通过提供与散射模型相关的物理算子给神经网络架构来实现深度学习在逆问题上无需标记数据并且具有学习意识的可能性。此外，还实施了基于深度学习的数据补全方案，以防止有限孔径数据导致逆问题解的失真。此外，DDM 不仅解决了逆问题本身的不适定性，还是一种具有解释性特性的物理意识机器学习技术。DDM 的收敛性结果已从理论上得到证明。数值实验展示了即使入射和观测孔径极其有限，所提出的 DDM 仍然有效。