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.

翻译：本文研究了有限孔径逆障碍散射问题的深度学习方法。众所周知，传统深度学习仅依赖数据，这可能导致其在仅获得间接观测数据和物理模型时对逆问题的求解性能受限。针对这些局限性，一个基本问题随之产生：能否在不使用标注数据的情况下使深度学习求解逆问题，并使其知晓自身学习内容？为此，本文提出了一种无需真实标签的深度分解方法（DDM）。该方法通过将散射模型相关的物理算子引入神经网络架构来实现这一目标。此外，DDM中实现了基于深度学习的数据补全机制，以避免有限孔径数据对逆问题解产生畸变。更进一步，除应对逆问题本身的病态性外，DDM作为一种具有物理感知能力的机器学习技术，还具备可解释性特征。本文从理论上证明了DDM的收敛性，并通过数值实验验证了即使在入射孔径和观测孔径极为有限的情况下，所提DDM依然有效。