Physics-aware deep learning framework for the limited aperture inverse obstacle scattering problem

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 the first physics-aware machine learning technique that can have interpretability property for the obstacle detection. The convergence result of DDM is theoretically investigated. We also prove that adding small noise to the input limited aperture data can introduce additional regularization terms and effectively improve the smoothness of the learned inverse operator. Numerical experiments are presented to demonstrate the validity of the proposed DDM even when the incident and observation apertures are extremely limited.