Deep decomposition method for the limited aperture inverse obstacle
  scattering problem
Yunwen Yin Liang Yan
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.