  The linear inverse problem is fundamental to the development of various
scientific areas. Innumerable attempts have been carried out to solve different
variants of the linear inverse problem in different applications. Nowadays, the
rapid development of deep learning provides a fresh perspective for solving the
linear inverse problem, which has various well-designed network architectures
results in state-of-the-art performance in many applications. In this paper, we
present a comprehensive survey of the recent progress in the development of
deep learning for solving various linear inverse problems. We review how deep
learning methods are used in solving different linear inverse problems, and
explore the structured neural network architectures that incorporate knowledge
used in traditional methods. Furthermore, we identify open challenges and
potential future directions along this research line.
