  This review provides an introduction to - and overview of - the current state
of the art in neural-network based regularization methods for inverse problems
in imaging. It aims to introduce readers with a solid knowledge in applied
mathematics and a basic understanding of neural networks to different concepts
of applying neural networks for regularizing inverse problems in imaging.
Distinguishing features of this review are, among others, an easily accessible
introduction to learned generators and learned priors, in particular diffusion
models, for inverse problems, and a section focusing explicitly on existing
results in function space analysis of neural-network-based approaches in this
context.
