Neural networks functions are considered to be able to describe the desired solution of an inverse problem very efficiently, thus allow for sparse encoding of the desired reconstruction.
In this paper we consider the problem of solving linear inverse problems with neural network coders with a Gauss-Newton method. In an abstract setting this problem has been considered for some time, for instance under the name of state space regularization. In this paper we prove a local convergence results for some Gauss-Newton method.

This is a joint work with Bernd Hofmann and Zuhair Nashed