On Deep Learning for Inverse Problems

This paper analyses the generalization behaviour of a deep neural networks with a focus on their use in inverse problems. In particular, by leveraging the robustness framework by Xu and Mannor, we provide deep neural network based regression generalization bounds that are also specialized to sparse approximation problems. The proposed bounds show that the sparse approximation performance of deep neural networks can be potentially superior to that of classical sparse reconstruction algorithms, with reconstruction errors limited only by the noise level independently of the underlying data