  In this work, we propose a deep neural network architecture motivated by
primal-dual splitting methods from convex optimization. We show theoretically
that there exists a close relation between the derived architecture and
residual networks, and further investigate this connection in numerical
experiments. Moreover, we demonstrate how our approach can be used to unroll
optimization algorithms for certain problems with hard constraints. Using the
example of speech dequantization, we show that our method can outperform
classical splitting methods when both are applied to the same task.
