  This paper proposes a federated learning technique for deep algorithm
unfolding with applications to sparse signal recovery and compressed sensing.
We refer to this architecture as Fed-CS. Specifically, we unfold and learn the
iterative shrinkage thresholding algorithm for sparse signal recovery without
transporting to a central location, the training data distributed across many
clients. We propose a layer-wise federated learning technique, in which each
client uses local data to train a common model. Then we transmit only the model
parameters of that layer from all the clients to the server, which aggregates
these local models to arrive at a consensus model. The proposed layer-wise
federated learning for sparse recovery is communication efficient and preserves
data privacy. Through numerical experiments on synthetic and real datasets, we
demonstrate Fed-CS's efficacy and present various trade-offs in terms of the
number of participating clients and communications involved compared to a
centralized approach of deep unfolding.
