A proximal splitting approach to regularized distributed adaptive estimation in diffusion networks

We propose a proximal splitting approach to regularized distributed estimation over networks employing diffusion adaptation strategies. Playing a central role in the proposed framework is the so-called proximity operator, which is a generalization of the convex projection mapping, that enables us to handle convex regularization terms efficiently. The diffusion algorithms developed using the proximal formalism endow networks with new learning abilities and open up possibilities for enhancing performance of the networks by utilizing more general convex penalties. We present performance analysis of the proposed method and provide simulations to demonstrate its feasibility in recovering sparse signals.