  In-network distributed estimation of sparse parameter vectors via diffusion
LMS strategies has been studied and investigated in recent years. In all the
existing works, some convex regularization approach has been used at each node
of the network in order to achieve an overall network performance superior to
that of the simple diffusion LMS, albeit at the cost of increased computational
overhead. In this paper, we provide analytical as well as experimental results
which show that the convex regularization can be selectively applied only to
some chosen nodes keeping rest of the nodes sparsity agnostic, while still
enjoying the same optimum behavior as can be realized by deploying the convex
regularization at all the nodes. Due to the incorporation of unregularized
learning at a subset of nodes, less computational cost is needed in the
proposed approach. We also provide a guideline for selection of the sparsity
aware nodes and a closed form expression for the optimum regularization
parameter.
