In this paper, we tackle the in-network recovery of sparse signals with innovations. We assume that the nodes of the network measure a signal composed by a common component and an innovation, both sparse and unknown, according to the joint sparsity model 1 (JSM-1). Acquisition is performed as in compressed sensing, hence the number of measurements is reduced. Our goal is to show that distributed algorithms based on the alternating direction method of multipliers (ADMM) can be efficient in this framework to recover both the common and the individual components. Specifically, we define a suitable functional and we show that ADMM can be implemented to minimize it in a distributed way, leveraging local communication between nodes. Moreover, we develop a second version of the algorithm, which requires only binary messaging, significantly reducing the transmission load.