Distributed ADMM for in-network reconstruction of sparse signals with innovations

In this paper, we address the problem of in-network reconstruction of correlated sparse signals. Specifically, we adopt a JSM-1 model by which the signals to be reconstructed are the sum of a common sparse term and an individual sparse term (or innovation). We tackle the problem using an Alternating Direction Method of Multipliers approach, which is prone to be distributed. We also propose a version that requires to exchange only binary messages among neighboring nodes. Performance of the different methods is shown to be satisfactory.