Decentralized Generalized Approximate Message-Passing for Tree-Structured Networks

This paper proposes decentralized generalized approximate message-passing (D-GAMP) for compressed sensing in a tree-structured network. In contrast to conventional GAMP that needs a central node to gather all measurements on the network, D-GAMP utilizes consensus propagation via message-passing between adjacent nodes to achieve the same performance as centralized GAMP. The Onsager correction in D-GAMP is designed via rigorous state evolution so that the asymptotic Gaussianity of estimation errors in D-GAMP is guaranteed in each iteration for consensus propagation. By following a recently developed long-memory proof strategy, state evolution recursion for Bayes-optimal D-GAMP is proved to converge toward the Bayes-optimal fixed point— achieved by Bayes-optimal centralized GAMP—when the fixed point is unique.