Decentralized generalized approximate message-passing (GAMP) is proposed for compressed sensing from distributed generalized linear measurements in a tree-structured network. Consensus propagation is used to realize average consensus required in GAMP via local communications between adjacent nodes. Decentralized GAMP is applicable to all tree-structured networks that do not necessarily have central nodes connected to all other nodes. State evolution is used to analyze the asymptotic dynamics of decentralized GAMP for zero-mean independent and identically distributed Gaussian sensing matrices. The state evolution recursion for decentralized GAMP is proved to have the same fixed points as that for centralized GAMP when homogeneous measurements with an identical dimension in all nodes are considered. Furthermore, existing long-memory proof strategy is used to prove that the state evolution recursion for decentralized GAMP with the Bayes-optimal denoisers converges to a fixed point. These results imply that the state evolution recursion for decentralized GAMP with the Bayes-optimal denoisers converges to the Bayes-optimal fixed point for the homogeneous measurements when the fixed point is unique. Numerical results for decentralized GAMP are presented in the cases of linear measurements and clipping. As examples of tree-structured networks, a one-dimensional chain and a tree with no central nodes are considered.

翻译：本文针对树状网络中的分布式广义线性测量，提出了去中心化广义近似消息传递（GAMP）方法。利用共识传播通过相邻节点间的局部通信实现GAMP所需的平均共识。去中心化GAMP适用于所有树状网络，无需存在连接所有其他节点的中心节点。采用状态演化分析去中心化GAMP在零均值独立同分布高斯感知矩阵下的渐近动态特性。当所有节点具有相同维度的均匀测量时，证明去中心化GAMP的状态演化递归与集中式GAMP具有相同的固定点。进一步采用现有长记忆证明策略，证明了采用贝叶斯最优去噪器的去中心化GAMP状态演化递归收敛至固定点。这些结果表明，当固定点唯一时，采用贝叶斯最优去噪器的去中心化GAMP状态演化递归对均匀测量收敛至贝叶斯最优固定点。文中给出了线性测量和限幅情况下去中心化GAMP的数值结果。以一维链状网络和无中心节点的树状网络作为树状网络的典型实例进行验证。