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：本文提出了一种面向树状网络的分布式广义近似消息传递（GAMP）算法，用于处理分布式广义线性测量下的压缩感知问题。通过相邻节点间的局部通信，采用一致性传播方法实现GAMP所需的平均一致性。该分布式GAMP算法适用于所有树状结构网络，且不要求存在与所有其他节点相连的中心节点。利用状态演化方法分析了当感知矩阵为零均值独立同分布高斯矩阵时，分布式GAMP算法的渐近动态特性。研究证明，在所有节点具有相同测量维度的同构测量场景下，分布式GAMP的状态演化递归与集中式GAMP具有相同的固定点。进一步地，采用现有长记忆证明策略，证明了配备贝叶斯最优去噪器的分布式GAMP状态演化递归会收敛至固定点。这些结果表明，当固定点唯一时，针对同构测量问题，配备贝叶斯最优去噪器的分布式GAMP状态演化递归将收敛至贝叶斯最优固定点。文中通过线性测量和限幅测量两种场景展示了分布式GAMP的数值实验结果。作为树状网络的典型案例，研究考察了一维链式结构和无中心节点的树状结构两种网络拓扑。