A Unified Framework of State Evolution for Message-Passing Algorithms
A Unified Framework of State Evolution for Message-Passing Algorithms
复制标题
消息传递算法状态演化的统一框架
DOI：
--
复制
发表时间：
2019
期刊：
影响因子：
--
通讯作者：
K. Takeuchi
中科院分区：
文献类型：
--
作者：
K. Takeuchi
本文提出了一个统一的框架，以了解压缩感知中的消息传递算法的动态。状态演化严格分析的一般误差模型，其中包含近似消息传递（AMP）的误差模型，以及正交AMP。作为一个副产品，AMP被证明是渐近收敛的，如果传感矩阵是正交不变的，如果其渐近奇异值分布的矩序列与Marčhenko-Pastur分布的矩序列相一致的顺序是最大的两倍大的最大迭代次数。
This paper presents a unified framework to understand the dynamics of message-passing algorithms in compressed sensing. State evolution is rigorously analyzed for a general error model that contains the error model of approximate message-passing (AMP), as well as that of orthogonal AMP. As a byproduct, AMP is proved to converge asymptotically if the sensing matrix is orthogonally invariant and if the moment sequence of its asymptotic singular-value distribution coincide with that of the Marčhenko-Pastur distribution up to the order that is at most twice as large as the maximum number of iterations.