Sufficient Statistic Memory Approximate Message Passing
Sufficient Statistic Memory Approximate Message Passing
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DOI：
10.48550/arxiv.2206.11674
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发表时间：
2022-06
期刊：
影响因子：
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通讯作者：
Lei Liu;Shunqi Huang;B. Kurkoski
中科院分区：
文献类型：
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作者：
Lei Liu;Shunqi Huang;B. Kurkoski
近似消息传递（AMP）类算法已广泛应用于某些大型随机线性系统的信号重构中。AMP类算法的一个关键特征是其动态过程可由状态演化正确描述。然而，状态演化并不一定能保证迭代算法的收敛性。为从原理上解决AMP类算法的收敛问题，本文在充分统计条件下提出了一种记忆AMP（MAMP），称为充分统计MAMP（SS - MAMP）。我们证明了SS - MAMP的协方差矩阵是L - 带状且收敛的。对于任意的MAMP，我们可以通过阻尼来构造SS - MAMP，这不仅确保了收敛性，还保留了正交性，即其动态过程可由状态演化正确描述。
Approximate message passing (AMP) type algorithms have been widely used in the signal reconstruction of certain large random linear systems. A key feature of the AMP-type algorithms is that their dynamics can be correctly described by state evolution. However, state evolution does not necessarily guarantee the convergence of iterative algorithms. To solve the convergence problem of AMP-type algorithms in principle, this paper proposes a memory AMP (MAMP) under a sufficient statistic condition, named sufficient statistic MAMP (SS-MAMP). We show that the covariance matrices of SS-MAMP are L-banded and convergent. Given an arbitrary MAMP, we can construct the SS-MAMP by damping, which not only ensures the convergence, but also preserves the orthogonality, i.e., its dynamics can be correctly described by state evolution.