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.

翻译：近似电文传递(AMP)类型算法被广泛用于某些大型随机线性系统的信号重建。AMP类型算法的一个关键特征是其动态可以通过国家演变得到正确的描述。然而,国家演变并不一定保证迭代算法的趋同。为了在原则上解决AMP型算法的趋同问题,本文件提议在充分统计条件下建立一个记忆AMP(MAMP ), 并命名为足够的统计 MAMP (SS-MAMP ) 。 我们表明SS-MAMP (SS-MAMP ) 的共变矩阵是L 带宽和聚合的 。 在任意的MAMP 情况下,我们可以通过阻隔来构建SS-MAMP,这不仅能确保趋同,而且能保护其正态性,即其动态可以通过国家演变得到正确的描述。