This paper considers a discrete-valued signal estimation scheme based on a low-complexity Bayesian optimal message passing algorithm (MPA) for solving massive linear inverse problems under highly correlated measurements. Gaussian belief propagation (GaBP) can be derived by applying the central limit theorem (CLT)-based Gaussian approximation to the sum-product algorithm (SPA) operating on a dense factor graph (FG), while matched filter (MF)-expectation propagation (EP) can be obtained based on the EP framework tailored for the same FG. Generalized approximate message passing (GAMP) can be found by applying a rigorous approximation technique for both of them in the large-system limit, and these three MPAs perform signal detection using MF by assuming large-scale uncorrelated observations. However, each of them has a different inherent self-noise suppression mechanism, which makes a significant difference in the robustness against the correlation of the observations when we apply an annealed discrete denoiser (ADD) that adaptively controls its nonlinearity with the inverse temperature parameter corresponding to the number of iterations. In this paper, we unravel the mechanism of this interesting phenomenon, and further demonstrate the practical applicability of the low-complexity Bayesian optimal MPA with ADD under highly correlated measurements.

翻译：本文研究一种基于低复杂度贝叶斯最优消息传递算法（MPA）的离散值信号估计方案，用于解决高度相关测量下的大规模线性逆问题。高斯置信传播（GaBP）可通过将基于中心极限定理（CLT）的高斯近似应用于稠密因子图（FG）上的和积算法（SPA）推导得出，而匹配滤波器（MF）-期望传播（EP）则可根据为同一FG定制的EP框架获得。广义近似消息传递（GAMP）可通过在大系统极限下对两者应用严格的近似技术得到，这三种MPA均通过假设大规模不相关观测，利用MF进行信号检测。然而，它们各自具有不同的固有自噪声抑制机制，当应用退火离散去噪器（ADD）——该去噪器通过对应于迭代次数的逆温度参数自适应控制其非线性——时，这种机制会在对抗观测相关性的鲁棒性方面产生显著差异。本文揭示了这一有趣现象的内在机制，并进一步论证了结合ADD的低复杂度贝叶斯最优MPA在高度相关测量条件下的实际适用性。