标题： 正交AMP 显示英文标题

标题： Orthogonal AMP

摘要： 近似消息传递（AMP）是一种用于线性系统模型的低成本迭代信号恢复算法。 当系统变换矩阵具有独立同分布（IID）高斯元素时，AMP的性能可以通过一个称为状态演化（SE）的简单标量递归来渐近表征。 然而，对于其他矩阵集合，特别是病态矩阵，SE可能变得不可靠。 这限制了AMP的应用。 在本文中，我们提出了一种基于去相关线性估计（LE）和无散度非线性估计（NLE）的正交AMP（OAMP）算法。 标准AMP中的Onsager项由于NLE的无散度约束而消失。 我们为OAMP开发了一个SE过程，并通过数值实验表明，OAMP的SE对于一般的酉不变矩阵是准确的，包括IID高斯矩阵和部分正交矩阵。 我们进一步推导了OAMP的优化选项，并表明相应的SE固定点与通过复制方法获得的最优性能相吻合。 我们的数值结果表明，OAMP在病态矩阵的情况下相比AMP具有优势。 显示英文摘要

摘要： Approximate message passing (AMP) is a low-cost iterative signal recovery algorithm for linear system models. When the system transform matrix has independent identically distributed (IID) Gaussian entries, the performance of AMP can be asymptotically characterized by a simple scalar recursion called state evolution (SE). However, SE may become unreliable for other matrix ensembles, especially for ill-conditioned ones. This imposes limits on the applications of AMP. In this paper, we propose an orthogonal AMP (OAMP) algorithm based on de-correlated linear estimation (LE) and divergence-free non-linear estimation (NLE). The Onsager term in standard AMP vanishes as a result of the divergence-free constraint on NLE. We develop an SE procedure for OAMP and show numerically that the SE for OAMP is accurate for general unitarily-invariant matrices, including IID Gaussian matrices and partial orthogonal matrices. We further derive optimized options for OAMP and show that the corresponding SE fixed point coincides with the optimal performance obtained via the replica method. Our numerical results demonstrate that OAMP can be advantageous over AMP, especially for ill-conditioned matrices