We propose an orthogonal approximate message passing (OAMP) algorithm for signal estimation in the rectangular spiked matrix model with general rotationally invariant (RI) noise. We establish a rigorous state evolution that exactly characterizes the high-dimensional dynamics of the algorithm. Building on this framework, we derive an optimal variant of OAMP that minimizes the predicted mean-squared error at each iteration. For the special case of i.i.d. Gaussian noise, the fixed point of the proposed OAMP algorithm coincides with that of the standard AMP algorithm. For general RI noise models, we conjecture that the optimal OAMP algorithm is statistically optimal within a broad class of iterative methods, and achieves Bayes-optimal performance in certain regimes.

翻译：我们提出了一种正交近似消息传递（OAMP）算法，用于具有一般旋转不变（RI）噪声的矩形尖峰矩阵模型中的信号估计。我们建立了一个严格的状态演化方程，精确刻画了该算法在高维情况下的动态特性。基于此框架，我们推导出OAMP的一种最优变体，该变体在每次迭代中最小化预测的均方误差。对于独立同分布高斯噪声的特殊情况，所提出的OAMP算法的定点与标准AMP算法的定点一致。对于一般的RI噪声模型，我们推测最优OAMP算法在一大类迭代方法中具有统计最优性，并在特定机制下达到贝叶斯最优性能。