提出最优谱初始化的正交AMP算法，提升矩形稀疏矩阵信号估计性能。
Orthogonal Approximate Message Passing with Optimal Spectral Initializations for Rectangular Spiked Matrix Models
- 基于正交近似消息传递框架，设计迭代最优去噪器。
- 在一般旋转不变噪声下，性能逼近贝叶斯最优解。
- 适用于非高斯信号的多异常值融合，适合高维信号恢复场景。
针对具有广义旋转不变（RI）噪声的矩形稀疏矩阵模型，我们提出一种正交近似消息传递（OAMP）算法，用于信号估计。建立了严格的动态状态演化方程，精确刻画算法在高维下的行为，并支持构造逐次迭代最优的去噪器。在此框架下，我们对经验噪声谱仅作最小假设，即可实现谱初始化。在矩形情形中，单个秩一成分常产生多个有信息量的异常值，我们进一步提出一种在温和非高斯信号假设下的异常值融合方法。对于一般RI噪声模型，所提最优OAMP算法的预测性能与关联贝叶斯最优估计器的复现对称预测一致，我们推测其在一大类迭代估计方法中具有统计最优性。
原文摘要 · Abstract (English)
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 precisely characterizes the algorithm's high-dimensional dynamics and enables the construction of iteration-wise optimal denoisers. Within this framework, we accommodate spectral initializations under minimal assumptions on the empirical noise spectrum. In the rectangular setting, where a single rank-one component typically generates multiple informative outliers, we further propose a procedure for combining these outliers under mild non-Gaussian signal assumptions. For general RI noise models, the predicted performance of the proposed optimal OAMP algorithm agrees with replica-symmetric predictions for the associated Bayes-optimal estimator, and we conjecture that it is statistically optimal within a broad class of iterative estimation methods.
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