2025/12/22 by Haohua Chen, Chen, Haohua, SongBin Liu +3
Computer Science · Engineering · #Direction-of-Arrival Estimation Techniques #Blind Source Separation Techniques #Sparse and Compressive Sensing Techniques
paper · doi:10.48550/arxiv.2512.19334
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.