Optimality of approximate message passing for spiked matrix models with rotationally invariant noise
旋转不变噪声尖峰矩阵模型中近似消息传递的最优性
We study the problem of estimating a rank-one signal matrix from a noisy observed matrix corrupted by additive rotationally invariant noise. We develop a new class of approximate message passing algorithms for this problem and provide a simple and concise characterization of their dynamics in the high-dimensional limit. At each iteration, these algorithms leverage prior knowledge about the noise structure by applying a nonlinear matrix denoiser to the eigenvalues of the…