Estimating a vector $\mathbf{x}$ from noisy linear measurements
$\mathbf{Ax}+\mathbf{w}$ often requires use of prior knowledge or structural
constraints on $\mathbf{x}$ for accurate reconstruction. Several recent works
have considered combining linear least-squares estimation with a generic or
"plug-in" denoiser function that can be designed in a modular manner based on
the prior knowledge about $\mathbf{x}$. While these methods have shown
excellent performance, it has been difficult to obtain rigorous performance
guarantees. This work considers plug-in denoising combined with the
recently-developed Vector Approximate Message Passing (VAMP) algorithm, which
is itself derived via Expectation Propagation techniques. It shown that the
mean squared error of this "plug-and-play" VAMP can be exactly predicted for
high-dimensional right-rotationally invariant random $\mathbf{A}$ and Lipschitz
denoisers. The method is demonstrated on applications in image recovery and
parametric bilinear estimation.

本研究探讨了结合向量近似消息传递算法 (VAMP) 的插件降噪方法，以及对高维旋转不变随机矩阵 A 和 Lipschitz 降噪器，可以精确预测这种 VAMP 方法的均方误差，并在图像恢复和参数双线性估计等应用上进行了演示。