标题： 奇异值阈值和谱估计器的无偏风险估计 显示英文标题

标题： Unbiased Risk Estimates for Singular Value Thresholding and Spectral Estimators

摘要： 在越来越多的应用中，人们感兴趣的是从噪声观测中恢复一个近似低秩的数据矩阵。 本文发展了一种无偏风险估计——适用于高斯模型——用于满足一些温和正则性假设的任何谱估计方法。 特别是，我们给出了奇异值阈值化（SVT）的无偏风险估计公式，这是一种流行的估计策略，它对噪声观测的奇异值应用软阈值规则。 我们的公式为多种问题中的正则化参数选择提供了一种原则性和自动化的途径。 特别是，我们展示了无偏风险估计对于基于SVT的临床心脏磁共振成像序列数据去噪的效用。 我们还给出了关于某些矩阵值函数可微性的新结果。 显示英文摘要

摘要： In an increasing number of applications, it is of interest to recover an approximately low-rank data matrix from noisy observations. This paper develops an unbiased risk estimate---holding in a Gaussian model---for any spectral estimator obeying some mild regularity assumptions. In particular, we give an unbiased risk estimate formula for singular value thresholding (SVT), a popular estimation strategy which applies a soft-thresholding rule to the singular values of the noisy observations. Among other things, our formulas offer a principled and automated way of selecting regularization parameters in a variety of problems. In particular, we demonstrate the utility of the unbiased risk estimation for SVT-based denoising of real clinical cardiac MRI series data. We also give new results concerning the differentiability of certain matrix-valued functions.