Unbiased Risk Estimates for Singular Value Thresholding and Spectral Estimators
Unbiased Risk Estimates for Singular Value Thresholding and Spectral Estimators
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DOI：
10.1109/tsp.2013.2270464
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发表时间：
2013-10-01
影响因子：
5.4
通讯作者：
Trzasko, Joshua D.
中科院分区：
文献类型：
--
作者：
Candes, Emmanuel J.;Sing-Long, Carlos A.;Trzasko, Joshua D.
在越来越多的应用中，从噪声观测中恢复近似低秩的数据矩阵是人们感兴趣的。本文给出了一个无偏风险估计--在高斯模型中保持--对于任何谱估计服从一些温和的正则性假设。特别是，我们给出了一个无偏的风险估计公式奇异值阈值（SVT），一个流行的估计策略，适用于软阈值规则的奇异值的噪声观测。除此之外，我们的公式提供了一个原则性和自动化的方式来选择正则化参数在各种问题。特别是，我们证明了效用的无偏风险估计的SVT为基础的去噪的真实的临床心脏MRI系列数据。我们也给出了一些矩阵值函数的可微性的新结果。
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 that 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.