Unbiased Risk Estimates for Singular Value Thresholding and Spectral Estimators

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.

• Publication year

  2012

• Venue

  IEEE Transactions on Signal Processing

• Publication date

  2012-10-15

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1109/TSP.2013.2270464arXiv 1210.4139
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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