Nuit Blanche: Unbiased Risk Estimates for Singular Value Thresholding and Spectral Estimators

Tuesday, October 23, 2012

Unbiased Risk Estimates for Singular Value Thresholding and Spectral Estimators - implementation -

Just received this from Josh Trzasko

Hi Igor-

I wanted to highlight some recent work by Emmanuel Candes, Carlos Sing-Long, and myself on unbiased risk estimates for singular value thresholding (SVT). Amongst other things, the models developed in this work can be used to automatically tune SVT-based denoising models for image series (e.g., cardiac MRI). The manuscript, code, and data needed to replicate all experiments can be found at: http://www-stat.stanford.edu/~candes/SURE/index.html. If you think this work would be of interest to the Nuit Blanche community, we'd appreciate it being featured.

All the best,
Josh Trzasko
Mayo Clinic

Thanks Josh for the heads-up:

Unbiased Risk Estimates for Singular Value Thresholding and Spectral Estimators by Emmanuel J. Candes, Carlos A. Sing-Long, Joshua D. Trzasko. The abstract reads:

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.