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. CandesCarlos A. Sing-LongJoshua 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.
Data and code are here.

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