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Unbiased Risk Estimates for Singular Value Thresholding and Spectral Estimators
Open accessAbstract
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.
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Cites
Sparse MRI: The application of compressed sensing for rapid MR imaging
Lustig, M., Donoho, D., & Pauly, J. M. (2007) · Magnetic Resonance in Medicine · doi:10.1002/mrm.21391 · Cited by 6,952
Cited by
Parikh, N., & Boyd, S. (2014) · Foundations and Trends® in Optimization · doi:10.1561/2400000003 · Cited by 4,102
Demene, C., Deffieux, T., Pernot, M., Osmanski, B.-F., Biran, V., Gennisson, J.-L., Sieu, L.-A., Bergel, A., Franqui, S., Correas, J.-M., et al. (2015) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2015.2428634 · Cited by 983
Baranger, J., Arnal, B., Perren, F., Baud, O., Tanter, M., & Demene, C. (2018) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2018.2789499 · Cited by 348
Ultrasound Small Vessel Imaging With Block-Wise Adaptive Local Clutter Filtering
Song, P., Manduca, A., Trzasko, J. D., & Chen, S. (2017) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2016.2605819 · Cited by 258
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Metadata
- Authors
- Candes, E. J., Sing-Long, C. A., & Trzasko, J. D.
- Venue
- IEEE Transactions on Signal Processing
- Published
- 2013-10
- Volume
- 61
- Issue
- 19
- Pages
- 4643-4657
- ISSN
- 1053-587X (ISSN-L)
- 1941-0476
- OpenAlex
- W2063942101
- Cited by
- 243
- References
- 1
- FWCI
- 19.51
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Candes, E. J., Sing-Long, C. A., & Trzasko, J. D. (2013). Unbiased Risk Estimates for Singular Value Thresholding and Spectral Estimators. IEEE Transactions on Signal Processing. https://doi.org/10.1109/tsp.2013.2270464
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