A data-driven block thresholding approach to wavelet estimation

By Tommaso Cai, Harrison H. Zhou. 2009

112 citations recorded by the source corpus.

A data-driven block thresholding procedure for wavelet regression is proposed and its theoretical and numerical properties are investigated. The procedure empirically chooses the block size and threshold level at each resolution level by minimizing Stein's unbiased risk estimate. The estimator is sharp adaptive over a class of Besov bodies and achieves simultaneously within a small constant factor of the minimax risk over a wide collection of Besov Bodies including both the ``dense'' and ``sparse'' cases. The procedure is easy to implement. Numerical results show that it has superior finite sample performance in comparison to the other leading wavelet thresholding estimators.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/9ad28227da4e89027abde4e6a29e530b88071541

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Tommaso Cai
2. Harrison H. Zhou
3. Weijie Su
4. G. Peyr'e
5. Lawrence D. Brown
6. Charles-Alban Deledalle
7. Mohamed-Jalal Fadili
8. E.J. Candes

In Computer Vision and Pattern Recognition

1. G. Peyr'e
2. Tommaso Cai
3. Mohamed-Jalal Fadili
4. Lawrence D. Brown
5. Weijie Su
6. Harrison H. Zhou
7. Charles-Alban Deledalle
8. E.J. Candes

In Statistics and Probability

1. Tommaso Cai
2. Weijie Su
3. Harrison H. Zhou
4. E.J. Candes
5. Lawrence D. Brown
6. Jianqing Fan
7. Mohamed-Jalal Fadili
8. G. Peyr'e

Citations in the corpus

• SLOPE is Adaptive to Unknown Sparsity and Asymptotically Minimax (2015, background): “It has been observed [29, 22] that SURE thresholding loses performance in cases of sparse signals β, an empirical phenomenon which can perhaps be made theoretically precise.”
• Robust nonparametric estimation via wavelet median regression (2008, methodology): “…asymptotic equivalence here implies that adaptive procedures including SureShrink of Donoho and Johnstone (1995), the empirical Bayes estimation of Zhang (2005) and SureBlock of Cai and Zhou (2006) can be carried over from the Gaussian regression to the Cauchy regression or more general regression.”
• Stein Unbiased GrAdient estimator of the Risk (SUGAR) for Multiple Parameter Selection (2014, background): “, with sparse regularizations [4, 6, 7, 11, 17, 45, 48, 51, 52, 53, 54, 70] or with nonlocal filters [16, 25, 68, 69].”