The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.
De-noising by soft-thresholding
Abstract
Donoho and Johnstone (1994) proposed a method for reconstructing an unknown function f on [0,1] from noisy data d/sub i/=f(t/sub i/)+/spl sigma/z/sub i/, i=0, ..., n-1,t/sub i/=i/n, where the z/sub i/ are independent and identically distributed standard Gaussian random variables. The reconstruction f/spl circ/*/sub n/ is defined in the wavelet domain by translating all the empirical wavelet coefficients of d toward 0 by an amount /spl sigma//spl middot//spl radic/(2log (n)/n). The authors prove two results about this type of estimator. [Smooth]: with high probability f/spl circ/*/sub n/ is at least as smooth as f, in any of a wide variety of smoothness measures. [Adapt]: the estimator comes nearly as close in mean square to f as any measurable estimator can come, uniformly over balls in each of two broad scales of smoothness classes. These two properties are unprecedented in several ways. The present proof of these results develops new facts about abstract statistical inference and its connection with an optimal recovery model.>
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Citations
Cites
Spline Models for Observational Data
Wahba, G. (1990) · doi:10.1137/1.9781611970128 · Cited by 4,184
Statistical Estimation and Optimal Recovery
Donoho, D. L. (1994) · The Annals of Statistics · doi:10.1214/aos/1176325367 · Cited by 263 · cited 1×
“2) as a norm equivalent to n 1PE(f̂ (ti) f(ti))2; and [4] (2.”
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Cited by
Boyd, S., Parikh, N., Chu, E., Peleato, B., & Eckstein, J. (2011) · Foundations and Trends® in Machine Learning · doi:10.1561/2200000016 · Cited by 17,075
A Non-Local Algorithm for Image Denoising
Buades, A., Coll, B., & Morel, J.-M. (2005) · 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) · doi:10.1109/cvpr.2005.38 · Cited by 7,616
Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries
Elad, M., & Aharon, M. (2006) · IEEE Transactions on Image Processing · doi:10.1109/tip.2006.881969 · Cited by 5,321
An iterative thresholding algorithm for linear inverse problems with a sparsity constraint.
Daubechies, I., Defrise, M., & De Mol, C. (2004) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.20042 · Cited by 4,958
Parikh, N., & Boyd, S. (2014) · Foundations and Trends® in Optimization · doi:10.1561/2400000003 · Cited by 4,102
Metadata
- Authors
- Donoho, D. L.
- Venue
- IEEE Transactions on Information Theory
- Published
- 1995-05
- Volume
- 41
- Issue
- 3
- Pages
- 613-627
- ISSN
- 0018-9448 (ISSN-L)
- OpenAlex
- W2146842127
- Cited by
- 9,619
- References
- 2
- FWCI
- 50.49
- Type
- journal article
- Language
- en
- Open access
- closed
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- Donoho, D. L. (1995). De-noising by soft-thresholding. IEEE Transactions on Information Theory. https://doi.org/10.1109/18.382009
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