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- Title
Estimation of the Loss Function When Using Wavelet-Vaguelette Decomposition for Solving Ill-Posed Problems.
- Authors
Kudryavtsev, A. A.; Shestakov, O. V.
- Abstract
The paper discusses the de-noising method in a model with an additive Gaussian noise, based on the wavelet-vaguelette decomposition and thresholding of the vaguelette coefficients. For soft and hard thresholding procedures, we derive the values of the thresholds and estimate asymptotically optimal orders of the loss function based on the probabilities of errors in calculating decomposition coefficients.
- Subjects
SOFT sets; LOSS functions (Statistics); RANDOM noise theory; ERROR probability; PROBLEM solving
- Publication
Journal of Mathematical Sciences, 2019, Vol 237, Issue 6, p804
- ISSN
1072-3374
- Publication type
Article
- DOI
10.1007/s10958-019-04206-z