Autors:

CiteWeb id: 20120000032

CiteWeb score: 4838

We attempt to recover a function of unknown smoothness from noisy sampled data. We introduce a procedure, SureShrink, that suppresses noise by thresholding the empirical wavelet coefficients. The thresholding is adaptive: A threshold level is assigned to each dyadic resolution level by the principle of minimizing the Stein unbiased estimate of risk (Sure) for threshold estimates. The computational effort of the overall procedure is order N · log(N) as a function of the sample size N. SureShrink is smoothness adaptive: If the unknown function contains jumps, then the reconstruction (essentially) does also; if the unknown function has a smooth piece, then the reconstruction is (essentially) as smooth as the mother wavelet will allow. The procedure is in a sense optimally smoothness adaptive: It is near minimax simultaneously over a whole interval of the Besov scale; the size of this interval depends on the choice of mother wavelet. We know from a previous paper by the authors that traditional smoot...

The publication "Adapting to Unknown Smoothness via Wavelet Shrinkage" is placed in the Top 10000 of the best publications in CiteWeb. Also in the category Mathematics it is included to the Top 1000. Additionally, the publicaiton "Adapting to Unknown Smoothness via Wavelet Shrinkage" is placed in the Top 100 among other scientific works published in 2012.
Links to full text of the publication: