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Wavelets, sparse representations, and denoising

Vrijeme: 25.2.2009
Predavaonica: 005
Predavač: Prof. Mladen Victor Wickerhauser, Washington University in Saint Louis, USA
Naziv: Wavelets, sparse representations, and denoising

We consider the ill-posed problem of recovering a function f
from the single measurement x=f+n, where n is an unknown
"noise" function. Much progress was made in the 1990s by
Donoho and Johnstone under the assumption that f is smoother
than n in the Sobolev sense. Simply thresholding to zero
any small components of a Fourier expansion of x in smooth
wavelets produces a near-minimax estimator for f. The same
idea works with the weaker hypothesis that f has a sparser
representation than n in some orthonormal basis. We will
exhibit some examples that have proved useful in practice.

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