Znanstveni kolokviji

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.