Adaptive de-noising of signals satisfying differential inequalities

Author

Goldenshluger, Alexander ; Nemirovski, Arkadi

Author_Institution

Fac. of Ind. Eng. & Manage., Technion-Israel Inst. of Technol., Haifa, Israel

Volume

43

Issue

3

fYear

1997

fDate

5/1/1997 12:00:00 AM

Firstpage

872

Lastpage

889

Abstract

The paper is devoted to spatial adaptive estimation of signals satisfying linear differential inequalities with an unknown differential operator of a given order. The classes of signals under consideration cover a wide variety of classes common to nonparametric regression. In particular, they contain the signals whose parameters of smoothness are not uniformly bounded, even locally. We develop an estimator which is optimal in order over a wide range of the classes and “discrete” global accuracy measures

Keywords

Gaussian noise; adaptive estimation; adaptive signal processing; parameter estimation; Gaussian noise; adaptive signal denoising; differential operator; discrete global accuracy measures; linear differential inequalities; nonparametric regression; random variable; smoothness parameter; spatial adaptive estimation; Adaptive estimation; Covariance matrix; Gaussian noise; Helium; Image restoration; Minimax techniques; Noise reduction; Nonlinear filters; Signal processing; Signal restoration;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.568698

Filename

568698