Deviation bounds for wavelet shrinkage

Author

Hong, Dawei ; Birget, Jean-Camille

Author_Institution

Dept. of Comput. Sci., Rutgers Univ., Camden, NJ, USA

Volume

49

Issue

7

fYear

2003

fDate

7/1/2003 12:00:00 AM

Firstpage

1851

Lastpage

1858

Abstract

We analyze the wavelet shrinkage algorithm of Donoho and Johnstone (1994) in order to assess the quality of the reconstruction of a signal obtained from noisy samples. We give a deviation estimate for the maximum squared error (and, consequently, for the average squared error), under the assumption that the signal comes from a Holder class, and the noise samples are independent, of zero mean, and bounded. Our main technique is Talagrand´s (1995) isoperimetric theorem. Our result shows a better behavior of the wavelet shrinkage.

Keywords

mean square error methods; signal reconstruction; signal sampling; wavelet transforms; Holder class; Talagrand isoperimetric theorem; average squared error; deviation bounds; deviation estimate; independent zero mean bounded samples; maximum squared error; noise samples; noisy samples; signal reconstruction; wavelet shrinkage; 3G mobile communication; Antennas and Propagation Society; Filtering; Matched filters; Particle scattering; Signal processing; Signal processing algorithms; Signal resolution; Speech processing; Wavelet analysis;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2003.813482

Filename

1207387