Robust multiscale representation of processes and optimal signal reconstruction

Author

Krim, H. ; Pesquet, J.-C. ; Willsky, A.S.

Author_Institution

Lab. for Inf. & Decision Syst., MIT, Cambridge, MA, USA

fYear

1994

fDate

25-28 Oct 1994

Firstpage

1

Lastpage

4

Abstract

We propose a statistical approach to obtain a “best basis” representation of an observed random process. We derive statistical properties of a criterion first proposed to determine the best wavelet packet basis, and, proceed to use it in constructing a statistically sound algorithm. For signal enhancement, this best basis algorithm is followed by a nonlinear filter based on the minimum description length (MDL) criterion. We show that it is equivalent to a min-max based algorithm proposed by Donoho and Johnstone (1992)

Keywords

Gaussian noise; filtering theory; nonlinear filters; random processes; signal reconstruction; signal representation; statistical analysis; wavelet transforms; white noise; Gaussian noise; best basis algorithm; min-max based algorithm; minimum description length criterion; nonlinear filter; optimal signal reconstruction; random process; robust multiscale representation; signal enhancement; statistical approach; statistically sound algorithm; wavelet packet basis; white noise; Acoustic noise; Noise robustness; Nonlinear filters; Random processes; Signal reconstruction; Statistics; Stochastic systems; Wavelet analysis; Wavelet packets; White noise;

fLanguage

English

Publisher

ieee

Conference_Titel

Time-Frequency and Time-Scale Analysis, 1994., Proceedings of the IEEE-SP International Symposium on

Conference_Location

Philadelphia, PA

Print_ISBN

0-7803-2127-8

Type

conf

DOI

10.1109/TFSA.1994.467377

Filename

467377