Wavelet-based combined signal filtering and prediction

Author

Renaud, Olivier ; Starck, Jean-Luc ; Murtagh, Fionn

Author_Institution

Methodology & Data Anal., Univ. of Geneva, Switzerland

Volume

35

Issue

6

fYear

2005

Firstpage

1241

Lastpage

1251

Abstract

We survey a number of applications of the wavelet transform in time series prediction. We show how multiresolution prediction can capture short-range and long-term dependencies with only a few parameters to be estimated. We then develop a new multiresolution methodology for combined noise filtering and prediction, based on an approach which is similar to the Kalman filter. Based on considerable experimental assessment, we demonstrate the powerfulness of this methodology.

Keywords

Kalman filters; autoregressive processes; filtering theory; prediction theory; signal denoising; time series; wavelet transforms; Kalman filter; autoregression; multiresolution prediction; noise filtering; noise prediction; signal filtering; signal prediction; time series prediction; wavelet transform; Continuous wavelet transforms; Discrete wavelet transforms; Filtering; Image reconstruction; Noise reduction; Parameter estimation; Predictive models; Signal resolution; Wavelet coefficients; Wavelet transforms; Autoregression; Kalman filter; filtering; forecasting; model; resolution; scale; time series; wavelet transform; Algorithms; Computer Simulation; Models, Statistical; Regression Analysis; Signal Processing, Computer-Assisted; Stochastic Processes; Time Factors;

fLanguage

English

Journal_Title

Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on

Publisher

ieee

ISSN

1083-4419

Type

jour

DOI

10.1109/TSMCB.2005.850182

Filename

1542269