Title :
Wavelet-based combined signal filtering and prediction
Author :
Renaud, Olivier ; Starck, Jean-Luc ; Murtagh, Fionn
Author_Institution :
Methodology & Data Anal., Univ. of Geneva, Switzerland
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;
Journal_Title :
Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on
DOI :
10.1109/TSMCB.2005.850182
