An intelligent noise reduction method for chaotic signals based on genetic algorithms and lifting wavelet transforms

Time series observed in real world is often nonlinear, even chaotic. However, observed data is often contaminated by noise of various types. To effectively extract desired information from observed data, it is vital to preprocess data to reduce noise for both the analysis of dynamical systems and many potential applications of these systems. In this paper, we present a noise reduction approach to the problem of additive source separation characterized by wide band power spectra when one of the sources is chaotic. The algorithm is based on a Center-Based Genetic Algorithm (CBGA) in lifting wavelet framework, in which the CBGA is used for threshold optimization. This method intelligently adapts itself to various types of noise, and it weighs preservation of dynamics and denoising through Signal-to-Noise Ratio (SNR) and Root-Mean-Square Error (RMSE). Computer simulations show that the approach is very effective in diminishing different kinds of noise, and performs better in terms of visual quality as well as quantitative metrics than existing algorithms.