Adaptive chaotic noise reduction method based on dual-lifting wavelet

For the subjectivity of lifting wavelet coefficients selection, an adaptive noise reduction method is proposed for chaotic signals corrupted by nonstationary noises. Here, wavelet coefficients including coarse approximation and detail information are obtained by dual-lifting wavelet transform. The coarse parts are handled by the singular spectrum analysis, whereas the detail parts are analyzed combining with gradient decent algorithm in neural networks for the adaptive choice of wavelet coefficients. The chaotic signals generated by Lorenz model as well as the observed monthly series of sunspots are respectively applied for simulation analysis. The experimental results show a dramatic improvement of the proposed method, the advantages of which include the simple of achieving, the small reconstruction error and the efficiency for the noisy chaotic signals.