Algorithm for noise reduction for strongly contaminated chaotic oscillators based on the local projection approach and 2D wavelet filtering

In this paper, a novel algorithm based on the local projection noise reduction approach is applied to smooth noise for strongly contaminated chaotic oscillators. Specifically, one-dimensional time series are embedded into a high dimensional phase space and the noise level is defined through orthogonal projections of the data points within the neighbourhood of the reference point onto linear subspaces. The current vector of the phase space is denoised by performing two-dimensional discrete stationary wavelet transform (SWT)-based filtering in the neighbourhood of the phase point. Numerical results show that our algorithm effectively recovers continuous-time chaotic signals in heavy-noise environments and outperforms the classical local projection noise reduction approach for simulated data from the Rossler system and Duffing oscillator at signal-to-noise ratios (SNRs) from 15 to 0 dB, either for the real world data – human breath time series.