Noise reduction in chaotic multi-dimensional time series using dictionary learning

Chaotic multi-dimensional time series (MDTS) exist in some fields such as stock markets and life sciences. To effectively extract the desired information from the measured MDTS, it is important to preprocess data to reduce noise. On the basis of dictionary learning, a method to remove noise is proposed, and the proposed approach is shown to be very effective in the case of MDTS. An MDTS is first considered as a whole, namely an image, and then the method is applied on it. Compared with traditional methods, the proposed approach can utilise the information among the different dimensional time series to improve noise reduction. Using the Lorenz data superimposed by the Gaussian noise as an example, the simulation results have validated the mathematical framework and the performance.