ITERATIVE SVD METHOD FOR NOISE REDUCTION OF LOWDIMENSIONAL CHAOTIC TIME SERIES

A new simple method using singular value decomposition (SVD) is presented for reducing noise from a sampled signal where the deterministic signal is from a low-dimensional chaotic dynamical system. The technique is concerned particularly with improving the reconstruction of the phase portrait. This method is based on time delay embedding theory to form a trajectory matrix. SVD is then used iteratively to distinguish the deterministic signal from the noise. Under certain conditions, the method can be used almost blindly, even in the case of a very noisy signal (e.g. a signal to noise ratio of 6 dB). The algorithm is evaluated for a chaotic signal generated by the Duffing system, to which white noise is added.