Automatic Nonlinear Noise Reduction using Local Principal Component Analysis and MDL Parameter Selection

R. Vetter, J.M. Vesin, P. Celka, P. Renevey, and J. Krauss (Switzerland)


Noise reduction, nonlinear dynamics, local principal component analysis, parsimonious subspace selection, minimum description length


We present a noise reduction algorithm for nonlinear signals with an associated automatic parameter selection method. The term automatic denotes the fact that the pro posed algorithm ensures a near-optimal de-noising using only the noisy data set, the assumption of white noise and nothing else. Various validations, such as improvement in SNR and visual inspection of enhanced phase portraits are presented. The algorithm is also validated as a preprocess ing tool to methods for the estimation of invariants of the dynamics of the signal, such as correlation dimension and largest Lyapounov exponent. All the validations point out, that the proposed algorithm provides considerable noise re duction while reconstructing the very essence of the dy namics of the signals.

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