Nonlinear Noise Reduction in Reconstructed Phase Space Based on Self-organizing Map

This paper presents an approach of nonlinear noise reduction for chaotic and quasi-deterministic signals based on the property of self-organizing map in reducing the dimensionality. The approach views the data series as the observation of an underlying dynamical system that can be reconstructed according to Takens´ embedding theorem. Utilizing the different nature of the signal and noise in the reconstructed phase space, the denoising scheme is performed by training the sub-areas of the attractors with self-organizing map and considering the weight vectors as the reference vector points used for adjusting the noisy trajectory. The approach is evaluated for deterministic chaotic signals contaminated with white noise and also applied to several processing areas of measured data, including the denoising of ship-radiated sound, the enhancement of Chinese speech and the separation of electrocardiogram signals. It shows efficacy in processing and superiority to the traditional methods