Chaotic signal denoising method based on independent component analysis and empirical mode decomposition

Abstract

According to the characteristics of empirical mode decomposition and denoise of independent component analysis, an adaptive denoising method of chaotic signal is proposed based on independent component analysis and empirical mode decomposition. First, the chaotic signal is decomposed into a set of intrinsic mode functions by empirical mode decomposition; then, the multi-dimensional input vectors are constructed based on the translation invariant empirical mode decomposition, and the noise of each intrinsic mode function is removed through the constructed multi-dimensional input vectors and the independent component analysis; finally, the denoisied chaotic signal is obtained by accumulating and reconstructing all the processed intrinsic mode functions. Both the chaotic signal generated by Lorenz map with different level Gaussian noises, and the observed monthly series of sunspots are respectively used for noise reduction using the proposed method. The results of numerical experiments show that the proposed method is efficient. It can better correct the positions of data points in phase space and approximate the real chaotic attractor trajectories more closely．