Signal Denoise Method Based on Fractal Dimension, the Higher Order Statistics and Local Tangent Space Arrangement

In denoise method for nonlinear time series based on principle manifold learning, reduction targets are chosen at random, using linear method of singular value decomposition solving local tangent space coordinate, these caused efficiency and effect of denoise lower. To solve this problem, a new denoise method based on based on the fractal dimension, higher order statistics and local tangent space arrangement is proposed. The intrinsic dimension is estimated as dimension of reduction targets by fractal geometry method, the data outside intrinsic dimension space will be regarded as noise signal to be eliminated . At the same time, making use of restraining characteristic to colored noise of high-order cumulan, covariance matrix is constructed with the fourth-order cumulant function instead of second-order moment function covariance matrix ,local tangent space alignment algorithm based on fourth-order cumulan is also proposed. Noise reduction experiments on lorenz signal and fan’s vibrating signal show that method proposed in this paper has better denoise effect.