Using PDE’s for Noise Reduction in Time Series

HAMID HASSANPOUR School of Information Technology and Computer Engineering, Shahrood University of Technology. ___________________________________________________________________________________ Abstract: In this paper, a new method is presented for noise reduction in signal using partial differential equations. In this approach, the signal is initially represented as a matrix. Then using singular values of the matrix, noisy data matrix is divided into signal subspace and noise subspace Since singular vectors are the span bases of the matrix, reducing the effect of noise from the singular vectors and using them in reproducing the matrix enhances the information embedded in the matrix. The proposed technique utilizes the Partial Differential Equations (PDEs) for noise attenuation from the singular vector.The enhanced matrix is finally transformed to a time series vector. To evaluate performance of the proposed method, a number of experiments have been performed on both multi-component and FM signals cluttered with noise. The results indicate that the proposed method outperforms the existing approach, in signal de-noising.