A Novel Noise Reduction Method Based on Subspace Division

This article presents a new subspace-based technique for reducing the noise of signals in time-series. In the proposed approach, the signal is initially represented as a data matrix. Then using Singular Value Decomposition (SVD), noisy data matrix is divided into signal subspace and noise subspace. In this subspace division, each derivative of the singular values with respect to rank order is used to reduce the effect of space intersections on altering the structure of important information in the signal. On the other hand, 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 Savitzky-Golay low-pass filter for noise attenuation from the singular vectors. The enhanced matrix is finally transformed to a timeseries signal. The obtained results in this research indicate that the proposed method excels the other existing time-domain approaches in noise reduction.