Noise subspaces subtraction in SVD based on the difference of variance values

Abstract

As a matrix decomposition method, Singular Value Decomposition (SVD) is introduced to signal processing such as denoising. Firstly, a polluted signal is constructed in Hankel matrix form, and then through SVD the Hankel matrix is decomposed to two unitary matrices and a diagonal matrix in which a series of singular values are arranged in a descending order. These singular values are considered to be located in a series of subspaces including signal subspaces and noise subspaces. The singular values in these subspaces are different because the signal magnitudes dominate noise magnitudes. Therefore, if these two kinds of subspaces are well separated, an ideal denoised signal could be achieved by reconstruction. This paper improves the traditional SVD denoising which merely does well in processing periodic signals’ subspaces separation. The improved SVD denoising method based on variance value extends SVD denoising to aperiodic signal denoising. The denoising results by improved SVD denoising, traditional SVD denoising, wavelet thresholding and EEMD denoising are compared and the improved SVD denoising method received an excellent numerical experimental effects.