a novel noise reduction method based on subspace division

this article presents a new subspace-based technique for reducing the noise ofsignals in time-series. in the proposed approach, the signal is initially representedas a data matrix. then using singular value decomposition (svd), noisy datamatrix 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 reducethe effect of space intersections on altering the structure of important information inthe signal. on the other hand, since singular vectors are the span bases of thematrix, reducing the effect of noise from the singular vectors and using them inreproducing the matrix, enhances the information embedded in the matrix. theproposed technique utilizes the savitzky-golay low-pass filter for noise attenuationfrom the singular vectors. the enhanced matrix is finally transformed to a timeseriessignal. the obtained results in this research indicate that the proposedmethod excels the other existing time-domain approaches in noise reduction.