An improved denoising method based on singular value decomposition of Hankel matrix and wavelet thresholding

This work proposes three approaches for reducing noise of signals. The first strategy is based on combining the Hankel matrix-based singular value decomposition (HSVD) and wavelet thresholding (WT) approaches. We consider both cases of applying HSVD followed by WT (HSVD-WT) and applying WT followed by HSVD (WT-HSVD). The other two approaches are proposed to accelerate the computational time of HSVD. One of these approaches is based on partitioning the signals into small intervals before applying HSVD and another one is based on modifying the Hankel matrix to have a smaller dimension. These approaches are tested on different signals, including synthetic periodic and aperiodic signals, as well as signals describing natural sound and images. We investigate the results for various levels of noise and measure the accuracies by mean squared error (MSE), signal-to-noise ratio (SNR) and peak signal to noise ratio (PSNR). The numerical results show that the HSVD-WT and WT-HSVD approaches can provide more accurate results compared to the cases when using HSVD and WT alone. The other two strategies based on partitioning signals and modifying Hankel matrix are shown to give the same level of accuracy as the standard of HSVD approach while using substantially less computational time.