Efficient Signal Denoising Methods Using Randomized HSVD and Wavelet Thresholding

This work introduces efficient signal denoising methods based on wavelet thresholding (WT) and Hankel matrix-based Singular Value Decomposition (HSVD) with a randomized algorithm. The sequential hybrid frameworks of these techniques are investigated—both WT followed by HSVD (WT-HSVD) and HSVD followed by WT (HSVD-WT)—across varying noise levels. Numerical tests are performed through different benchmark signals, including dual harmonic, damped sine, and dual frequency signals, as well as a natural phonocardiogram recording. Different types of corrupted noises, including white Gaussian, colored (brown), and impulsive noises, are considered in the numerical tests. For moderate and high noise levels, hybrid frameworks can significantly improve the final accuracy of the denoised signals, as measured by reconstruction error metrics and Signal-to-Noise Ratio. These hybrid frameworks are also shown to be advantageous in compensating for suboptimal parameter selections that may occur when using either method individually. Furthermore, to mitigate the computational burden inherent to exact SVD, this work employs a randomized Singular Value Decomposition (rSVD) algorithm. Depending on the signal size, the proposed hybrid frameworks with rSVD achieve a 30% to 80% reduction in CPU execution time while maintaining denoised signal reconstruction accuracy across test cases.