Research on Denoising Method Based on Iterative SVD Decomposition

In response to the poor denoising ability of Singular Value Decomposition (SVD), and the extracted motion waveform containing some residual noise signals, this paper proposes an iterative SVD decomposition denoising method. Firstly, the original signal is constructed into a binary recursive matrix form, and then SVD decomposition is used to obtain singular values with different contributions to the original matrix. Then, singular values with small contributions are discarded, while those with large contributions are retained. By modifying the signal reconstruction method, the denoised signal can be obtained once, and the required signal can be obtained by repeating the above process continuously. In simulation experiments and tuning fork vibration experiments, this article uses the iterative SVD decomposition denoising method and two existing denoising methods to denoise signals containing noise and uses signal-to-noise ratio (SNR) and root mean square error method (RMSE) as denoising performance indicators for data comparison, confirming the effectiveness and superiority of iterative SVD decomposition denoising method and its excellent denoising ability. In the tuning fork vibration experiment, the error between the measured results and the actual results is 0.3125%, proving that this denoising method has practical application value.