Aiming at improving noise reduction effect for mechanical vibration signal, a Gaussian mixture model (SGMM) and a quantum-inspired standard deviation (QSD) are proposed and applied to the denoising method using the thresholding function in wavelet domain. Firstly, the SGMM is presented and utilized as a local distribution to approximate the wavelet coefficients distribution in each subband. Then, within Bayesian framework, the maximum a posteriori (MAP) estimator is employed to derive a thresholding function with conventional standard deviation (CSD) which is calculated by the expectation-maximization (EM) algorithm. However, the CSD has a disadvantage of ignoring the interscale dependency between wavelet coefficients. Considering this limit for the CSD, the quantum theory is adopted to analyze the interscale dependency between coefficients in adjacent subbands, and the QSD for noise-free wavelet coefficients is presented based on quantum mechanics. Next, the QSD is constituted for the CSD in the thresholding function to shrink noisy coefficients. Finally, an application in the mechanical vibration signal processing is used to illustrate the denoising technique. The experimental study shows the SGMM can model the distribution of wavelet coefficients accurately and QSD can depict interscale dependency of wavelet coefficients of true signal quite successfully. Therefore, the denoising method utilizing the SGMM and QSD performs better than others.