Abstract
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.
Highlights
With the science and technology developing, the mechanical equipment is becoming more and more complicated, which indicates that intelligent controlling and monitoring methods are necessary for machineries
It has been demonstrated that the thresholding function based denoising algorithms utilizing local probability density function (PDF) [15] or utilizing interscale dependency of wavelet coefficients [16, 17] are among the best
In order to enhance the denoising effect, a subband based on Gaussian mixture model (SGMM) is proposed as a local PDF for each wavelet coefficient in its neighborhood
Summary
With the science and technology developing, the mechanical equipment is becoming more and more complicated, which indicates that intelligent controlling and monitoring methods are necessary for machineries. In order to enhance the denoising effect, a subband based on Gaussian mixture model (SGMM) is proposed as a local PDF for each wavelet coefficient in its neighborhood. The conventional standard deviation (CSD) is mostly used to estimate the standard deviation of noise-free coefficients and it will appear in the thresholding function after MAP estimation based on SGMM, which will strongly influence the noise reduction effect. We will try to derive a quantum-inspired standard deviation (QSD) for noise-free wavelet coefficients in order to improve noise reduction effect of denoising method with CSD. In this paper the clean coefficients are estimated from the noisy data observations considering both local PDF using SGMM and interscale dependency using QSD while processing the wavelet coefficients with Bayesian estimation techniques.
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