In order to remove the ambient noise and increase the signal-to-noise ratio (SNR) in an electromagnetic acoustic transducer (EMAT), we proposed a new closed-form shrinkage function based on Gauss-Laplace mixture distribution in the wavelet domain, and they studied the work to evaluate the denoising performance of a new shrinkage function compared with classical methods through the experiment.
First, the statistical modeling for wavelet coefficients of EMAT signal was carried out. We proved that Gauss–Laplace mixture distribution was well fitted to the statistical model for wavelet coefficients of noise-free signal of EMAT.
Second, we derived GaussLapMixShrinkGMAP that was a closed-form shrinkage function based on Gauss–Laplace mixture distribution, and proposed an analytical solution of a Bayesian MAP estimator. GaussLapMixShrinkGMAP shrinkage function is the continuous function as well as the monotone increasing function. This showed that this shrinkage function solved problems of discontinuity and constant error.
Third, we evaluated the performance of wavelet denoising method using the GaussLapMixShrinkGMAP compared with various denoising methods using Hard and Soft thresholding, GaussShrinkGMAP, GaussMixShrinkGMAP and LapMixShrinkGMAP shrinkage functions.
Results showed that ISNRs of proposed method was largest, RMSE and EN of proposed method were smallest of the other existing denoising methods for received noisy signal of EMAT at different ambient noise levels. This implies that the ambient denoising performance using GaussLapMixShrinkGMAP shrinkage function is best of the six denoising methods. Thus, the wavelet denoising method using GaussLapMixShrinkGMAP shrinkage function is more appropriate to remove the ambient noise than the other five denoising methods for received noisy signal of EMAT.
The research results were published in "International Journal of Wavelet, Multi-resolution and Information Processing" in 2023 under the title of "Closed-form shrinkage function based on mixture of Gauss–Laplace distributions for dropping ambient noise" (https://doi.org/10.1142/S0219691322500618).
