Closed-form shrinkage function based on mixture of Gauss–Laplace distributions for dropping ambient noise

Abstract

Removing the ambient noise and increasing the signal-to-noise ratio are very important for detecting defects and corrosions of conductive material by using the electromagnetic acoustic transducer. It is still an issue to remove the ambient noise without losing the original signal information. The aim of this paper is to solve the issue by using a new closed-form shrinkage function based on Gauss–Laplace mixture distribution in wavelet domain. First, we prove that Gauss–Laplace mixture distribution is well fitted to the statistical model for wavelet coefficients of noise-free signal of electromagnetic acoustic transducer. As well, we use Gauss–Laplace mixture distribution and Gauss distribution for statistical modeling on the wavelet coefficients of noise-free signal and ambient noise, respectively. Using these distributions, we derive a new closed-form shrinkage function that is an analytical solution of a Bayesian maximum a posteriori estimator. Next, we evaluate the denoising performance of new shrinkage function compared with various shrinkage functions in terms of the improved signal-to-noise ratio, root mean squared error and entropy. The experiment results show that the wavelet denoising method using the proposed shrinkage function effectively removes the ambient noise than the other existing denoising methods for noisy signal of electromagnetic acoustic transducer.