Wavelet denoising techniques with applications to experimental geophysical data

In this paper, we compare Fourier-based and wavelet-based denoising techniques applied to both synthetic and real experimental geophysical data. The Fourier-based technique used for comparison is the classical Wiener estimator, and the wavelet-based techniques tested include soft and hard wavelet thresholding and the empirical Bayes (EB) method. Both real and synthetic data sets were used to compare the Wiener estimator in the Fourier domain, soft thresholding, hard thresholding, and the EB wavelet-based estimators. Four synthetic data sets, originally designed by Donoho and Johnstone to isolate and mimic various features found in real signals, were corrupted with correlated Gaussian noise to test the various denoising methods. Quantitative comparison of the error between the true and estimated signal revealed that the wavelet-based methods outperformed the Wiener estimator in most cases. Also, the EB method outperformed the soft and hard thresholding methods in general because the wavelet representation is not sparse at the coarsest levels, which leads to poor estimation of the noise variance by the thresholding methods. Microseismic and streaming potential data from laboratory tests were used for comparison and showed similar trends as in the synthetic data analysis.