Time series: data analysis and theory
Time series: data analysis and theory
Extrapolation, Interpolation, and Smoothing of Stationary Time Series
Extrapolation, Interpolation, and Smoothing of Stationary Time Series
Wavelet-based image denoising using a Markov random field a priori model
IEEE Transactions on Image Processing
Short Communication: Wavelet denoising using principal component analysis
Expert Systems with Applications: An International Journal
Denoising of event-related potential signal based on wavelet method
LSMS/ICSEE'10 Proceedings of the 2010 international conference on Life system modeling and simulation and intelligent computing, and 2010 international conference on Intelligent computing for sustainable energy and environment: Part III
Wavelet based seismic signal de-noising using Shannon and Tsallis entropy
Computers & Mathematics with Applications
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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.