Modeling heavy-tailed correlated noise with wavelet packet basis functions

Empirical Bayes (EB) methods are used to model correlated and heavy-tailed time series background noise. Background noise is modeled as a multiband Studentʹs t process and estimates of the degree of freedom parameters and scaling parameters at each subband are used to characterize the background clutter. We compare this model with a multiband Gaussian model to demonstrate its robustness and accuracy with both underwater acoustic and seismic recordings. We demonstrate the usefulness of this model as a means of parameter estimation for wavelet packet denoising by applying the model to ocean acoustic recordings of whale calls and ground motion measurements of quarry blast explosions.