Abstract
A model for correlated and heavy-tailed background noise in time series data is introduced. The approach is based on a multi-resolution time adaptive wavelet packet expansion that assigns to each resolution and band a measure of spikiness associated with independent t distributed variates. The model is adaptive similarly in time, scale, and correlation structure within the dyadic structure of the wavelet packet framework. Parameter estimation is accomplished by recursions in time at each frequency band/scale. The model is applied to both ground motion data and shallow water ocean acoustic background noise. A comparison with the Gaussian model suggest its favorable advantage. Estimators for transient signals based on the new model are derived and show usefulness in extracting transients with unknown or weakly specified characteristics. The usefulness of the model and the estimator is demonstrated via a comparison with the fixed transform DWT on quarry blast seisms. The results show that the method outperforms DWT based estimation in MSE by a factor of 2 at a moderate SNR for these classes of transients. [Work supported by ONR.]