A novel Bayesian nonparametric estimator in the Wavelet domain is presented. In this approach, a prior model is imposed on the wavelet coefficients designed to capture the sparseness of the wavelet expansion. Seeking probability models for the marginal densities of the wavelet coefficients, the new family of Bessel K forms (BKF) densities are shown to fit very well to the observed histograms. Exploiting this prior, we designed a Bayesian nonlinear denoiser and we derived a closed form for its expression. We then compared it to other priors that have been introduced in the literature, such as the generalized Gaussian density (GGD) or the alpha-stable models, where no analytical form is available for the corresponding Bayesian denoisers. Specifically, the BKF model turns out to be a good compromise between these two extreme cases (hyperbolic tails for the alpha-stable and exponential tails for the GGD). Moreover, we demonstrate a high degree of match between observed and estimated prior densities using the BKF model. Finally, a comparative study is carried out to show the effectiveness of our denoiser which clearly outperforms the classical shrinkage or thresholding wavelet-based techniques.

This article presents a general methodology for processing non-stationary signals for the purpose of classification and localization. The methodology combines methods adapted from three complementary areas: time-frequency signal analysis, multichannel signal analysis and image processing. The latter three combine in a new methodology referred to as multichannel time-frequency image processing which is applied to the problem of classifying electroencephalogram (EEG) abnormalities in both adults and newborns. A combination of signal related features and image related features are used by merging key instantaneous frequency descriptors which characterize the signal non-stationarities. The results obtained show that, firstly, the features based on time-frequency image processing techniques such as image segmentation, improve the performance of EEG abnormalities detection in the classification systems based on multi-SVM and neural network classifiers. Secondly, these discriminating features are able to better detect the correlation between newborn EEG signals in a multichannel-based newborn EEG seizure detection for the purpose of localizing EEG abnormalities on the scalp.

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