A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
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We deal in this paper with the extraction of multiresolution statistical signatures for the characterization of transient signals in strongly noisy contexts. These short-time signals have sharp and highly variable frequency components. The time/frequency window to choose for our analysis is then a major issue. We have chosen the Wavelet Packet Transform (WPT) due to its ability to provide multiple windows analysis with different time/frequency resolutions. We propose a new oriented Hidden Markov Tree (HMT) dedicated to the tree structure of the WPT, which offers promising statistical characterization of time/frequency variations in a signal, by exploiting several time/frequency resolutions. This model is exploited in a Bayesian context for the segmentation of signals containing transient components. The chosen data likelihood is a Generalized Gaussian Distributions (GGD), well suited for the modeling of Wavelet Packet Coefficients (WPC) distributions. We demonstrate the efficiency of our method on synthetic signals with several Signal to Noise Ratio (SNR). Our application domain is related to biomedical signals, and more specifically for the detection of uprising abnormalities in pulmonary sounds. This original method shows remarkable ability to detect such sounds, which are usually buried in the normal lung noise and are often very difficult to perceive with the human earing.