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Paulo Gonçalves


Inria senior researcher in the project DANTE
A joint team of Inria Rhone-Alpes and ENS Lyon (LIP)


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Signal Processing applied to Networks
Time-Frequency Analysis
Time-Scale Analysis
Wavelets and Fractals
Wavelets History
by I. Daubechies
Wavelets and Statistics Description:: The hidden Markov tree models were introduced by Crouse, Nowak and Baraniuk (1998) for modeling non-independent, non-Gaussian wavelet transform coefficients. In their article, they developed the equivalent of the forward-backward algorithm for hidden Markov tree models, termed the "upward-downward algorithm". This algorithm is subject to the same numerical limitations as the forward-backward algorithm for hidden Markov chains. In this paper, adapting the ideas of Devijver (1985), we propose a new "upward-downward" algorithm which is a true smoothing algorithm and which is immune to numerical underflow. Furthermore, we propose a Viterbi-like algorithm for global restoration of the hidden state tree. The contribution of those algorithms as diagnosis tools is illustrated through the modeling of statistical dependencies between wavelet coefficients with a special emphasis on local regularity changes.
Joint work with:: Jean-Baptiste Durand (INP Grenoble), Yann Guédon
Other applications



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