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Paulo Gonçalves Inria senior researcher in the project DANTE A joint team of Inria Rhone-Alpes and ENS Lyon (LIP) |
| Signal Processing applied to Networks | ||
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Time-Frequency Analysis Time-Scale Analysis |
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Wavelets and Fractals Wavelets History by I. Daubechies |
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| 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 |
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| Other applications |
