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Hierarchical adaptive filtering

In the previous algorithm we do not use the hierarchy of structures. We have explored many approaches for introducing a non-linear hierarchical law in the adaptive filtering and we found that the best way was to link the threshold to the wavelet coefficient of the previous plane wh. We get:

\begin{eqnarray*}W_i(x) = & w_i(x) & \mbox{ if } \mid w_i(x) \mid \geq L \\
W_i(x) = & 0 & \mbox{ if } \mid w_i(x) \mid < L

and L is a threshold estimated by:

\begin{eqnarray*}\mbox{ if } \mid w_i(x) \mid \geq kB_i & \mbox{ then } L = & kB...
... < kB_i & \mbox{ then } L = & kB_i t(\mid\frac{w_h}{S_h}\mid)\\

where Sh is the standard deviation of wh. The function t(a)must return a value between 0 and 1. A possible function for t is:

Petra Nass