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 w_h. We get:

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

and L is a threshold estimated by:

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

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

• t(a) = 0 if $a \geq k$
• $t(a) = 1 - \frac{1}{k} a$ if a < k