In the above process, we do not use the information between the wavelet
coefficients at different scales. We modify the previous
algorithm by introducing a prediction 
of the wavelet coefficient from
the upper scale. This prediction could be determined from the regression
[2] between the two scales but better results are obtained
when we only set 
to 
. Between the expectation
coefficient 
and the prediction, a dispersion exists where we
assume that it is a Gaussian distribution:
The relation which gives the coefficient 
knowing 
and 
is:
with:
and:
This follows a Gaussian distribution with a mathematical expectation:
with:
is the barycentre of the three values 
, 
, 0 with the
weights 
, 
, 
. The particular cases are:
) and even if the correlation
between the two scales is good (
is low), we get 
.
then 
.
then 
.
then 
.
At each scale, by changing all the wavelet coefficients 
of the
plane by the estimate value 
, we get a Hierarchical Wiener
Filter. The algorithm is:
.
of the first plane
from the histogram of 
.
from 
.
where 
is the variance of 
to 
and compute the standard deviation 
of 
.
