We chose to view a signal f as being noisy or incoherent relative to the
basis 
if its entropy is of the same order of magnitude as
giving a poor compression rate 
, leading us to
the following method.
Start with a signal f of length N, find the best basis in each library and
select among them the basis minimizing 
. Reorder the
coefficients 
in decreasing order
where 
for 
are all below a precision threshold (say 0.1% of energy). Then decompose
We will say that 
is coherent and 
is incoherent if
The threshold 
is chosen to determine if the compression of 
using 
is unacceptably bad. We proceed by testing 
until we reach M for which
or
We can now consider 
as a new signal for which we repeat the
decomposition, i.e. pick a best basis and decompose
iterating a fixed number of times or stopping whenever no new coherent part is obtained.
The Xwpl program automatically determines the threshold using heuristics on the coefficient curve.