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Дата изменения: Fri Feb 23 12:58:05 1996 Дата индексирования: Tue Oct 2 17:59:25 2012 Кодировка: Поисковые слова: star |
Let us consider a measured wavelet coefficient at the scale i.
We assume
that its value, at a given scale and a given position,
results from a noisy process, with a Gaussian distribution with a
mathematical expectation
, and a standard deviation
:
Now, we assume that the set of expected coefficients for a given
scale also follows a Gaussian distribution, with a null mean and a
standard deviation
:
The null mean value results from the wavelet property:
We want to get an estimate of knowing
. Bayes' theorem gives:
We get:
where:
the probability follows a Gaussian distribution with a mean:
and a variance:
The mathematical expectation of is
.
With a simple multiplication of the coefficients by the constant ,
we get a linear filter. The algorithm is: