
218 A Computational Introduction to Digital Image Processing, Second Edition
8.7 Wiener Filtering
As we have seen from the previous section, inverse filtering does not necessarily produce
particularly pleasing results. The situation is even worse if the original image has been
corrupted by noise. Here we would have an image X filtered with a filter F and corrupted
by noise N. If the noise is additive (for example, Gaussian noise), then the linearity of the
Fourier transform gives us
Y (i, j) = X(i, j)F (i, j) + N(i, j)
and so
X(i, j) =
Y (i, j) − N(i, j)
F (i, j)
as we have seen in the introduction to this chapter. So not only do we have the problem
of dividing ...