A Computational Introduction to Digital Image Processing, 2nd Edition

Image Restoration 203

same place. Another example is in microscopy, where many different images of the same

object may be taken. In such a case a very simple approach to cleaning Gaussian noise is

to simply take the average—the mean—of all the images.

To see why this works, suppose we have 100 copies of an image, each with noise; then

the i -th noisy image will be:

M + N

i

where M is the matrix of original values, and N

i

is a matrix of normally distributed random

values with mean 0. We can find the mean M



of these images by the usual add and divide

method:

M



=

1

100

100



i=1

(M + N

i

)

=

1

100

100



i=1

M +

1

100

100



i=1

N

i

= M +

1

100

100



i=1

N

i

Since N

i

is normally distributed ...