Image Processing Techniques in Emission Tomography - Correction Techniques in Emission Tomography - page 122

(a) Original (b) Mean (c) Median (d) Wiener

FIGURE 7.1: The original noisy image (a) of a human heart was filtered
using different standard denoising techniques. (b) Mean filtering. (c) Median
filtering. (d) Wiener filtering.

7.2.1 Image domain
To get a sense of denoising it is helpful to look at basic image domain{
based filtering techniques. In the following, denoising is illustrated using 2D
examples of mean filtering , median filtering , and a local adaptive version of
Wiener filtering .
An example of denoising in PET is given in Figure 7.1. The original image
is shown in Figure 7.1(a). The noise visible in the image is caused by low
statistics. The amount of noise is reduced using mean filtering in Figure 7.1(b),
median filtering in Figure 7.1(c), and Wiener filtering in Figure 7.1(d). In the
following these techniques are discussed in detail.

Mean filtering.
The mean filter is a linear filter technique. Each pixel of the image is replaced
by the mean value of its neighborhood. Technically, the noisy input image I
is convolved with a filter mask M delivering the denoised image

I d = M ? I: (7.3)

For a lter size of 3 3 the mean lter mask is dened as

0 1

1 1 1

1
9

@ A :

M := 1 1 1 (7.4)

1 1 1

M is always scaled in such a way that its values sum up to 1. This normaliza-
tion prevents a shift of intensities. Mean filtering leads to blurring and does
not preserve edges as is apparent in Figure 7.1(b).
A related approach is Gaussian filtering where the filter mask M is defined
as a (two-dimensional) Gaussian function.

Median filtering
Median filtering is a non-linear method which is in particular suited to remove
salt and pepper noise. For every pixel of the image a neighborhood is chosen
which is, including the pixel itself, sorted by value. The median of these sorted
values is chosen as the new value for the pixel. Looking at the torso outline
in Figure 7.1(c) it can be seen that edges are preserved better compared to
mean filtering.