Biomedical Engineering Reference
In-Depth Information
5
1
4
3
0.5
2
1
0
0
−
1
−
2
−
0.5
−
3
−
4
−
1
−
5
−
1
−
0.5
0
0.5
1
−
1
−
0.5
0
0.5
1
(a)
(b)
Figure 6.11: Example of enhancement functions, assuming that the input data
was normalized to the range of [
−
1, 1]. (a) Piecewise linear function,
T
=
0
.
2,
K
=
20. (b) Sigmoid enhancement function,
b
=
0
.
35,
c
=
20. Notice the differ-
ent scales of the
y
-axis for the two plots.
Such enhancement is simple to implement, and was used successfully for con-
trast enhancement on mammograms [19, 38, 39].
From the analysis in the previous subsection, wavelet coefficients with small-
magnitude were also related to noise. A simple amplification of small-magnitude
coefficients as performed in Eq. (6.39) will certainly also amplify noise compo-
nents. This enhancement operator is therefore limited to contrast enhancement
of data with very low noise level, such as mammograms or CT images. Such
a problem can be alleviated by combining the enhancement with a denoising
operator presented in the previous subsection [35].
A more careful design can provide more reliable enhancement procedures
with a control of noise suppression. For example, a sigmoid function [37], plotted
in Fig. 6.11 (b), can be used:
E
(
x
)
=
a
[sigm(
c
(
x
−
b
))
−
sigm(
−
c
(
x
+
b
))]
,
(6.40)
where
1
sigm(c(1
−
b))
−
sigm(
−
c(1
+
b))
,
a
=
0
<
b
<
1
,
1
1
+
e
−
y
. The parameters
b
and
c
respectively
control the threshold and rate of enhancement. It can be easily shown that
E
(
x
)
in Eq. (6.40) is continuous and monotonically increasing within the interval
and sigm(
y
) is defined as sigm(
y
)
=
