Biomedical Engineering Reference
In-Depth Information
T
1
T
2
Wavelet
Decomposition
Wavelet
Reconstruction
T
3
Input Image
DC
Figure 6.9:
A Multiscale framework of denoising and enhancement using dis-
crete dyadic wavelet transform. A three-level decomposition was shown.
domain) followed by reconstruction of the signal to the original image (spatial)
domain.
Typical threshold operators for denoising include
hard thresholding
:
x
,
if
|
x
|
>
T
ρ
T
(
x
)
=
(6.36)
|
x
|≤
T
,
0
,
if
soft thresholding
(wavelet shrinkage) [33]:
⎧
⎨
x
−
T
,
if
x
≥
T
ρ
T
(
x
)
=
x
+
T
,
if
x
≤−
T
,
(6.37)
⎩
0
,
if
|
x
|
<
T
and
affine (firm) thresholding
[34]:
⎧
⎨
x
,
if
|
x
|≥
T
2
x
+
T
,
if
−
T
≤
x
≤−
T
/
2
ρ
T
(
x
)
=
.
(6.38)
⎩
2
x
−
T
,
if
T
/
2
≤
x
≤
T
0
,
if
|
x
|
<
T
The shapes of these thresholding operators are illustrated in Fig. 6.10.
6.3.2 Enhancement Operators
Magnitude of wavelet coefficients measures the correlation between the image
data and the wavelet functions. For first-derivative-based wavelet, the magnitude
