Biomedical Engineering Reference
In-Depth Information
Figure 6.5: Filter bank implementation of a multidimensional discrete dyadic
wavelet transform decomposition (left) and reconstruction (right) for two levels
of analysis.
In this framework, reconstruction with an
N
-dimensional dyadic wavelet trans-
form requires a nonseparable filter
L
N
to compensate the interdimension cor-
relations. This is formulated in a general context as:
N
l
=
1
|
H
(
ω
l
)
|
N
2
K
(
ω
l
)
G
(
ω
l
)
L
N
(
ω,...,ω
l
−
1
,ω
l
+
1
,...,ω
N
)
+
=
1
.
(6.19)
l
=
1
Figure 6.5 illustrates a filter bank implementation with a multidimensional dis-
crete dyadic wavelet transform. For more details and discussions we refer to
[19].
6.2.3 Other Multiscale Representations
Wavelet transforms are part of a general framework of multiscale analysis. Var-
ious multiscale representations have been derived from the spatial-frequency
framework offered by wavelet expansion, many of which were introduced to
provide more flexibility for the spatial-frequency selectivity or better adaptation
to real-world applications.
In this section, we briefly review several multiscale representations de-
rived from wavelet transforms. Readers with an intention to investigate more
