Digital Signal Processing Reference
In-Depth Information
Algorithm 41
Curvelet Transform on the Sphere
Task:
Compute the curvelet transform on the sphere of a discrete image
X
.
Parameters:
Image
X
and number of scales
J
.
Initialization:
B
1
=
B
min
.
Compute the isotropic UWTS of
X
with
J
scales; get
{
w
1
,...,w
J
,
c
J
}
.
for
j
=
0
to
J
−
2
do
1. Partition the wavelet subband
w
j
with a block size
B
j
.
2. Apply the digital ridgelet transform to each block; get the curvelet coeffi-
cients at scale
j
.
if
j
modulo 2
=
1
then
B
j
+
1
=
2
B
j
,else
B
j
+
1
=
B
j
.
Output:
The curvelet transform on the sphere of
X
.
ridgelet transform on the wavelet scale, is unchanged. The pyramidal curvelet trans-
form on the sphere (PCTS) algorithm is summarized in Algorithm 42.
In the next section, it is shown how the pyramidal curvelet transform can be used
for image filtering.
Figure 10.14. Flow graph of the curvelet transform on the sphere. (
See color plates.
)
