Digital Signal Processing Reference
In-Depth Information
Figure 5.15. Enhanced coefficient versus original coefficient with
σ
= 1. (left)
Parameters are (
γ,,μ,τ
) = (0
.
5
,
0
,
30
,
3). (right) Parameters are (
γ,,μ,τ
) =
(0
.
5
,
0
.
6
,
30
,
3).
The first choice allows the user to define the coefficients to be amplified as a func-
tion of their SNR, whereas the second one gives an easy alternative independent of
the range of the original coefficients. Figure 5.15 exemplifies the obtained curve of
E
1intheseplots.
To summarize, the curvelet-domain enhancement algorithm for gray scale is as
follows:
(
t
;
σ
) for two sets of parameters;
σ
=
Algorithm 16
Curvelet-Domain Contrast Enhancement
Task:
Enhance the contrast of a discrete image
f
.
Parameters:
Coarsest scale
J
, parameters (
γ,,ρ,τ
).
Estimate the noise standard deviation
σ
in the input image
f
.
Compute the curvelet transform of
f
to get (
α
k
)
j
,,
k
.
j
,,
Compute the noise standard deviation
σ
j
,
at each subband (
j
,
)bymulti-
plying
σ
by the
2
norm of the curvelet at subband (
j
,
); see the end of
Section 5.4.2.2. (If the
2
norms are not known in closed form, they can be
estimated in practice by taking the transform of a Dirac image and then com-
puting the
2
norm of each subband.)
for
Each
scale
j
and orientation
do
max
1. Compute the maximum of the subband:
α
j
,
=
max
k
|
α
j
,,
k
|
.
2. Compute the modified coefficient: ˜
α
j
,,
k
=
α
j
,,
k
E
(
|
α
j
,,
k
|
;
σ
j
,
).
Reconstruct the enhanced image
f
from the modified curvelet coefficients.
Output:
Contrast-enhanced image
f
.
For color images, the contrast enhancement approach can be applied according
to the following steps:
Convert the original color image to the Luv color space.
Compute the curvelet transform of the
L
,
u
, and
v
color components. Get the
u
j
,α
j
,,
k
)
j
,,
k
.
curvelet coefficients (
α
L
j
,α
,,
k
,,
k
