Digital Signal Processing Reference
In-Depth Information
Fig. 8.1
Desired amplitude
response of the 2D filter
by
1if
ω
1
+
ω
2
<
0
.
04
π,
0
.
5 f0
.
04
π<
ω
1
+
M
d
=
(8.30)
ω
2
<
0
.
08
π,
0
otherwise
.
The desired amplitude response of the 2D filter is shown in Fig.
8.1
. For our
experiment we choose
N
1
=
100 and
N
2
=
100. Results have been reported for
b
1
,
2
,
4, and 8. The efficiency of our approach to the filter design problem is
demonstrated through comparisons of our results with state-of-the-art methodolo-
gies, namely MEPSO, G3 with PCX, and DE reported in [
4
]. The parameter settings
for our proposed IIWO algorithm have been tabulated below in Table
8.1
. They were
set after a set of tuning experiments and were left unaltered for the entire simulation.
The amplitude responses of the filters obtained by the above mentioned algorithms
are shown in Fig.
8.2
.
The problem constraints are handled using the method outlined in [
6
]asfollows:
=
- Any feasible solution is preferred to any infeasible solution;
- Between two feasible solutions, the one with better fitness is preferred;
- Between two infeasible solutions, the one with a smaller constraint violation is
preferred.
In order to test the accuracy of the IIWO algorithm, we ran it along with the com-
petitor algorithms for 50,000 function evaluations. Each algorithm was executed for
30 independent runs. The mean of the objective function values
J
b
(where
b
denotes
the value of the exponent) of the 30 independent runs are reported in Table
8.2
.The
best objective filter coefficients obtained with exponent
b
2 after 50,000 function
evaluations for all the competitor algorithms have been presented in Table
8.3
.
Finally, as an illustration of the performance of the designed low pass filters we
demonstrate an image denoising experiment on the 256
=
256 gray scale image
of Lenna. Denoising of digital images is one generic application of the lowpass
×
Search WWH ::
Custom Search