Digital Signal Processing Reference
In-Depth Information
Figure 9.5. (top) The 256×256 source images. (bottom) Two noisy mix-
tures SNR= 10 dB.
hereinafter, we used the RNA on the channels transformed in the 2-D OWT
domain
3.
Efficient fast independent component analysis (EFICA):
This separation
method improves the FastICA algorithm for sources following a GGD prior;
we thus applied EFICA on the channels transformed by a 2-D OWT to spar-
sify them, and hence the leptokurticity assumption on the source marginal
statistics becomes valid
2 mixtures. The sources
s
1
and
s
2
are normalized to a unit variance. The mixing matrix
A
is such that
y
1
=
Figure 9.5 shows the original
N
s
=
2 sources and
N
c
=
0
.
25
s
1
+
0
.
5
s
2
+
ε
1
and
y
2
=−
0
.
75
s
1
+
0
.
5
s
2
+
ε
2
, where
ε
1
and
ε
2
are zero-
mean white Gaussian noise vectors that are mutually independent.
The comparisons we carry out here are twofold: (1) we assess the separation
quality in terms of the correlation between the original and estimated sources as the
SNR varies and (2) as the estimated sources are also perturbed by noise, we also
quantify the performance of each method by computing the mixing matrix criterion
C
A
. The GMCA algorithm was applied using a dictionary containing the DCTG2
and the local DCT.
Figure 9.6 portrays the evolution of the correlation coefficient of source 1 and
source 2 as a function of the SNR. At first glance, GMCA, RNA, and EFICA are
