Mathematics in Independent Component Analysis

Chapter 6. LNCS 3195:726-733, 2004 119
6 Fabian J. Theis, Anke Meyer-Baese, and Elmar W. Lang
crosstalking error E1( Â, A)
PSfrag replacements
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SOBI K=32
SOBI K=128
mdSOBI K=32
mdSOBI K=128
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0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Fig. 3. SOBI and mdSOBI performance dependence on noise level σ. Plotted is the
crosstalking error E1 of the recovered matrix  with the real mixing matrix A. See
text for more details.
images, whereas performance of SOBI strongly depends on whether column or
row concatenation was used to construct a one-dimensional random process out
of each image. The SOBI breakpoint of around K = 52 can be decreased by
choosing smaller stripes. In future works we want to provide an analytical discussion
of performance increase when comparing SOBI and mdSOBI similar to
the performance evaluation in [4].
4 Results
Artificial mixtures. We consider the linear mixture of three images (baboon,
black-haired lady and Lena) with a randomly chosen 3 × 3 matrix A. Figure
3 shows how SOBI and mdSOBI perform depending on the noise level σ. For
small K, both SOBI and mdSOBI perform equally well in the low noise case, but
mdSOBI performs better in the case of stronger noise. For larger K mdSOBI
substantially outperforms SOBI, which is due to the fact that natural images do
not have any substantial long-distance autocorrelations (see figure 1), whereas
mdSOBI uses the non-trivial two-dimensional autocorrelations.
fMRI analysis. We analyze the performance of mdSOBI when applied to fMRI
measurements. fMRI data were recorded from six subjects (3 female, 3 male,
age 20–37) performing a visual task. In five subjects, five slices with 100 images
(TR/TE = 3000/60 msec) were acquired with five periods of rest and five
σ