Image Processing Reference
In-Depth Information
that the spatial distribution of the independent components does not change with
time and that they are linearly mixed [35]. Temporal ICA assumes that there are
statistically independent temporal processes [36]. These two approaches seem to
give similar results in the case of one expected task-related component [37]. In
Reference 38 it was shown that they give similar results in decomposing data with
two components that are both spatially and temporally independent. In general,
the two methods give divergent results depending on the agreement with the
hypothesis of spatial or temporal independence. In this study [38], different spa-
tiotemporal patterns of activation were simulated, and it was shown that the two
methods produce similar results if the two components are both spatially and
temporally uncorrelated. If the components are correlated in time, time-domain
ICA will not give good correct results; similarly, spatial ICA will not give correct
results in the case of spatially dependent patterns of activation. From these con-
siderations, it emerges that the ICA model must be applied carefully, and the
experimenters have to know that it can lead to incorrect results. Even if a paradigm
is supposed to give temporally independent activations, there may be some inter-
esting components temporally correlated to each other that are not supposed in
advance. One way to proceed is to perform both spatial and temporal ICA and
then use consensus methods [74] to find regions that are activated independently
of the chosen model. Stone [39] introduced a spatiotemporal approach that max-
imizes simultaneously the independence in spatial and temporal domains. Spatial
ICA has been the most used approach mainly because of fewer computational
demands owing to the fact that in fMRI data sets the spatial dimension is much
larger than the temporal one. In fact, in spatial ICA the variables are represented
by the time points, whereas the observations are the voxels values; hence, the
computational benefit of the spatial ICA approach is clear.
16.5.2
M
ETHODS
FOR
ICA
16.5.2.1
Historical Background
One of the first solutions to the BSS problem was given by Cardoso [71],
who used higher-order moments. The work on higher-order cumulant tensors
led to the development of the JADE algorithm [75]. The work by Pham, using
a maximum likelihood criterion [76], was further developed by Cardoso and
led to the EASI method [77]. A great improvement to ICA was due to the
algorithm developed by Bell and Sejnowski based on the InfoMax approach
[78]. This algorithm was then modified by Amari, using the natural gradient
[79]. It has been shown that this method has connections with the maximum
likelihood approach and with the earlier work of Cichocki et al. [80]. A very
popular algorithm, widely used for its computational efficiency, is the fastICA
algorithm based on a fixed-point iteration scheme [81]. A good review of
these algorithms and their relations can be found in Reference 82. Now, we
will briefly review some of the principles used to extract the independent
component from a data set.
Search WWH ::
Custom Search