Image Processing Reference
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These components can be considered super-Gaussian distributed in the spatial
domain because they are focused activations in small clusters compared with
the whole volume. In Reference 34 and Reference 35 the ICA decomposition
was applied without PCA reduction and usually one component for each trial
was found to highly correlate with the task (r
0.6). Some components that
showed abrupt changes in the associated time courses or ring-like spatial
distributions were thought to be related to movement effects. Other components
may have been diffuse and noisy. Quasi-periodic components, probably due to
the physiological pulsations, heartbeat, and respiratory effects, were found. Because
sampling times are often less than a second, aliasing often cannot be avoided, and
these quasi-periodic effects can also be derived from spin excitation history
effects. Several TTR components were also found, showing a correlation with
the task only for one or two repetitions of the task blocks. Although the
advantages of exploratory analysis performed with ICA were stressed because
these TTR maps could not be detected by correlation analysis that computes
the average over all the cycles, the question was if these components could
be modified by the requirement of spatial independence of the CTR maps. In
order to perform this test, ICA was performed again on the data with the CTR
removed, showing that even if some TTR components were unaffected by the
CTR removal, others changed sensibly, suggesting a spatial dependence among
these components. The component removal can be performed by multiplying
the components matrix, found by ICA, by a copy of the mixing matrix whose
columns corresponding to the components to be removed are zeroed. If
W
is
the unmixing matrix and is its inverse with the columns zeroed, then the
reconstructed data matrix can be written as . In Reference 41 it
is suggested that the presence of TTR activations may originate from interest-
ing physiological processes but may originate also from an overfitting problem
and the lack of a significance test for the components. In this work a proba-
bilistic PCA model order reduction was used, which, starting from the cova-
riance matrix of the data, estimated the posterior distribution of the model
order. In Reference 40 the problem of identification and characterization of
the maps was outlined. In this work the maps obtained after spatial ICA were
classified according to three descriptive measures: the kurtosis of the map
values, the degree of spatial clustering of each map, and the one-lag autocor-
relation of each map time series. The kurtosis takes into account the distribu-
tion properties of each map intensity. The degree of spatial clustering of each
map, after a thresholding operation by means of a z score, was chosen because
activation maps usually have a defined spatial structure. The one-lag autocor-
relation of each map time series was chosen in order to detect a temporal
structure in the maps. This procedure was applied to voxels belonging to the
cortex individuated by means of the segmentation of a high-resolution T1
anatomical image coregistered with the functional images. The method showed
that the simultaneous inspection of these values could reveal potentially mean-
ingful phenomena because in different tasks the interesting components show
similar combinations of these parameters.
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