Image Processing Reference
In-Depth Information
16.1
INTRODUCTION
The study of brain function with magnetic resonance imaging (MRI), which is
sensitive to changes in blood flow and oxygenation [1,2], is a widely used tech-
nique, and its applications are growing rapidly—from the early attempts with
simple block-designed paradigms to the study of more complex cognitive functions
until the study of emotions and behavior [3,4]. Moreover, functional MRI (f MRI)
is becoming increasingly important in clinical applications, for example, in neu-
rology and in planning surgical intervention of the brain. The utility of an explor-
atory data analysis approach is important in order to improve knowledge about the
brain function as more complex processes are studied and because it allows the
detection and characterization of unexpected phenomena that are not modeled or
cannot be modeled
. Several components may affect signal generation and
the experimenter's model, such as subject movement, physiological changes such
as heartbeat and respiration, and noise due to the instrumentation. All these com-
ponents will bias the results of a model-driven approach that relies on as good a
model as possible of the signal as good as possible [5-7]. The knowledge obtained
by an explorative approach can be used in confirmatory data analysis (CDA)
methods that rely on a precise model of the expected activations. In this framework,
exploratory data analysis methods can be seen as hypotheses-generating tools.
Moreover, in clinical applications these methods are thought to play an increasingly
important role because in these kinds of applications the brain responses typically
cannot be modeled in advance. Even if the BOLD signal has been demonstrated
to be correlated with the underlying neural activity, several aspects remain to be
understood, and exploratory analysis may play a vital role in this. The strength of
these exploratory data analysis methods is that information is extracted from the
data [8] using only general assumptions, and there is no need of specifying in
advance the shape and the extent of a phenomenon. These can be achieved by
taking advantage of the multivariate nature of the fMRI data set [9] and the fact
that both physiological phenomena of interest, due to the principles of localization
and integration of the neural processes [10], and artifacts, may concern measure-
ments in different brain regions. In this chapter we will introduce some methods
applied in exploratory data analysis of f MRI data, such as clustering techniques
[11-26], principal-component analysis (PCA) [27-32], and independent compo-
nent analysis (ICA) [33-46]. We will show that even if these methods are powerful
tools, in order to improve the knowledge about the brain function the experimenter
is required to make some fundamental choices during their applications that can
heavily influence the final results.
a priori
16.2
MULTIVARIATE APPROACHES
fMRI data are composed by a time sequence of
p
images or volumes, made
of
volume elements (voxels) each. The data set can be arranged in matrix
form, where, for example, in a
n
n
×
p
matrix
X
whose rows are the voxels time
series, the
j
th column, the
j
th image in the time sequence, is written as a vector
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