Abstract |
As the field of brain monitoring is evolving rapidly, there is an increasing demand for innovative
approaches to handle relevant signals. Recently, a powerful tool has employed
the research interest, namely the graph signal processing, as it provides the opportunity
to treat signal ensembles, in contrary to the conventional per-signal techniques. Electroencephalogram
(EEG) signals belong to a biosignals’ family, which can naturally admit
graph representations. However, a main disadvantage of these signals is that they often
be corrupted by impulsive noise. The nature of this noise can be best characterized by
heavy-tailed statistics, thus driving the conventional denoising methods to failure. To
address this problem, an efficient regularized graph filtering method was proposed, based
on the fractional lower-order moments which better adapt to heavy-tailed statistics.
Human brain connectivity was also one of the main interests of this dissertation. The
most well-established approach of describing the interrelations between pairs of brain
regions is via the Pearson’s correlation. Nevertheless, brain functionality is mostly dynamic,
a fact which attracted our research interest and led to an alternative procedure of approaching
such interrelations. Specifically, cross recurrence quantification analysis is an efficient
mathematical tool which can quantify the dynamic behavior of two time series via the
analysis of their recurrence plots, thus leading to a group of features. The application of
this method on a satisfying number of resting-state functional magnetic resonance imaging
examinations, in the form of time series, proved to be more sensitive in recognizing
significant interrelations among brain regions, than the conventional ones. Furthermore,
we extended this application to the introduction of these features to brain networks. The
construction of graphs, via a group of features which better describe the dynamic behavior
of human brains, and their analysis via conventional graph-based methods, such as the
small-world procedure, proved to be more effective than the existing tools, in the analysis
of a set combined of healthy controls and neuropsychiatric lupus diseased subjects.
Finally, we aimed to extend our analyses from signals to images, which were acquired
through the Diffusion-Weighted magnetic resonance imaging technique. More specifically,
a main issue of this technique is its long examination time, thus increasing the patients’
discomfort. An effective signal processing technique is the sparse representations. Sparse
representations aim to undersample a quantity and via the use of a fully-trained dictionary
reconstruct the missing values. In our case, this quantity was the so-called b-value, the
most important quantity of this technique. Sparse representations proved to be promising
to the improvement of the solution of this main biomedical issue.
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