The diagnosis of neurodegenerative diseases, particularly Alzheimer’s Dis-
ease (AD) and Parkinsonian Syndrome (PS), has been significantly enhanced by
the advent of Computer Aided Diagnosis (CAD) systems. These systems, lever-
aging advanced computational methodologies, aim to automate the recogni-
tion of neurodegenerative patterns characteristic of these diseases. This disser-
tation presents a series of innovative methodologies that have been developed
to address the challenges and nuances of medical image processing in the
context of these diseases.
A cornerstone of this research is the application of Robust Principal Compo-
nent Analysis (RPCA) to brain imaging. This technique facilitates the automatic
computation of Regions of Interest (ROIs) in brain images, ranking them based
on their diagnostic relevance. The sparse error matrix, derived from RPCA, has
emerged as a pivotal tool in determining brain areas intrinsically linked to AD.
Furthermore, the fusion of features from diverse image modalities, such as
functional Positron Emission Tomography (PET) and structural Magnetic Res-
onance Imaging (MRI) data, has been explored, yielding promising results in
both exploratory analysis and classification tasks.
The challenge of feature extraction, especially in high-dimensionality data-
sets, remains a significant hurdle in medical image processing. This research
addresses this challenge through sparse representations of data, offering a
solution to the curse of dimensionality. By combining specialized classifiers,
this approach not only aids in classification but also provides insights into the
progression of illnesses. Notably, while functional changes are evident in AD
patients, structural alterations become more pronounced during the disease’s
early stages.