The use of functional imaging has been proven very helpful for the process of diagnosis of neurodegenerative diseases, such as Alzheimer's Disease (AD). In many cases, the analysis of these images is performed by manual reorientation and visual interpretation. Therefore, new statistical techniques to perform a more quantitative analysis are needed. In this work, a new statistical approximation to the analysis of functional images, based on significance measures and Independent Component Analysis (ICA) is presented. After the images preprocessing, voxels that allow better separation of the two classes are extracted, using significance measures such as the Mann–Whitney–Wilcoxon U-Test (MWW) and Relative Entropy (RE). After this feature selection step, the voxels vector is modelled by means of ICA, extracting a few independent components which will be used as an input to the classifier. Naive Bayes and Support Vector Machine (SVM) classifiers are used in this work. The proposed system has been applied to two different databases. A 96-subjects Single Photon Emission Computed Tomography (SPECT) database from the “Virgen de las Nieves” Hospital in Granada, Spain, and a 196-subjects Positron Emission Tomography (PET) database from the Alzheimer's Disease Neuroimaging Initiative (ADNI). Values of accuracy up to 96.9% and 91.3% for SPECT and PET databases are achieved by the proposed system, which has yielded many benefits over methods proposed on recent works.