Alzheimer's disease is the most prevalent type of dementia amongst older population and it represents more than 50 % of all types of dementia. Incidence of this disease increases with aging population, stressing the importance of early diagnostics. Positron emission tomography (PET) imaging of $^{18}$F-fluorodeoxyglucose distribution measures metabolic activity, enabling us to recognise brain regions with lowered metabolic activity that is characteristic for the individual neurodegenerative disease. In an early phase of Alzheimer's dementia or in patients with mild cognitive impairment deviation from normal metabolic activity can be relatively small, meaning we can not get sufficient information from visually inspecting PET images. This is when statistical methods such as statistical parametric mapping (SPM) and scaled subprofile model/principal component analysis (SSM/PCA) are used. Despite the fundamental differences between those two methods and their results, visual comparison of the results implies resemblance between methods. In the thesis, comparison between SPM and SSM/PCA methods was analytically derived. Theoretically predicted resemblance between those methods has been verified by analysing clinical images as well as simulated noise images, which was used to clarify the connection between SPM and SSM/PCA results. We have discovered that SSM/PCA result is proportional to the logarithm of sum of number 1 and the product of SPM result and correction factor, related to relative image uncertainty.
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