Functional Magnetic Resonance Imaging (fMRI) is a recently developed neuroimaging technique with capacity to map neural activity with high spatial precision. To locate active brain areas, the method utilizes local blood oxygenation changes which are reflected as small intensity changes in a special type of MR images. The ability to non-invasively map brain functions provides new opportunities to unravel the mysteries and advance the understanding of the human brain, as well as to perform pre-surgical examinations in order to optimize surgical interventions.

This dissertation introduces new approaches for the analysis of fMRI data. The detection of active brain areas is a challenging problem due to high noise levels and artifacts present in the data. A fundamental tool in the developed methods is Canonical Correlation Analysis (CCA). CCA is used in two novel ways. First as a method with the ability to fully exploit the spatia-temporal nature of fMRI data for detecting active brain areas. Established analysis approaches mainly focus on the temporal dimension of the data and they are for this reason commonly referred to as being mass-univariate. The new CCA detection method encompasses and generalizes the traditional mass-univariate methods and can in this terminology be viewed as a mass-multivariate approach. The concept of spatial basis functions is introduced as a spatial counterpart of the temporal basis functions already in use in fMRI analysis. The spatial basis functions implicitly perform an adaptive spatial filtering of the fMRI images, which significantly improves detection performance. It is also shown how prior information can be incorporated into the analysis by imposing constraints on the temporal and spatial models and a constrained version of CCA is devised to this end. A general Principal Component Analysis technique for generating and constraining temporal and spatial subspace models is proposed to be used in combination with the constrained CCA analysis approach.

The second use of CCA is found in a novel so-called exploratory analysis method which extracts interesting and representative structures in fMRI data. Functional MRI data sets are large, and exploratory analysis methods are useful for probing the data for unexpected components. It is also shown how drift and trend models adapted to the fMRI data set at hand can be constructed with this new exploratory CCA technique. Compared to traditionally employed drift models, such adaptive drift models better account for the temporal autocorrelation in the data.