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Magnetic resonance imaging (MRI) is a very versatile imaging modality which can be used to acquire several different types of images. Some examples include anatomical images, images showing local brain activation and images depicting different types of pathologies. Brain activation is detected by means of functional magnetic resonance imaging (fMRI). This is useful e.g. in planning of neurosurgical procedures and in neurological research. To find the activated regions, a sequence of images of the brain is collected while a patient or subject alters between resting and performing a task. The variations in image intensity over time are then compared to a model of the variations expected to be found in active parts of the brain. Locations with high correlation between the intensity variations and the model are considered to be activated by the task. Since the images are very noisy, spatial filtering is needed before the activation can be detected. If adaptive filtering is used, i.e. if the filter at each location is adapted to the local neighborhood, very good detection performance can be obtained. This thesis presents two methods for adaptive spatial filtering of fMRI data. One of these is a modification of a previously proposed method, which at each position maximizes the similarity between the filter response and the model. A novel feature of the presented method is rotational invariance, i.e. equal sensitivity to activated regions in different orientations. The other method is based on bilateral filtering. At each position, this method averages pixels which are located in the same type of brain tissue and have similar intensity variation over time. A method for robust correlation estimation is also presented. This method automatically detects local bursts of noise in a signal and disregards the corresponding signal segments when the correlation is estimated. Hence, the correlation estimate is not affected by the noise bursts. This method is useful not only in analysis of fMRI data, but also in other applications where correlation is used to determine the similarity between signals. Finally, a method for correcting artifacts in complex MR images is presented. Complex images are used e.g. in the Dixon technique for separate imaging of water and fat. The phase of these images is often affected by artifacts and therefore need correction before the actual water and fat images can be calculated. The presented method for phase correction is based on an image integration technique known as the inverse gradient. The method is shown to provide good results even when applied to images with severe artifacts.