We consider the problem of increasing the spatial resolution of fMRI images. Main contributions are: (1) the definition of the protocol to acquire shifted images in order to be able to obtain images with increased resolution in the slice shift direction; (2) the use of discontinuity preserving regularization methods to solve the problem of superresolution; (3) an evaluation of the results based on human fMRI time series. Activated areas from low, high and superresolved images are compared. We conclude on the usefulness of using superresolution for task related activation detection.