Magnetic resonance imaging, during bolus passage of a paramagnetic contrast agent, is used world-wide to obtain parameters that reflect the pathological state of tissue. Abnormal perfusion occurs in diseases such as stoke and tumour. Consequently, perfusion quantication could have signi cant clinical value both in diagnosis and treatment of such pathologies. One approach for perfusion quanti cation involves using the contrast mechanism that a ects the transverse relaxation rates of the magnetization, R2 or R 2 , since this provides the most pronounced effect. However, the linearity between the contrastagent concentration, [Ca], and the changes in R2 or R 2 has been questioned. In this thesis, an MRI scanner sequence for detection of the longitudinal relaxation rate, R1 during bolus passage was modied for brain perfusion measurements, since the linearity between the changes in R1 and [Ca] is expected to be more robust. Successful brain perfusion quantication based on R1 weighted signals has not previously been reported, due to the poor signal to noise ratio of the images. Initial experiments reported in this thesis show that improved sequence may provide more accurate perfusion estimates in the brain. Images obtained during bolus passage are noisy, and the bolus is not an ideal impulse as it reaches the brain. The brain response to an ideal impulse is called the residual impulse response function, IRF. Thus, the measured tissue curves are expressed as the convolution of the input function with the tissue IRF. To obtain the IRF, the tissue curves and the input curves are deconvolved and perfusion is related to the peak of IRF. In this thesis, a new method for deconvolution of perfusion data is introduced. It is the Gaussian process for deconvolution, GPD. The method is compared to singular value decomposition, SVD, which is the currently most frequently used method for deconvolution. It is shown that GPD has several important advantages over the optimized SVD as a method for deconvolution in perfusion imaging.