Pixel-wise quantification of myocardial perfusion by dynamic contrast-enhanced magnetic resonance imaging allows for a non-invasive, observer independent and reproducible evaluation of the perfusion with high spatial resolution. The method suggested here, exploits the spatial smoothness of the perfusion using a spatial Tikhonov regularization to cope with the low signal-to-noise ratio of the data. This allows us to obtain quantitative perfusion values with high spatial resolution to detect small ischemic regions. The parameter regulating the strength of regularization is determined from the L-curve criterion and does not require any manual adjustments. The feasibility of the method is demonstrated in three patients.