Analysis of DCE-MRI data is often carried out by fitting parametric models. However, one major factor of uncertainty is the determination of the arterial input function (AIF). We introduce a novel approach to estimate kinetic parameters in DCE-MRI without an AIF. An existing method by Riabkov et al., where the AIF is introduced as an additional unknown, is extended by the addition of spatial diffusive regularization of the parameter maps and a control term for the scale of the AIF. We validate our method on artificial data, where it significantly reduces the relative error as compared to the original method by Riabkov. Additionally, we present first promising results on real data.