Direct reconstruction of tracer kinetic (TK) parameter maps from under-sampled DCE-MRI has recently been demonstrated. However, this method assumes the arterial input function (AIF) is known or pre-determined. Any mismatches between the assumed AIF and the underlying patient-specific AIF can cause large inaccuracies in the final TK parameters. We propose a novel approach to extract patient-specific AIFs from under-sampled data, while jointly estimating the TK parameter maps. Reconstruction is performed by cycling through the problems of AIF extraction, TK parameter estimation and, data consistency. We demonstrate this approach on brain tumor DCE data sets, where high fidelity AIFs are extracted up to an under-sampling rate of 100x.