Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) provides a noninvasive method for evaluating tumor vasculature patterns based on contrast accumulation and washout. However, due to limited imaging resolution and tumor tissue heterogeneity, tracer concentrations at many pixels often represent a mixture of more than one distinct compartment. This pixel-wise partial volume effect (PVE) would have profound impact on the accuracy of pharmacokinetics studies using existing compartmental modeling (CM) methods. We, therefore, propose a convex analysis of mixtures (CAM) algorithm to explicitly mitigate PVE by expressing the kinetics in each pixel as a nonnegative combination of underlying compartments and subsequently identifying pure volume pixels at the corners of the clustered pixel time series scatter plot simplex. The algorithm is supported theoretically by a well-grounded mathematical framework and practically by plug-in noise filtering and normalization preprocessing. We demonstrate the principle and feasibility of the CAM-CM approach on realistic synthetic data involving two functional tissue compartments, and compare the accuracy of parameter estimates obtained with and without PVE elimination using CAM or other relevant techniques. Experimental results show that CAM-CM achieves a significant improvement in the accuracy of kinetic parameter estimation. We apply the algorithm to real DCE-MRI breast cancer data and observe improved pharmacokinetic parameter estimation, separating tumor tissue into regions with differential tracer kinetics on a pixel-by-pixel basis and revealing biologically plausible tumor tissue heterogeneity patterns. This method combines the advantages of multivariate clustering, convex geometry analysis, and compartmental modeling approaches. The open-source MATLAB software of CAM-CM is publicly available from the Web.