<p>4D Flow Magnetic Resonance Imaging (MRI) is the state-of-the-art technique for measuring blood flow and provides valuable data for inverse problems in the cardiovascular system. However, acquiring 4D Flow MRI data requires long scan times, placing a burden on healthcare resources and causing discomfort for patients. To mitigate this, only part of the k-space is typically acquired, requiring additional assumptions for image reconstruction, introducing inaccuracies that can degrade the results of inverse problems. Moreover, a wide range of sampling patterns is available, and it is often unclear which one is most suitable. Here, we present a parameter estimation framework that directly uses highly undersampled k-space measurements. We solve the resulting problem numerically using a Reduced-Order Unscented Kalman Filter. We show that this approach yields more accurate estimates of boundary-condition parameters in a synthetic aortic blood flow model than approaches based on compressed-sensing reconstructions of the flow images. We also compare different sampling patterns and show how estimation accuracy depends on the sampling strategy. The results demonstrate substantially higher accuracy than inverse problems based on velocity fields reconstructed via compressed sensing. Finally, we validate these findings using real MRI data from a mechanical phantom.</p>