On the stable estimation of flow geometry and wall shear stress from magnetic resonance images

We consider the stable reconstruction of flow geometry and wall shear stress from measurements obtained by magnetic resonance imaging (MRI). As noted in a review article by Petersson, most approaches considered so far in the literature seem to not be satisfactory. We therefore propose a systematic reconstruction procedure that allows us to obtain stable estimates of flow geometry and wall shear stress and we are able to quantify the reconstruction errors in terms of bounds for the measurement errors under reasonable smoothness assumptions. A complete analysis of our approach is given in the framework of regularization methods. In addition, we briefly discuss the implementation of our method and we demonstrate its viability, accuracy, and regularizing properties for experimental data.