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

Abstract

We consider the stable reconstruction of flow geometry and wall shear stress from measurements obtained by magnetic resonance imaging. As noted in a review article by Petersson, most approaches considered so far in the literature seem not be satisfactory. We therefore propose a systematic reconstruction procedure that allows 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 full analysis of the approach is given in the framework of regularization methods. In addition, we discuss the efficient implementation of our method and we demonstrate its viability, accuracy, and regularizing properties for experimental data.