  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.
