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

## TL;DR

This paper introduces a systematic and stable method for reconstructing flow geometry and wall shear stress from MRI data, with error quantification and validation on experimental data.

## Contribution

It proposes a new regularization-based reconstruction approach that improves stability and error estimation in flow geometry and wall shear stress from MRI measurements.

## Key findings

- The method provides stable estimates under measurement noise.
- Error bounds are derived based on smoothness assumptions.
- Experimental data demonstrates the approach's accuracy and robustness.

## 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.